Some Aspects of Fixed Point Theory!
Indian Academy of Sciences (India)
1999-01-22
Jan 22, 1999 ... game theory and optimization theory. Apart from establishing the existence of a fixed point, it often becomes necessary to prove the uniqueness of the fixed point. Besides, from a computational point of view, an algorithm for calculating the value of the fixed point to a given degree of accuracy is desirable.
About Applications of the Fixed Point Theory
Directory of Open Access Journals (Sweden)
Bucur Amelia
2017-06-01
Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
Topological fixed point theory of multivalued mappings
Górniewicz, Lech
1999-01-01
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...
Fixed point theory of parametrized equivariant maps
Ulrich, Hanno
1988-01-01
The first part of this research monograph discusses general properties of G-ENRBs - Euclidean Neighbourhood Retracts over B with action of a compact Lie group G - and their relations with fibrations, continuous submersions, and fibre bundles. It thus addresses equivariant point set topology as well as equivariant homotopy theory. Notable tools are vertical Jaworowski criterion and an equivariant transversality theorem. The second part presents equivariant cohomology theory showing that equivariant fixed point theory is isomorphic to equivariant stable cohomotopy theory. A crucial result is the sum decomposition of the equivariant fixed point index which provides an insight into the structure of the theory's coefficient group. Among the consequences of the sum formula are some Borsuk-Ulam theorems as well as some folklore results on compact Lie-groups. The final section investigates the fixed point index in equivariant K-theory. The book is intended to be a thorough and comprehensive presentation of its subjec...
Fixed point theory in metric type spaces
Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco
2015-01-01
Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...
Gravitational fixed points from perturbation theory.
Niedermaier, Max R
2009-09-04
The fixed point structure of the renormalization flow in higher derivative gravity is investigated in terms of the background covariant effective action using an operator cutoff that keeps track of powerlike divergences. Spectral positivity of the gauge fixed Hessian can be satisfied upon expansion in the asymptotically free higher derivative coupling. At one-loop order in this coupling strictly positive fixed points are found for the dimensionless Newton constant g(N) and the cosmological constant lambda, which are determined solely by the coefficients of the powerlike divergences. The renormalization flow is asymptotically safe with respect to this fixed point and settles on a lambda(g(N)) trajectory after O(10) units of the renormalization mass scale to accuracy 10(-7).
Renormalization-group flows and fixed points in Yukawa theories
DEFF Research Database (Denmark)
Mølgaard, Esben; Shrock, R.
2014-01-01
We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar....... In the regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared....
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 5. Fixed Points - From Russia with Love - A Primer of Fixed Point Theory. A K Vijaykumar. Book Review Volume 5 Issue 5 May 2000 pp 101-102. Fulltext. Click here to view fulltext PDF. Permanent link:
Fixed point theory, variational analysis, and optimization
Al-Mezel, Saleh Abdullah R; Ansari, Qamrul Hasan
2015-01-01
""There is a real need for this book. It is useful for people who work in areas of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics.""-Nan-Jing Huang, Sichuan University, Chengdu, People's Republic of China
GUT precursors and fixed points in higher-dimensional theories
Indian Academy of Sciences (India)
context of high-scale gauge coupling unification. More generally, our results also suggest that it is possible to construct self-consistent 'hybrid' models containing widely separated energy scales, and give rise to a Kaluza-Klein realization of non-trivial fixed points in higher-dimensional gauge theories. Keywords. Unification ...
The fixed point structure of lattice field theories
International Nuclear Information System (INIS)
Baier, R.; Reusch, H.J.; Lang, C.B.
1989-01-01
Monte-Carlo renormalization group methods allow to analyze lattice regularized quantum field theories. The properties of the quantized field theory in the continuum may be recovered at a critical point of the lattice model. This requires a study of the phase diagram and the renormalization flow structure of the coupling constants. As an example the authors discuss the results of a recent MCRG investigation of the SU(2) adjoint Higgs model, where they find evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β
Stability by fixed point theory for functional differential equations
Burton, T A
2006-01-01
This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicia
Intensional type theory with guarded recursive types qua fixed points on universes
DEFF Research Database (Denmark)
Møgelberg, Rasmus Ejlers; Birkedal, Lars
2013-01-01
and types. When applied to the groupoid model of intensional type theory with the universe of small discrete groupoids, the construction gives a model of guarded recursion for which there is a one-to-one correspondence between fixed points of functions on the universe of types and fixed points of (suitable......Guarded recursive functions and types are useful for giving semantics to advanced programming languages and for higher-order programming with infinite data types, such as streams, e.g., for modeling reactive systems. We propose an extension of intensional type theory with rules for forming fixed...... points of guarded recursive functions. Guarded recursive types can be formed simply by taking fixed points of guarded recursive functions on the universe of types. Moreover, we present a general model construction for constructing models of the intensional type theory with guarded recursive functions...
Directory of Open Access Journals (Sweden)
Ishak Altun
2016-01-01
Full Text Available We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings T,S:X→X, where X is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.
International Nuclear Information System (INIS)
Neves, A.G.M.
1988-01-01
The renormalization transformation e sup(-S 1) sup((B)) const. ζ e sup(-S o (A) - V(A)) δ (B-C sub(1) A) δ sub(Ax) (A)DA for the U(1) lattice gauge theory, where S sub(o) (A) is the gaussian fixed point of the transformation, V(A) is a gauge invariant perturbation, C sub(1) is the averaging operator and δ sub(Ax) (A) fixes the local axial gauge is studied via an equivalent renormalization transformation on the 2-forms F = dA. The transformation is linearized in the neighborhood of the fixed point and then diagonalized. (author)
1989-01-01
This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.
Agarwal Ravi P Fixed point theory for composite maps on almost ...
Indian Academy of Sciences (India)
AUTHOR INDEX. Agarwal Ravi P. Fixed point theory for composite maps on almost dominating extension spaces 339. Aithal A R see Anisa M H C. 93. Amini Massoud see Saadati Reza. 483. Anisa M H C. On two functionals connected to the Lapla- cian in a class of doubly connected domains in space-forms. 93. Anuradha ...
$β'_{IR}$ at an Infrared Fixed Point in Chiral Gauge Theories
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2018-01-01
We present scheme-independent calculations of the derivative of the beta function, denoted $\\beta'_{IR}$, at a conformally invariant infrared (IR) fixed point, in several asymptotically free chiral gauge theories, namely SO($4k+2$) with $2 \\le k \\le 4$ with respective numbers $N_f$ of fermions...
Fixed-point bifurcation analysis in biological models using interval polynomials theory.
Rigatos, Gerasimos G
2014-06-01
The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the evaluation of the type of stability for each fixed point through the computation of the eigenvalues of the Jacobian matrix that is associated with the system's nonlinear dynamics model. Stage (ii) requires the computation of the roots of the characteristic polynomial of the Jacobian matrix. This problem is nontrivial since the coefficients of the characteristic polynomial are functions of the bifurcation parameter and the latter varies within intervals. To obtain a clear view about the values of the roots of the characteristic polynomial and about the stability features they provide to the system, the use of interval polynomials theory and particularly of Kharitonov's stability theorem is proposed. In this approach, the study of the stability of a characteristic polynomial with coefficients that vary in intervals is equivalent to the study of the stability of four polynomials with crisp coefficients computed from the boundaries of the aforementioned intervals. The efficiency of the proposed approach for the analysis of fixed-point bifurcations in nonlinear models of biological neurons is tested through numerical and simulation experiments.
Topological fixed point theory for singlevalued and multivalued mappings and applications
Ben Amar, Afif
2016-01-01
This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of ax...
Fixed points in perturbative non-Abelian four-Fermi theory in (3+1)D
Energy Technology Data Exchange (ETDEWEB)
Alves, Van Sérgio, E-mail: vansergi@ufpa.br [Faculdade de Física, Universidade Federal do Pará, 66075-110, Belém, PA (Brazil); Nascimento, Leonardo, E-mail: lnascimento@ufpa.br [Faculdade de Física, Universidade Federal do Pará, 66075-110, Belém, PA (Brazil); Peña, Francisco, E-mail: francisco.pena@ufrontera.cl [Departamento de Ciencias Físicas, Facultad de Ingeniería, Ciencias y Administración, Universidad de La Frontera, Avda. Francisco Salazar 01145, Casilla 54-D, Temuco (Chile)
2013-12-09
We analyze the structure of fixed points for the non-Abelian four-fermion interactions model in (3+1) dimensions, which has SU(N{sub c})⊗SU(N{sub f}){sub L}⊗SU(N{sub f}){sub R} symmetry from the perturbative calculation of the beta function of the reduced system. We treat the model as an effective theory valid in a scale of energy on which p≪M, where p are the external momenta and M is a massive parameter that characterizes the coupling constants. Using the Zimmermann reduction mechanism, we show up to 1-loop order, that beyond the infrared fixed point at the origin there is a line of non-trivial ultraviolet fixed points that depend on N{sub c} and N{sub f}.
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this article we prove the existence and approximations of solutions of periodic boundary-value problems of second-order ordinary nonlinear hybrid differential equations. We rely our results on Dhage iteration principle or method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. Our resutls are proved under weaker continuity and Lipschitz conditions. An example illustrates the theory developed in this article.
The resolution of field identification fixed points in diagonal coset theories
International Nuclear Information System (INIS)
Fuchs, J.; Schellekens, B.; Schweigert, C.
1995-09-01
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use ''orbit Lie algebras'' and ''twining characters'', which were introduced in a previous paper. The characters of the primary fields are expressed in terms branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of ''generalized diagonal cosets''. (orig.)
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
Brânzei, R.; Morgan, J.; Scalzo, V.; Tijs, S.H.
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... of our methods to Markov-driven processes.......This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_D f(V), where f(v)=Av+g(v) for a random function g(v)=o(v) a.s. as v tends to infinity. Specifically, we provide an explicit characterization of the pair (C,r) in the tail...
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
Fixed points of quantum operations
International Nuclear Information System (INIS)
Arias, A.; Gheondea, A.; Gudder, S.
2002-01-01
Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation, and quantum information theory. If an operator A is invariant under a quantum operation φ, we call A a φ-fixed point. Physically, the φ-fixed points are the operators that are not disturbed by the action of φ. Our main purpose is to answer the following question. If A is a φ-fixed point, is A compatible with the operation elements of φ? We shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes. Our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von Neumann algebras
Itou, Etsuko
2013-08-01
We report the nonperturbative behavior of the twisted Polyakov loop (TPL) coupling constant for the SU(3) gauge theories defined by the ratio of Polyakov loop correlators in finite volume with twisted boundary condition. We reveal the vacuum structures and the phase structure for the lattice gauge theory with the twisted boundary condition. Carrying out the numerical simulations, we determine the nonperturbative running coupling constant in this renormalization scheme for the quenched QCD and N_f=12 SU(3) gauge theories. First, we study the quenched QCD theory using the plaquette gauge action. The TPL coupling constant has a fake fixed point in the confinement phase. We discuss this fake fixed point of the TPL scheme and obtain the nonperturbative running coupling constant in the deconfinement phase, where the magnitude of the Polyakov loop shows the nonzero values. We also investigate the system coupled to fundamental fermions. Since we use the naive staggered fermion with the twisted boundary condition in our simulation, only multiples of 12 are allowed for the number of flavors. According to the perturbative two-loop analysis, the N_f=12 SU(3) gauge theory might have a conformal fixed point in the infrared region. However, recent lattice studies show controversial results for the existence of the fixed point. We point out possible problems in previous work, and present our careful study. Finally, we find the infrared fixed point (IRFP) and discuss the robustness of the nontrivial IRFP of a many-flavor system under the change of the analysis method. Some preliminary results were reported in the proceedings [E. Bilgici et al., PoS(Lattice 2009), 063 (2009); Itou et al., PoS(Lattice 2010), 054 (2010)] and the letter paper [T. Aoyama et al., arXiv:1109.5806 [hep-lat
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Directory of Open Access Journals (Sweden)
Martin Väth
2004-12-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
Padgett, Wayne T
2009-01-01
This book is intended to fill the gap between the ""ideal precision"" digital signal processing (DSP) that is widely taught, and the limited precision implementation skills that are commonly required in fixed-point processors and field programmable gate arrays (FPGAs). These skills are often neglected at the university level, particularly for undergraduates. We have attempted to create a resource both for a DSP elective course and for the practicing engineer with a need to understand fixed-point implementation. Although we assume a background in DSP, Chapter 2 contains a review of basic theory
International Nuclear Information System (INIS)
Znojil, M.
1986-01-01
The radial Schroedinger equation and its bound-state solutions for the interaction V(r)=Vsub(coulomb)+Vsub(Pade), where Vsub(Pade)(r)=(b+cr)/(1+drsup(2)) are considered. In order to construct exactly the Feshbach effective Hamiltonian Hsup(eff), the fixed-point-substraction technique is employed and its simplification is proposed. The first two terms in the resulting asymptotic expansions of PSIsub(n) and Hsup(eff) are calculated and interpreted as a new type of perturbation theory
Shapiro, Joel H
2016-01-01
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests ...
Magnetic Fixed Points and Emergent Supersymmetry
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Pica, Claudio
2013-01-01
We establish in perturbation theory the existence of fixed points along the renormalization group flow for QCD with an adjoint Weyl fermion and scalar matter reminiscent of magnetic duals of QCD [1-3]. We classify the fixed points by analyzing their basin of attraction. We discover that among...
The Infrared Fixed Points of 3d $\\mathcal{N}=4$ $USp(2N)$ SQCD Theories arXiv
Assel, Benjamin
We derive the algebraic description of the Coulomb branch of 3d $\\mathcal{N}=4$ $USp(2N)$ SQCD theories with $N_f$ fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For $N_f>2N$ (good theories) it sits at the origin of the conical variety as expected. For $N_f =2N$ we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental $SU(2)$ global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For $2 \\le N_f < 2N$ the most singular locus has one or two extended com...
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
Fixed points of quantum gravity
Litim, D F
2003-01-01
Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.
ORIGINAL Some Generalized Fixed Point Results on Compact ...
African Journals Online (AJOL)
Fixed point theory is a fascinating subject with an enormous number of ... Fixed point theory in metric spaces perhaps originated from the well ... existence of a fixed point? In general, the answer to this question is no. In this regard, we observe the following interesting example. Example 1.1 (Kannan and Sharma, 1990 ). Let.
Flat Coalgebraic Fixed Point Logics
Schröder, Lutz; Venema, Yde
Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the μ-calculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the μ-calculus. The family of such flat fixed point logics includes, e.g., CTL, the *-nesting-free fragment of PDL, and the logic of common knowledge. Here, we extend this notion to the generic semantic framework of coalgebraic logic, thus covering a wide range of logics beyond the standard μ-calculus including, e.g., flat fragments of the graded μ-calculus and the alternating-time μ-calculus (such as ATL), as well as probabilistic and monotone fixed point logics. Our main results are completeness of the Kozen-Park axiomatization and a timed-out tableaux method that matches ExpTime upper bounds inherited from the coalgebraic μ-calculus but avoids using automata.
Fixed points of zircon automorphisms
Hultman, Axel
2007-01-01
A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups.
Two general fixed point principles and applications
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2016-06-01
Full Text Available We present a couple of general fixed point principles using the constructive approach and derive some interesting well-known fixed point theorems in a metric space and a partially ordered metric space as corollaries. Our general fixed point principles include more than 100 fixed point theorems in different metric spaces as special cases.
The computation of fixed points and applications
Todd, Michael J
1976-01-01
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore ...
The universal cardinal ordering of fixed points
International Nuclear Information System (INIS)
San Martin, Jesus; Moscoso, Ma Jose; Gonzalez Gomez, A.
2009-01-01
We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. Interestingly enough, it is important to point that this theorem needs no previous information about any other orbit; also the cardinal ordering is achieved automatically with no need to compare numerical values associated with every point of the orbit (as would be the case if kneading theory were used).
Fixed point of the parabolic renormalization operator
Lanford III, Oscar E
2014-01-01
This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...
On Convergence of Fixed Points in Fuzzy Metric Spaces
Directory of Open Access Journals (Sweden)
Yonghong Shen
2013-01-01
Full Text Available We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.
Infra-red fixed points in supersymmetry
Indian Academy of Sciences (India)
¾c /font>, and c stands for the color quadratic Casimir of the field. Fixed points arise when R* ¼ or when R*. /nobr>. ´S-½. µ ´r ·b¿µ. The stability of the solutions may be tested by linearizing the system about the fixed points. For the non-trivial fixed points we need to consider the eigenvalues of the stability matrix whose ...
Homotopies and the Universal Fixed Point Property
DEFF Research Database (Denmark)
Szymik, Markus
2015-01-01
. To even specify the problem, we introduce the universal fixed point property. Our results apply in particular to the analysis of convex subspaces of Banach spaces, to the topology of finite-dimensional manifolds and CW complexes, and to the combinatorics of Kolmogorov spaces associated with finite posets.......A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points that is continuous whenever the self-map varies continuously...
Product fixed points in ordered metric spaces
Turinici, Mihai
2011-01-01
All product fixed point results in ordered metric spaces based on linear contractive conditions are but a vectorial form of the fixed point statement due to Nieto and Rodriguez-Lopez [Order, 22 (2005), 223-239], under the lines in Matkowski [Bull. Acad. Pol. Sci. (Ser. Sci. Math. Astronom. Phys.), 21 (1973), 323-324].
Fixed point theorems for paracompact convex sets
International Nuclear Information System (INIS)
Jiang Jiahe.
1986-08-01
In the present paper a few fixed point theorems are given for upper hemi-continuous mappings from a paracompact convex set to its embracing space, a real, locally convex, Hausdorff topological vector space. (author)
Anderson Acceleration for Fixed-Point Iterations
Energy Technology Data Exchange (ETDEWEB)
Walker, Homer F. [Worcester Polytechnic Institute, MA (United States)
2015-08-31
The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.
Random fixed points and random differential inclusions
Directory of Open Access Journals (Sweden)
Nikolaos S. Papageorgiou
1988-01-01
Full Text Available In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
Metaharmonic Lattice Point Theory
Freeden, Willi
2011-01-01
Metaharmonic Lattice Point Theory covers interrelated methods and tools of spherically oriented geomathematics and periodically reflected analytic number theory. The book establishes multi-dimensional Euler and Poisson summation formulas corresponding to elliptic operators for the adaptive determination and calculation of formulas and identities of weighted lattice point numbers, in particular the non-uniform distribution of lattice points. The author explains how to obtain multi-dimensional generalizations of the Euler summation formula by interpreting classical Bernoulli polynomials as Green
Quantum entanglement and fixed-point bifurcations
International Nuclear Information System (INIS)
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
Fixed point algebras for easy quantum groups
DEFF Research Database (Denmark)
Gabriel, Olivier; Weber, Moritz
2016-01-01
Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author,we prove...... that free easy quantum groups satisfy these conditions and we compute the K-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group S+ n,the free orthogonal quantum group O+ n and the quantum reflection groups Hs+ n. Our fixed point......-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions....
Duan's fixed point theorem: Proof and generalization
Directory of Open Access Journals (Sweden)
Arkowitz Martin
2006-01-01
Full Text Available Let be an H-space of the homotopy type of a connected, finite CW-complex, any map and the th power map. Duan proved that has a fixed point if . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a -structure as defined by Hemmi-Morisugi-Ooshima. The conclusion is that and each has a fixed point.
On Fixed Point Theorems in Probabilistic Metric Spaces and Applications
GoleÅ£, Ioan; GoleÅ£, IonuÅ£
2008-09-01
In [4] S. Gähler formulated an appropriate system of axioms for a distance between three points and developed a theory of 2-metric spaces. A slight enlargement of the concept of 2-metric space was given in [3], where B. C. Dhage studied so called generalized metric spaces. In the present paper we have studied contraction conditions for mappings defined on a class of probabilistic metric space and fixed point theorems for such mappings. As a particular cases we have obtain fixed point theorems for random operator and for mappings defined on deterministic metric spaces.
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
Fixed Points in the Ambient Logic
Dal Zilio, Silvano
2009-01-01
We present an extension of the ambient logic with fixed points operators in the style of the mu-calculus. We give a simple syntactic condition for the equivalence between minimal and maximal fixpoint formulas and show how to subsume spatial analogues of the usual box and diamond operators.
Common fixed points for weakly compatible maps
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
Indian Acad. Sci. (Math. Sci.), Vol. 111, No. 2, May 2001, pp. 241–247. Printed in India. Common fixed points for weakly compatible maps. RENU CHUGH and SANJAY KUMAR. Department of Mathematics, Maharshi Dayanand University, Rohtak 124 001, India. MS received 31 January 2000; revised 11 December 2000.
ASIC For Complex Fixed-Point Arithmetic
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Common fixed points for weakly compatible maps
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
flood of papers involving contractive definition that do not require the continuity of T . This result was further generalized and extended in various ways by many authors. On the other hand Sessa [11] defined weak commutativity and proved common fixed point theorem for weakly commuting maps. Further Jungck [5] ...
Improved fixed point iterative method for blade element momentum computations
DEFF Research Database (Denmark)
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...
Radiative symmetry breaking from interacting UV fixed points
DEFF Research Database (Denmark)
Abel, Steven; Sannino, Francesco
2017-01-01
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin...
Lefschetz Fixed Point Theorem and Lattice Points in Convex Polytopes
Sardo-Infirri, Sacha
1993-01-01
A simple convex lattice polytope $\\Box$ defines a torus-equivariant line bundle $\\LB$ over a toric variety $\\XB.$ Atiyah and Bott's Lefschetz fixed-point theorem is applied to the torus action on the $d''$-complex of $\\LB$ and information is obtained about the lattice points of $\\Box$. In particular an explicit formula is derived, computing the number of lattice points and the volume of $\\Box$ in terms of geometric data at its extreme points. We show this to be equivalent the results of Brion...
Duan's fixed point theorem: proof and generalization
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Let X be an H-space of the homotopy type of a connected, finite CW-complex, f:X→X any map and p k :X→X the k th power map. Duan proved that p k f :X→X has a fixed point if k≥2 . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a θ -structure μ θ :X→X as defined by Hemmi-Morisugi-Ooshima. The conclusion is that μ θ f and f μ θ each has a fixed point.
Fixed points of IA-endomorphisms of a free metabelian Lie algebra
Indian Academy of Sciences (India)
Free metabelian Lie algebra; fixed point. 1. Introduction. One of the important problem in the theory of Lie algebras is to determine the non-trivial fixed points of endomorphisms of free Lie algebras. The most important results about fixed points of a finite group acting on a free alge- bra were obtained by Formanek [5]. Similar ...
Time Stamps for Fixed-Point Approximation
DEFF Research Database (Denmark)
Damian, Daniela
2001-01-01
Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed-point approximat......Time stamps were introduced in Shivers's PhD thesis for approximating the result of a control-flow analysis. We show them to be suitable for computing program analyses where the space of results (e.g., control-flow graphs) is large. We formalize time-stamping as a top-down, fixed...
A new 6d fixed point from holography
Energy Technology Data Exchange (ETDEWEB)
Apruzzi, Fabio [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); CUNY Graduate Center, Initiative for the Theoretical Sciences,New York, NY 10016 (United States); Department of Physics, Columbia University,New York, NY 10027 (United States); Dibitetto, Giuseppe; Tizzano, Luigi [Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden)
2016-11-22
We propose a stringy construction giving rise to a class of interacting and non-supersymmetric CFT’s in six dimensions. Such theories may be obtained as an IR conformal fixed point of an RG flow ending up in a (1,0) theory in the UV. We provide the due holographic evidence in the context of massive type IIA on AdS{sub 7}×M{sub 3}, where M{sub 3} is topologically an S{sup 3}. In particular, in this paper we present a 10d flow solution which may be interpreted as a non-BPS bound state of NS5, D6 and (D6)-bar branes. Moreover, by adopting its 7d effective description, we are able to holographically compute the free energy and the operator spectrum in the novel IR conformal fixed point.
Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Radenović Stojan
2010-01-01
Full Text Available We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.
Duan's fixed point theorem: Proof and generalization
Directory of Open Access Journals (Sweden)
Martin Arkowitz
2006-02-01
Full Text Available Let X be an H-space of the homotopy type of a connected, finite CW-complex, f:XÃ¢Â†Â’X any map and pk:XÃ¢Â†Â’X the kth power map. Duan proved that pkf:XÃ¢Â†Â’X has a fixed point if kÃ¢Â‰Â¥2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a ÃŽÂ¸-structure ÃŽÂ¼ÃŽÂ¸:XÃ¢Â†Â’X as defined by Hemmi-Morisugi-Ooshima. The conclusion is that ÃŽÂ¼ÃŽÂ¸f and fÃŽÂ¼ÃŽÂ¸ each has a fixed point.
On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
A Dual of the Compression-Expansion Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Henderson Johnny
2007-01-01
Full Text Available This paper presents a dual of the fixed point theorems of compression and expansion of functional type as well as the original Leggett-Williams fixed point theorem. The multi-valued situation is also discussed.
Fixed Points of Meromorphic Solutions for Some Difference Equations
Directory of Open Access Journals (Sweden)
Zong-Xuan Chen
2013-01-01
Full Text Available We investigate fixed points of meromorphic solutions for the Pielou logistic equation and obtain some estimates of exponents of convergence of fixed points of and its shifts , differences , and divided differences .
Fixed point theorems for generalized weakly contractive mappings
Directory of Open Access Journals (Sweden)
Ramendra Krishna Bose
2009-12-01
Full Text Available In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.
Global gauge fixing in lattice gauge theories
Energy Technology Data Exchange (ETDEWEB)
Fachin, S.; Parrinello, C. (Physics Department, New York University, 4 Washington Place, New York, New York (USA))
1991-10-15
We propose a covariant, nonperturbative gauge-fixing procedure for lattice gauge theories that avoids the problem of Gribov copies. This is closely related to a recent proposal for a gauge fixing in the continuum that we review. The lattice gauge-fixed model allows both analytical and numerical investigations: on the analytical side, explicit nonperturbative calculations of gauge-dependent quantities can be easily performed in the framework of a generalized strong-coupling expansion, while on the numerical side a stochastic gauge-fixing algorithm is very naturally associated with the scheme. In both applications one can study the gauge dependence of the results, since the model actually provides a smooth'' family of gauge-fixing conditions.
Coincidence and common fixed point theorems in compact Hausdorff spaces
Directory of Open Access Journals (Sweden)
Zeqing Liu
2005-01-01
Full Text Available The existence of coincidence and fixed points for continuous mappings in compact Hausdorff spaces is established. Some equivalent conditions of the existence of fixed and common fixed points for any continuous mapping and a pair of mappings in compact Hausdorff spaces are given, respectively. Our results extend, improve, and unify the corresponding results due to Jungck, Liu, and Singh and Rao.
Fixed points of quantum gravity in extra dimensions
International Nuclear Information System (INIS)
Fischer, Peter; Litim, Daniel F.
2006-01-01
We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low scale quantum gravity and compact extra dimensions
Impulsive differential inclusions a fixed point approach
Ouahab, Abdelghani; Henderson, Johnny
2013-01-01
Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, etc. The questions of existence and stability of solutions for different classes of initial values problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems and relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simple
Floating-to-Fixed-Point Conversion for Digital Signal Processors
Directory of Open Access Journals (Sweden)
Menard Daniel
2006-01-01
Full Text Available Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.
Fixed points in a group of isometries
Voorneveld, M.
2000-01-01
The Bruhat-Tits xed point theorem states that a group of isometries on a complete metric space with negative curvature possesses a xed point if it has a bounded orbit. This theorem is extended by a relaxation of the negative curvature condition in terms of the w-distance functions introduced by Kada
Some Fixed Points Results of Quadratic Functions in Split Quaternions
Directory of Open Access Journals (Sweden)
Young Chel Kwun
2016-01-01
Full Text Available We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternion. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences.
Fixed point theorems for densifying mappings and compact mappings
Directory of Open Access Journals (Sweden)
Zeqing Liu
2002-01-01
Full Text Available The purpose of this note is to establish fixed point theorems for densifying mappings and compact mappings which are contractive in metric spaces and to investigate the existence of fixed points for a family of mappings in bounded metric spaces. The results of this note generalize the results of Bailey (1966 and Liu (1994.
Caristi Fixed Point Theorem in Metric Spaces with a Graph
Directory of Open Access Journals (Sweden)
M. R. Alfuraidan
2014-01-01
Full Text Available We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.
Some Generalized Fixed Point Results on Compact Metric Spaces ...
African Journals Online (AJOL)
The goal of this research is to study some generalized fixed point results in compact metric space. It mainly focuses on the existence and unique fixed point of a selfmap on a compact metric space and its generalizations. In this study iterative techniques due to Edelstein, Bhardwaj et al. and Sastry et al. are used to show ...
Fixed point of multivalued mapping in uniform spaces
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Fixed point; multivalued mappings; orbitally complete; uniform space. 1. Introduction. Let (X, U) be a ... Let A be a nonempty subset of a uniform space X. Define. ∗(A) = sup {di(x,y) : x,y ∈ A, i ∈ I} , ..... [6] Taylor W W, Fixed point theorems for nonexpansive mappings in linear topological spaces,. J. Math. Anal. Appl. 40 (1972) ...
Fixed Points on Abstract Structures without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita
2002-01-01
The aim of this talk is to present a study of definability properties of fixed points of effective operators on abstract structures without the equality test. The question of definability of fixed points of -operators on abstract structures with equality was first studied by Gandy, Barwise, Mosch...
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
Wall shear stress fixed points in blood flow
Arzani, Amirhossein; Shadden, Shawn
2017-11-01
Patient-specific computational fluid dynamics produces large datasets, and wall shear stress (WSS) is one of the most important parameters due to its close connection with the biological processes at the wall. While some studies have investigated WSS vectorial features, the WSS fixed points have not received much attention. In this talk, we will discuss the importance of WSS fixed points from three viewpoints. First, we will review how WSS fixed points relate to the flow physics away from the wall. Second, we will discuss how certain types of WSS fixed points lead to high biochemical surface concentration in cardiovascular mass transport problems. Finally, we will introduce a new measure to track the exposure of endothelial cells to WSS fixed points.
A new compact fixed-point blackbody furnace
International Nuclear Information System (INIS)
Hiraka, K.; Oikawa, H.; Shimizu, T.; Kadoya, S.; Kobayashi, T.; Yamada, Y.; Ishii, J.
2013-01-01
More and more NMIs are realizing their primary scale themselves with fixed-point blackbodies as their reference standard. However, commercially available fixed-point blackbody furnaces of sufficient quality are not always easy to obtain. CHINO Corp. and NMIJ, AIST jointly developed a new compact fixed-point blackbody furnace. The new furnace has such features as 1) improved temperature uniformity when compared to previous products, enabling better plateau quality, 2) adoption of the hybrid fixed-point cell structure with internal insulation to improve robustness and thereby to extend lifetime, 3) easily ejectable and replaceable heater unit and fixed-point cell design, leading to reduced maintenance cost, 4) interchangeability among multiple fixed points from In to Cu points. The replaceable cell feature facilitates long term maintenance of the scale through management of a group of fixed-point cells of the same type. The compact furnace is easily transportable and therefore can also function as a traveling standard for disseminating the radiation temperature scale, and for maintaining the scale at the secondary level and industrial calibration laboratories. It is expected that the furnace will play a key role of the traveling standard in the anticipated APMP supplementary comparison of the radiation thermometry scale
Coincidence and common fixed point of F-contractions via $CLR_{ST}$ property
Directory of Open Access Journals (Sweden)
Anita Tomar
2016-03-01
Full Text Available The aim of this paper is to establish the existence of coincidence and common fixed point of F-contractions via CLRST property. Our results generalize, extend and improve the results of Wardowski [D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications (2012 2012:94, 6 pages, doi: 10.1186/1687-1812-2012-94], Batra et al. [Coincidence Point Theorem for a New Type of Contraction on Metric Spaces, Int. Journal of Math. Analysis, Vol. 8(27 2014, 1315-1320] and others existing in literature. Examples are also given in support of our results.
Revisiting the dilatation operator of the Wilson-Fisher fixed point
Liendo, Pedro
2017-07-01
We revisit the order-ε dilatation operator of the Wilson-Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.
Revisiting the dilatation operator of the Wilson-Fisher fixed point
Energy Technology Data Exchange (ETDEWEB)
Liendo, Pedro [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2017-01-15
We revisit the order ε dilatation operator of the Wilson-Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.
Accuracy Constraint Determination in Fixed-Point System Design
Directory of Open Access Journals (Sweden)
Serizel R
2008-01-01
Full Text Available Most of digital signal processing applications are specified and designed with floatingpoint arithmetic but are finally implemented using fixed-point architectures. Thus, the design flow requires a floating-point to fixed-point conversion stage which optimizes the implementation cost under execution time and accuracy constraints. This accuracy constraint is linked to the application performances and the determination of this constraint is one of the key issues of the conversion process. In this paper, a method is proposed to determine the accuracy constraint from the application performance. The fixed-point system is modeled with an infinite precision version of the system and a single noise source located at the system output. Then, an iterative approach for optimizing the fixed-point specification under the application performance constraint is defined and detailed. Finally the efficiency of our approach is demonstrated by experiments on an MP3 encoder.
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
2010-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...
Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces
Directory of Open Access Journals (Sweden)
Taoudi Mohamed-Aziz
2010-01-01
Full Text Available Abstract We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.
Tripled Fixed Point in Ordered Multiplicative Metric Spaces
Directory of Open Access Journals (Sweden)
Laishram Shanjit
2017-06-01
Full Text Available In this paper, we present some triple fixed point theorems in partially ordered multiplicative metric spaces depended on another function. Our results generalise the results of [6] and [5].
On a fixed point theorem Krasnoselskii-Shafer type
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2002-01-01
Full Text Available In this paper a variant of a fixed point theorem to Krasnoselskii-Schaefer type is proved and it is further applied to certain nonlinear integral equation of mixed type for proving the existence of the solution.
Measures of Noncircularity and Fixed Points of Contractive Multifunctions
Directory of Open Access Journals (Sweden)
Marrero Isabel
2010-01-01
Full Text Available In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.
Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2014-10-01
Full Text Available In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968 and Bose and Mukherjee (1981 as the special cases with a different and constructive method.
Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions
Directory of Open Access Journals (Sweden)
Nawab Hussain
2016-01-01
Full Text Available Remarkable feature of contractions is associated with the concept Mizoguchi-Takahashi function. For the purpose of extension and modification of classical ideas related with Mizoguchi-Takahashi contraction, we define generalized Mizoguchi-Takahashi G-contractions and establish some generalized fixed point theorems regarding these contractions in this paper. Some applications to the construction of a fixed point of multivalued mappings in ε-chainable metric space are also discussed.
Fixed Points of Multivalued Maps in Modular Function Spaces
Directory of Open Access Journals (Sweden)
Kutbi MarwanA
2009-01-01
Full Text Available The purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of -modular function and prove fixed point results for weakly-modular contractive maps in modular function spaces. These results extend several similar results proved in metric and Banach spaces settings.
A-properness and fixed point theorems for dissipative type maps
Directory of Open Access Journals (Sweden)
K. Q. Lan
1999-01-01
Full Text Available We obtain new A-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach space X with uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.
A fixed-point theorem for holomorphic maps
TIMONEY, RICHARD
1994-01-01
PUBLISHED We consider the action on the maximal ideal space M of the algebra H of bounded analytic functions, induced by an analytic self?map of a complex manifold, X. After some general preliminaries, we focus on the question of the existence of fixed points for this action, in the case when X is the open unit disk, D. We classify the fixed?point?free M?obius transformations, and we show that for an arbitrary analytic map from D into itself, the induced map has a fixed poin...
Some Aspects of Fixed Point Theory!
Indian Academy of Sciences (India)
1999-01-22
Jan 22, 1999 ... the quadratic equation ax2+bx+c = 0 may not have real solutions for real numbers a, band c with a i= O. How- ever, it will always have a pair of solutions in the system of complex numbers. More generally, one can consider an equation of the form g(x) = 0, where 9 is a real- valued function of a real variable.
Qualitative versus quantitative fixed point techniques in computer ...
African Journals Online (AJOL)
In 1970, a qualitative xed point technique useful to model the recursive specications in denotational semantics was developed by means of the celebrated Kleene's xed point theorem. Later on, in 1994 and 1995, quantitative counterparts of the aforesaid technique, but now based on generalized versions of Banach fixed ...
Design and DSP Implementation of Fixed-Point Systems
Directory of Open Access Journals (Sweden)
Martin Coors
2002-09-01
Full Text Available This article is an introduction to the FRIDGE design environment which supports the design and DSP implementation of fixed-point digital signal processing systems. We present the tool-supported transformation of signal processing algorithms coded in floating-point ANSI C to a fixed-point representation in SystemC. We introduce the novel approach to control and data flow analysis, which is necessary for the transformation. The design environment enables fast bit-true simulation by mapping the fixed-point algorithm to integral data types of the host machine. A speedup by a factor of 20 to 400 can be achieved compared to C++-library-based bit-true simulation. FRIDGE also provides a direct link to DSP implementation by processor specific C code generation and advanced code optimization.
Fixed Points in Discrete Models for Regulatory Genetic Networks
Directory of Open Access Journals (Sweden)
Orozco Edusmildo
2007-01-01
Full Text Available It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models, a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new, more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system, that is, all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems (monomial dynamical systems over finite fields are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system (defined over a finite field is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system.
Fixed Points, Inner Product Spaces, and Functional Equations
Directory of Open Access Journals (Sweden)
Park Choonkil
2010-01-01
Full Text Available Rassias introduced the following equality , , for a fixed integer . Let be real vector spaces. It is shown that, if a mapping satisfies the following functional equation for all with , which is defined by the above equality, then the mapping is realized as the sum of an additive mapping and a quadratic mapping. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.
Fixed Point Learning Based Intelligent Traffic Control System
Zongyao, Wang; Cong, Sui; Cheng, Shao
2017-10-01
Fixed point learning has become an important tool to analyse large scale distributed system such as urban traffic network. This paper presents a fixed point learning based intelligence traffic network control system. The system applies convergence property of fixed point theorem to optimize the traffic flow density. The intelligence traffic control system achieves maximum road resources usage by averaging traffic flow density among the traffic network. The intelligence traffic network control system is built based on decentralized structure and intelligence cooperation. No central control is needed to manage the system. The proposed system is simple, effective and feasible for practical use. The performance of the system is tested via theoretical proof and simulations. The results demonstrate that the system can effectively solve the traffic congestion problem and increase the vehicles average speed. It also proves that the system is flexible, reliable and feasible for practical use.
Fundamental flavours, fields and fixed points: a brief account
Energy Technology Data Exchange (ETDEWEB)
Kundu, Arnab [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhannagar, Kolkata 700064 (India); Homi Bhaba National Institute, Training School Complex,Anushakti Nagar, Mumbai 400085 (India); Kundu, Nilay [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP),Kyoto University,Kyoto 606-8502 (Japan)
2017-03-13
In this article we report on a preliminary study, via Holography, of infrared fixed points in a putative strongly coupled SU(N{sub c}) gauge theory, with N{sub f} fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently effective or a bottom up approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS{sub m}×ℝ{sup n}-type, which has appeared in the literature before; and AdS{sub m}×EAdS{sub n}-type, where m and n are suitable integers. Both these classes of solutions are non-perturbative in back-reaction. The AdS{sub m}×EAdS{sub n}-type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS{sub 5} ultraviolet to both an AdS{sub 2} and an AdS{sub 3} IR.
Probabilistic G-Metric space and some fixed point results
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A. R. Janfada
2013-01-01
Full Text Available In this note we introduce the notions of generalized probabilistic metric spaces and generalized Menger probabilistic metric spaces. After making our elementary observations and proving some basic properties of these spaces, we are going to prove some fixed point result in these spaces.
Critical types of Krasnoselskii fixed point theorems in weak topologies
African Journals Online (AJOL)
In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.
On stability of fixed points and chaos in fractional systems
Edelman, Mark
2018-02-01
In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.
Fixed Points on the Real numbers without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita
2002-01-01
In this paper we present a study of definability properties of fixed points of effective operators on the real numbers without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive...
Approximation of Common Fixed Points of a Finite
African Journals Online (AJOL)
Computer1
ϕ demicontractive maps;complement and generalize several others in the literature. KEY WORDS AND PHRASES: -. ϕ Demicontractive Maps, Implicit Iteration Process, Fixed Points,Strong. Convergence. INTRODUCTION AND PRELIMINARIES. Let E be a real Banach space. Let J denote the normalized duality mapping ...
Common fixed points of single-valued and multivalued maps
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Yicheng Liu
2005-01-01
Full Text Available We define a new property which contains the property (EA for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
Fixed Points in Grassmannians with Applications to Economic Equilibrium
DEFF Research Database (Denmark)
Keiding, Hans
2017-01-01
not allow immediate application of fixed point theorems, the problem must be reformulated using a suitable parametrization of subspaces. One such parametrization, the Plücker coordinates, is used here to prove a general equilibrium existence theorem. Applications to economic problems involving hierarchies...... of consumers or incomplete markets with real assets are outlined....
A fixed-point framework for launch vehicle ascent guidance
Zhang, Lijun
Recent interests in responsive launch have highlighted the need for rapid and fully automated ascent guidance planning and guidance parameter generation for launch vehicles. This dissertation aims at developing methodology and algorithms for on-demand generation of optimal launch vehicle ascent trajectories from lift-off to achieving targeting conditions outside the atmosphere. The entire ascent trajectory from lift-off to final target point is divided into two parts: atmospheric ascent portion and vacuum ascent portion. The two portions are integrated via a fixed-point iteration based on the continuity condition at the switch point between atmospheric ascent portion and vacuum ascent portion. The previous research works on closed-loop endo-atmospheric ascent guidance shows that the classical finite difference method is well suited for fast solution of the constrained optimal three-dimensional ascent problem. The exploitation of certain unique features in the integration procedure between the atmospheric portion and vacuum portion and the finite difference method, allows us to cast the atmospheric ascent problem into a nested fixed-point iteration problem. Therefore a novel Fixed-Point Iteration algorithm is presented for solving the endo-atmospheric ascent guidance problem. Several approaches are also provided for facilitating the convergence of the fixed-point iteration. The exo-atmospheric ascent portion allows an optimal coast in between the two vacuum powered stages. The optimal coast enables more efficient usage of the propellant. The Analytical Multiple-Shooting algorithm is developed to find the optimal trajectory for this portion. A generic launch vehicle model is adopted in the numerical simulation. A series of open-loop and closed-loop simulations are performed. The results verify the effectiveness, robustness and reliability of the Fixed-Point Iteration (FPI) algorithm and Analytical Multiple-Shooting (AMS) algorithm developed in this research. In
arXiv Radiative symmetry breaking from interacting UV fixed points
Abel, Steven
2017-09-28
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin to the radiative symmetry breaking that occurs in the supersymmetric standard model.
Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays
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Chang-Wen Zhao
2008-07-01
Full Text Available We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.
Chen, Guiling
2013-01-01
This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study
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Ilić Dejan
2010-01-01
Full Text Available We introduce the concept of a -compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with -distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend, and unify several well-known comparable results in the literature.
Gauge-fixing parameter dependence of two-point gauge-variant correlation functions
International Nuclear Information System (INIS)
Zhai, C.
1996-01-01
The gauge-fixing parameter ξ dependence of two-point gauge-variant correlation functions is studied for QED and QCD. We show that, in three Euclidean dimensions, or for four-dimensional thermal gauge theories, the usual procedure of getting a general covariant gauge-fixing term by averaging over a class of covariant gauge-fixing conditions leads to a nontrivial gauge-fixing parameter dependence in gauge-variant two-point correlation functions (e.g., fermion propagators). This nontrivial gauge-fixing parameter dependence modifies the large-distance behavior of the two-point correlation functions by introducing additional exponentially decaying factors. These factors are the origin of the gauge dependence encountered in some perturbative evaluations of the damping rates and the static chromoelectric screening length in a general covariant gauge. To avoid this modification of the long-distance behavior introduced by performing the average over a class of covariant gauge-fixing conditions, one can either choose a vanishing gauge-fixing parameter or apply an unphysical infrared cutoff. copyright 1996 The American Physical Society
New results for the Liebau phenomenon via fixed point index
Czech Academy of Sciences Publication Activity Database
Cid, J.A.; Infante, G.; Tvrdý, Milan; Zima, M.
2017-01-01
Roč. 35, June (2017), s. 457-469 ISSN 1468-1218 R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : cone * fixed point index * Green's function Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.659, year: 2016 http://www.sciencedirect.com/science/article/pii/S1468121816301511
Some fixed point theorems on non-convex sets
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Mohanasundaram Radhakrishnan
2017-10-01
Full Text Available In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\\to K$ is a nonexpansive map satisfying $\\frac{x+Tx}{2}\\in K$ for all $x\\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$
New results for the Liebau phenomenon via fixed point index
Czech Academy of Sciences Publication Activity Database
Cid, J.A.; Infante, G.; Tvrdý, Milan; Zima, M.
2017-01-01
Roč. 35, June (2017), s. 457-469 ISSN 1468-1218 R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : cone * fixed point index * Green's function Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.659, year: 2016 http://www. sciencedirect .com/science/article/pii/S1468121816301511
Fixed Points of Multivalued Contractive Mappings in Partial Metric Spaces
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Abdul Rahim Khan
2014-01-01
Full Text Available The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established.
ESTAR model with multiple fixed points. Testing and Estimation
I A Venetis; I Paya; D Peel
2009-01-01
In this paper we propose a globally stationary augmentation of the Exponential Smooth Transition Autoregressive (ESTAR) model that allows for multiple fixed points in the transition function. An F-type test statistic for the null of nonstationarity against such globally stationary nonlinear alternative is developed. The test statistic is based on the standard approximation of the nonlinear function under the null hypothesis by a Taylor series expansion. The model is applied to the U.S real in...
Fixed point theorems in complex valued metric spaces
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Naval Singh
2016-07-01
Full Text Available The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces. Our results generalize and extend the results of Azam et al. (2011 [1], Sintunavarat and Kumam (2012 [2], Rouzkard and Imdad (2012 [3], Sitthikul and Saejung (2012 [4] and Dass and Gupta (1975 [5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also furnished.
Semicompatibility and fixed point theorems in an unbounded D-metric space
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Bijendra Singh
2005-01-01
Full Text Available Rhoades (1996 proved a fixed point theorem in a bounded D-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unbounded D-metric space, for two self-maps satisfying a general contractive condition with a restricted domain of x and y. This has been done by using the notion of semicompatible maps in D-metric space. These results generalize and improve the results of Rhoades (1996, Dhage et al. (2000, and Veerapandi and Rao (1996. These results also underline the necessity and importance of semicompatibility in fixed point theory of D-metric spaces. All the results of this paper are new.
International Nuclear Information System (INIS)
Anselmi, Damiano
2004-01-01
I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: (i) the scheme-invariant area Δ a' of the graph of the effective beta function between the fixed points defines the length of the RG flow; (ii) the minimum of Δ a' in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points and (iii) in even dimensions, the distance between the fixed points is equal to Δ a = a UV - a IR . In even dimensions, these statements imply the inequalities 0 ≤ Δ a ≤ Δ a' and therefore the irreversibility of the RG flow. Another consequence is the inequality a ≤ c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain 'oriented-triangle inequalities', imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is also irreversible in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d = 3 theories where the RG flow is integrable at each order of the large N expansion
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N. Shahzad
2013-01-01
Full Text Available In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.
Algorithm for output of floating-point numbers in fixed-point form ...
African Journals Online (AJOL)
Presented in this paper is an algorithm with which floating-point numbers can be converted to their American Standard Code for Information Interchange (ASCII) equivalents in fixed-point form ready for output. The algorithm is so written that it can be implemented easily and requires just the address of the buffer to contain ...
Iterative approximation of fixed points of nonexpansive mappings
International Nuclear Information System (INIS)
Chidume, C.E.; Chidume, C.O.
2007-07-01
Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gateaux differentiable norm and T : K → K be a nonexpansive mapping with F(T) := { x element of K : Tx = x} ≠ 0 . For a fixed δ element of (0, 1), define S : K → K by Sx := (1- δ)x+ δ Tx , for all x element of K. Assume that { z t } converges strongly to a fixed point z of T as t → 0, where z t is the unique element of K which satisfies z t = tu + (1 - t)Tz t for arbitrary u element of K. Let {α n } be a real sequence in (0, 1) which satisfies the following conditions: C1 : lim α n = 0; C2 : Σαn = ∞. For arbitrary x 0 element of K, let the sequence { x n } be defined iteratively by x n+1 = α n u + (1 - α n )Sx n . Then, {x n } converges strongly to a fixed point of T. (author)
Fixed Points, Inner Product Spaces, and Functional Equations
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Choonkil Park
2010-01-01
Full Text Available Rassias introduced the following equality ∑i,j=1n∥xi-xj∥2=2n∑i=1n∥xi∥2, ∑i=1nxi=0, for a fixed integer n≥3. Let V,W be real vector spaces. It is shown that, if a mapping f:V→W satisfies the following functional equation ∑i,j=1nf(xi-xj=2n∑i=1nf(xi for all x1,…,xn∈V with ∑i=1nxi=0, which is defined by the above equality, then the mapping f:V→W is realized as the sum of an additive mapping and a quadratic mapping. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.
Closed String Amplitudes from Gauge Fixed String Field Theory
Drukker, Nadav
2002-01-01
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems
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A. E. Al-Mazrooei
2014-01-01
Full Text Available We propose two iterative algorithms for finding a common element of the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inclusions for maximal monotone and inverse strong monotone mappings, and the set of common fixed points of infinite nonexpansive mappings and an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions.
Existence results for trifunction equilibrium problems and fixed point problems
Mahato, Nihar Kumar; Noor, Muhammad Aslam; Sahu, Nabin Kumar
2017-10-01
In this paper, we establish the existence and uniqueness solutions of trifunction equilibrium problems using the generalized relaxed α -monotonicity in Banach spaces. By using the generalized f-projection operator, a hybrid iteration scheme is presented to find a common element of the solutions of a system of trifunction equilibrium problems and the set of fixed points of an infinite family of quasi-φ -nonexpansive mappings. Moreover, the strong convergence of our new proposed iterative method under generalized relaxed α -monotonicity is considered.
Study on the fixed point in crustal deformation before strong earthquake
Niu, A.; Li, Y.; Yan, W. Mr
2017-12-01
Usually, scholars believe that the fault pre-sliding or expansion phenomenon will be observed near epicenter area before strong earthquake, but more and more observations show that the crust deformation nearby epicenter area is smallest(Zhou, 1997; Niu,2009,2012;Bilham, 2005; Amoruso et al., 2010). The theory of Fixed point t is a branch of mathematics that arises from the theory of topological transformation and has important applications in obvious model analysis. An important precursory was observed by two tilt-meter sets, installed at Wenchuan Observatory in the epicenter area, that the tilt changes were the smallest compared with the other 8 stations around them in one year before the Wenchuan earthquake. To subscribe the phenomenon, we proposed the minimum annual variation range that used as a topological transformation. The window length is 1 year, and the sliding length is 1 day. The convergence of points with minimum annual change in the 3 years before the Wenchuan earthquake is studied. And the results show that the points with minimum deformation amplitude basically converge to the epicenter region before the earthquake. The possible mechanism of fixed point of crustal deformation was explored. Concerning the fixed point of crust deformation, the liquidity of lithospheric medium and the isostasy theory are accepted by many scholars (Bott &Dean, 1973; Merer et al.1988; Molnar et al., 1975,1978; Tapponnier et al., 1976; Wang et al., 2001). To explain the fixed point of crust deformation before earthquakes, we study the plate bending model (Bai, et al., 2003). According to plate bending model and real deformation data, we have found that the earthquake rupture occurred around the extreme point of plate bending, where the velocities of displacement, tilt, strain, gravity and so on are close to zero, and the fixed points are located around the epicenter.The phenomenon of fixed point of crust deformation is different from former understandings about the
On the Computational Content of the Krasnoselski and Ishikawa Fixed Point Theorems
DEFF Research Database (Denmark)
Kohlenbach, Ulrich
2001-01-01
This paper is part of a case study in proof mining applied to non-effective proofs in nonlinear functional analysis. More specifically, we are concerned with the fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study Krasnoselski and more general so-called K......This paper is part of a case study in proof mining applied to non-effective proofs in nonlinear functional analysis. More specifically, we are concerned with the fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study Krasnoselski and more general so...... and Shafrir (1992) to unbounded sets C. Our explicit bounds also imply new qualitative results concerning the independence of the rate of asymptotic regularity from various data....
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Adrian Petruşel
2015-01-01
Full Text Available We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence (fn(xn∈N of successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappings t1:X1×X2→X1 and t2:X1×X2→X2 are discussed and an application to a system of nonlinear integral equations is given.
Fixed-point image orthorectification algorithms for reduced computational cost
French, Joseph Clinton
Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation
Fixing the Big Bang Theory's Lithium Problem
Kohler, Susanna
2017-02-01
How did our universe come into being? The Big Bang theory is a widely accepted and highly successful cosmological model of the universe, but it does introduce one puzzle: the cosmological lithium problem. Have scientists now found a solution?Too Much LithiumIn the Big Bang theory, the universe expanded rapidly from a very high-density and high-temperature state dominated by radiation. This theory has been validated again and again: the discovery of the cosmic microwave background radiation and observations of the large-scale structure of the universe both beautifully support the Big Bang theory, for instance. But one pesky trouble-spot remains: the abundance of lithium.The arrows show the primary reactions involved in Big Bang nucleosynthesis, and their flux ratios, as predicted by the authors model, are given on the right. Synthesizing primordial elements is complicated! [Hou et al. 2017]According to Big Bang nucleosynthesis theory, primordial nucleosynthesis ran wild during the first half hour of the universes existence. This produced most of the universes helium and small amounts of other light nuclides, including deuterium and lithium.But while predictions match the observed primordial deuterium and helium abundances, Big Bang nucleosynthesis theory overpredicts the abundance of primordial lithium by about a factor of three. This inconsistency is known as the cosmological lithium problem and attempts to resolve it using conventional astrophysics and nuclear physics over the past few decades have not been successful.In a recent publicationled by Suqing Hou (Institute of Modern Physics, Chinese Academy of Sciences) and advisorJianjun He (Institute of Modern Physics National Astronomical Observatories, Chinese Academy of Sciences), however, a team of scientists has proposed an elegant solution to this problem.Time and temperature evolution of the abundances of primordial light elements during the beginning of the universe. The authors model (dotted lines
Fixed-point auto-landing algorithm for UAV based on point tracking
Shao, Zhiyu; Nie, Zhengang; Feng, Yuan; Feng, Shunshan
2009-12-01
A new automatic fixed-point landing algorithm for UAV using the instantaneous speed obtained by image sensors and computer vision method is proposed. In the proposed scheme, once the specified land pad for landing is captured, the UAV will switch from auto-seeking mode to landing mode. In the landing mode, the feature point of the prospective zone is extracted and then being tracked. The noise in the motion parameter introduced by the feature point mismatching is reduced by fast iterative least square algorithm, and the accurate instantaneous speed of UAV is obtained. The simulation results show that the proposed algorithm efficiently improve the accuracy of the estimation of instantaneous velocity for the fixed-point landing system of UAV.
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
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S. Cobzaş
2006-03-01
Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.
Approximation of fixed points of strongly pseudo-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1991-10-01
Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Let T:K→K be a continuous strongly pseudocontractive mapping of K into itself. Let {c n } n=1 ∞ be a real sequence satisfying: (i) 0 n n=1 ∞ c n =∞; and (iii) Σ n=1 ∞ c n b(c n ) n } n=1 ∞ generated by x 1 is an element of K. x n+1 =(1-c n )x n +c n Tx n , n≥1, converges strongly to the unique fixed point of T. A related result deals with the Ishikawa iteration scheme when T is Lipschitzian and strongly pseudocontractive. (author). 28 refs
Multi-Valued Modal Fixed Point Logics for Model Checking
Nishizawa, Koki
In this paper, I will show how multi-valued logics are used for model checking. Model checking is an automatic technique to analyze correctness of hardware and software systems. A model checker is based on a temporal logic or a modal fixed point logic. That is to say, a system to be checked is formalized as a Kripke model, a property to be satisfied by the system is formalized as a temporal formula or a modal formula, and the model checker checks that the Kripke model satisfies the formula. Although most existing model checkers are based on 2-valued logics, recently new attempts have been made to extend the underlying logics of model checkers to multi-valued logics. I will summarize these new results.
Fixed-point error analysis of Winograd Fourier transform algorithms
Patterson, R. W.; Mcclellan, J. H.
1978-01-01
The quantization error introduced by the Winograd Fourier transform algorithm (WFTA) when implemented in fixed-point arithmetic is studied and compared with that of the fast Fourier transform (FFT). The effect of ordering the computational modules and the relative contributions of data quantization error and coefficient quantization error are determined. In addition, the quantization error introduced by the Good-Winograd (GW) algorithm, which uses Good's prime-factor decomposition for the discrete Fourier transform (DFT) together with Winograd's short length DFT algorithms, is studied. Error introduced by the WFTA is, in all cases, worse than that of the FFT. In general, the WFTA requires one or two more bits for data representation to give an error similar to that of the FFT. Error introduced by the GW algorithm is approximately the same as that of the FFT.
On a fixed point theorem of Greguš
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Brian Fisher
1986-01-01
Full Text Available We consider two selfmaps T and I of a closed convex subset C of a Banach space X which are weakly commuting in X, i.e.‖TIx−ITx‖≤‖Ix−Tx‖ for any x in X,and satisfy the inequality‖Tx−Ty‖≤a‖Ix−Iy‖+(1−amax{‖Tx−Ix‖,‖Ty−Iy‖}for all x, y in C, where 0fixed point in C.
(0,2) SCFTs from the Leigh-Strassler fixed point
International Nuclear Information System (INIS)
Bobev, Nikolay; Pilch, Krzysztof; Vasilakis, Orestis
2014-01-01
We show that there is a family of two-dimensional (0,2) SCFTs associated with twisted compactifications of the four-dimensional N=1 Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and c-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric AdS 3 solutions that are holographic duals of those two-dimensional (0,2) SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.
Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation
International Nuclear Information System (INIS)
Goryainov, V V
2015-01-01
The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution family of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles
Fixed point theorems in CAT(0 spaces and Ã¢Â„Â-trees
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W. A. Kirk
2004-12-01
Full Text Available We show that if U is a bounded open set in a complete CAT(0 space X, and if f:UÃ‚Â¯Ã¢Â†Â’X is nonexpansive, then f always has a fixed point if there exists pÃ¢ÂˆÂˆU such that xÃ¢ÂˆÂ‰[p,f(x for all xÃ¢ÂˆÂˆÃ¢ÂˆÂ‚U. It is also shown that if K is a geodesically bounded closed convex subset of a complete Ã¢Â„Â-tree with int(KÃ¢Â‰Â Ã¢ÂˆÂ…, and if f:KÃ¢Â†Â’X is a continuous mapping for which xÃ¢ÂˆÂ‰[p,f(x for some pÃ¢ÂˆÂˆint(K and all xÃ¢ÂˆÂˆÃ¢ÂˆÂ‚K, then f has a fixed point. It is also noted that a geodesically bounded complete Ã¢Â„Â-tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
A fixed point of generalized T F -contraction mappings in cone metric spaces
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Moradi Sirous
2011-01-01
Full Text Available Abstract In this paper, the existence of a fixed point for TF -contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X → X is a one to one and closed graph function and F : P → P is non-decreasing and right continuous, with F -1(0 = -0} and F(tn → 0 implies tn → 0. Our results, extend previous results given by Meir and Keeler (J. Math. Anal. Appl. 28, 326-329, 1969, Branciari (Int. J. Math. sci. 29, 531-536, 2002, Suzuki (J. Math. Math. Sci. 2007, Rezapour et al. (J. Math. Anal. Appl. 345, 719-724, 2010, Moradi et al. (Iran. J. Math. Sci. Inf. 5, 25-32, 2010 and Khojasteh et al. (Fixed Point Theory Appl. 2010. MSC(2000: 47H10; 54H25; 28B05.
Learning multiple belief propagation fixed points for real time inference
Furtlehner, Cyril; Lasgouttes, Jean-Marc; Auger, Anne
2010-01-01
In the context of inference with expectation constraints, we propose an approach based on the “loopy belief propagation” algorithm ( LPB), as a surrogate to an exact Markov Random Field ( MRF) modelling. A prior information composed of correlations among a large set of N variables, is encoded into a graphical model; this encoding is optimized with respect to an approximate decoding procedure ( LBP), which is used to infer hidden variables from an observed subset. We focus on the situation where the underlying data have many different statistical components, representing a variety of independent patterns. Considering a single parameter family of models we show how LPB may be used to encode and decode efficiently such information, without solving the NP-hard inverse problem yielding the optimal MRF. Contrary to usual practice, we work in the non-convex Bethe free energy minimization framework, and manage to associate a belief propagation fixed point to each component of the underlying probabilistic mixture. The mean field limit is considered and yields an exact connection with the Hopfield model at finite temperature and steady state, when the number of mixture components is proportional to the number of variables. In addition, we provide an enhanced learning procedure, based on a straightforward multi-parameter extension of the model in conjunction with an effective continuous optimization procedure. This is performed using the stochastic search heuristic CMAES and yields a significant improvement with respect to the single parameter basic model.
Simulating full QCD with the fixed point action
International Nuclear Information System (INIS)
Hasenfratz, Anna; Hasenfratz, Peter; Niedermayer, Ferenc
2005-01-01
Because of its complex structure the parametrized fixed point action can not be simulated with the available local updating algorithms. We constructed, coded, and tested an updating procedure with 2+1 light flavors, where the targeted s quark mass is at its physical value while the u and d quarks should produce pions lighter than 300 MeV. In the algorithm a partially global gauge update is followed by several accept/reject steps, where parts of the determinant are switched on gradually in the order of their costs. The trial configuration that is offered in the last, most expensive, stochastic accept/reject step differs from the original configuration by a Metropolis + over-relaxation gauge update over a subvolume of ∼(1.3 fm) 4 . The acceptance rate in this accept/reject step is ∼0.4. The code is optimized on different architectures and is running on lattices with L s ≅1.2 fm and 1.8 fm at a resolution of a≅0.15 fm
Fixed points of IA-endomorphisms of a free metabelian Lie algebra
Indian Academy of Sciences (India)
Let be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an -endomorphism of and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix of an -endomorphism of is not finitely generated.
Fixed point theorems under $w$-distance on a metric space endowed with a graph
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Rakesh Batra
2015-04-01
Full Text Available In the present article, we exend the concept of $G$-contraction by introducing a $(p, G$-contraction in which, we use $w$-distance in the contractive condition instead of a metric. Our work may be used to deduce many results in the area of fixed point theory particularly in partial ordered metric spaces where two comparable elements can be thought of to be connected by an edge of a graph. Applications and examples are produced to justify the usability of our results.
Directory of Open Access Journals (Sweden)
H. Zegeye
2012-01-01
Full Text Available We introduce an iterative process which converges strongly to a common point of set of solutions of equilibrium problem and set of fixed points of finite family of relatively nonexpansive multi-valued mappings in Banach spaces.
Fixed Orientation Interconnection Problems: Theory, Algorithms and Applications
DEFF Research Database (Denmark)
Zachariasen, Martin
— the so-called fixed orientation Steiner tree problem — has received significant attention. This doctoral dissertation is a collection of twelve research papers and a survey on the fixed orientation Steiner tree problem and some of its generalizations. One of the main contributions is a linear time...... algorithm for computing a Steiner minimum tree for a given full topology. Also, a linear programming formulation is presented for the problem. For the general problem an exact algorithm that computes optimal solutions to problem instances with thousands of points is described and implemented. A novel...
Interior point algorithms theory and analysis
Ye, Yinyu
2011-01-01
The first comprehensive review of the theory and practice of one of today's most powerful optimization techniques. The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject.
Kurt Symanzik-a stable fixed point beyond triviality
International Nuclear Information System (INIS)
Kleefeld, Frieder
2006-01-01
In 1970 Kurt Symanzik proposed a 'precarious' Φ 4 -theory with a negative quartic coupling constant as a valid candidate for an asymptotically free theory of strong interactions. Symanzik's deep insight into the non-trivial properties of this theory has been overruled since then by the Hermitian intuition of generations of scientists, who considered or consider this actually non-Hermitian highly important theory to be unstable. This short-certainly controversial-communication tries to shed some light on the historical and formalistic context of Symanzik's theory in order to sharpen our (quantum) intuition about non-perturbative theoretical physics between (non-)triviality and asymptotic freedom. (letter to the editor)
$G$-asymptotic contractions in metric spaces with a graph and fixed point results
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Kamal Fallahi
2017-07-01
Full Text Available In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metric spaces endowed with a graph.
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Magnolia Tilca
2014-10-01
Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008
Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces
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O'Regan D
2010-01-01
Full Text Available We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature.
Fixed point results in cone metric spaces endowed with a graph
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Kamal Fallahi
2017-04-01
Full Text Available In this paper, we prove the existence of fixed point for Chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. The main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.
2016-08-04
DRIVER FIXED HEEL POINT (FHP) CAD ACCOMMODATION MODEL FOR MILITARY GROUND VEHICLE DESIGN Frank J. Huston II Gale L. Zielinski US Army, Tank ...Registration No. -Technical Report- U.S. Army Tank Automotive Research, Development, and Engineering Center Detroit Arsenal Warren, Michigan 48397...Institute, Ann Arbor, MI UNCLASSIFIED: Distribution Statement A Approved for Public Release Creation of the Driver Fixed Heel Point (FHP) CAD
Area law for fixed points of rapidly mixing dissipative quantum systems
International Nuclear Information System (INIS)
Brandão, Fernando G. S. L.; Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David
2015-01-01
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure or the system is frustration free
Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-05-01
Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banach spaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs
Fixed Points of Belief Propagation - An Analysis via Polynomial Homotopy Continuation.
Knoll, Christian; Mehta, Dhagash; Chen, Tianran; Pernkopf, Franz
2017-09-07
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find all fixed points.
Some Properties of Fixed Point for Contraction Mappings in Quasi 𝜶b-metric Space
Nurwahyu, Budi; Nasrun, Asriadi; Aris, Naimah
2018-03-01
We propose fixed point theorems for some contraction mappings in quasi 𝛼b-metric-metric space. Especially, the sufficient conditions to obtain an existence and uniqueness of fixed point on certain contraction mappings. The quasi 𝛼b-metric-metric space is extension of quasi b-metric space.
Stability of Quadratic Functional Equations via the Fixed Point and Direct Method
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Son Eunyoung
2010-01-01
Full Text Available Cădariu and Radu applied the fixed point theorem to prove the stability theorem of Cauchy and Jensen functional equations. In this paper, we prove the generalized Hyers-Ulam stability via the fixed point method and investigate new theorems via direct method concerning the stability of a general quadratic functional equation.
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Chang Tong-Huei
2009-01-01
Full Text Available We use a concept of abstract convexity to define the almost - property, al- - family, and almost -spaces. We get some new approximate fixed point theorems and fixed point theorems in almost -spaces. Our results extend some results of other authors.
Strong convergence to common fixed points of a finite family of Z ...
African Journals Online (AJOL)
user
In this paper, we consider an implicit iteration process for approximating common fixed points of a finite family of Z- operators and ... We recall some definitions in a metric space (. ),. X d . .... Later on, Chidume and Shahzad studied the strong convergence of the this implicit process to a common fixed point for a finite family of ...
Fixing All Moduli in a Simple F-Theory Compactification
Energy Technology Data Exchange (ETDEWEB)
Denef, F.
2005-04-28
We discuss a simple example of an F-theory compactification on a Calabi-Yau fourfold where background fluxes, together with nonperturbative effects from Euclidean D3 instantons and gauge dynamics on D7 branes, allow us to fix all closed and open string moduli. We explicitly check that the known higher order corrections to the potential, which we neglect in our leading approximation, only shift the results by a small amount. In our exploration of the model, we encounter interesting new phenomena, including examples of transitions where D7 branes absorb O3 planes, while changing topology to preserve the net D3 charge.
New fixed and periodic point results on cone metric spaces
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Ghasem Soleimani Rad
2014-05-01
Full Text Available In this paper, several xed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.
Fixed Points of Maps of a Nonaspherical Wedge
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Merrill Keith
2009-01-01
Full Text Available Abstract Let be a finite polyhedron that has the homotopy type of the wedge of the projective plane and the circle. With the aid of techniques from combinatorial group theory, we obtain formulas for the Nielsen numbers of the selfmaps of .
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
DEFF Research Database (Denmark)
Ryttov, Thomas A.
2016-01-01
_*$ can be calculated exactly and fully scheme independently through $O(\\Delta_f^n )$ where $\\Delta_f = \\bar{N_f} - N_f$ and $N_f$ is the number of flavors and $\\bar{N}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry...
The general problem of the motion of coupled rigid bodies about a fixed point
Leimanis, Eugene
1965-01-01
In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.
Fourier acceleration in lattice gauge theories. I. Landau gauge fixing
International Nuclear Information System (INIS)
Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.
1988-01-01
Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations
Eigenvectors and fixed point of non-linear operators
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Giulio Trombetta
2007-12-01
Full Text Available Let X be a real inﬁnite-dimensional Banach space and ψ a measure of noncompactness on X. Let Ω be a bounded open subset of X and A : Ω → X a ψ-condensing operator, which has no ﬁxed points on ∂Ω.Then the ﬁxed point index, ind(A,Ω, of A on Ω is deﬁned (see, for example, ([1] and [18]. In particular, if A is a compact operator ind(A,Ω agrees with the classical Leray-Schauder degree of I −A on Ω relative to the point 0, deg(I −A,Ω,0. The main aim of this note is to investigate boundary conditions, under which the ﬁxed point index of strict- ψ-contractive or ψ-condensing operators A : Ω → X is equal to zero. Correspondingly, results on eigenvectors and nonzero ﬁxed points of k-ψ-contractive and ψ-condensing operators are obtained. In particular we generalize the Birkhoff-Kellog theorem [4] and Guo’s domain compression and expansion theorem [17]. The note is based mainly on the results contained in [7] and [8].
Problems in the theory of point explosions
Korobeinikov, V. P.
The book is concerned with the development of the theory of point explosions, which is relevant to the study of such phenomena as the initiation of detonation, high-power explosions, electric discharges, cosmic explosions, laser blasts, and hypersonic aerodynamics. The discussion covers the principal equations and the statement of problems; linearized non-self-similar one-dimensional problems; spherical, cylindrical, and plane explosions with allowance for counterpressure under conditions of constant initial density; explosions in a combustible mixture of gases; and point explosions in inhomogeneous media with nonsymmetric energy release. Attention is also given to point explosions in an electrically conducting gas with allowance for the effect of the magnetic field and to the propagation of perturbations from solar flares.
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
Nikolić, Zoran; Nguyen, Ha Thai; Frantz, Gene
2007-12-01
Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs) to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.
Finite size scaling of the Higgs-Yukawa model near the Gaussian fixed point
Energy Technology Data Exchange (ETDEWEB)
Chu, David Y.J.; Lin, C.J. David [National Chiao-Tung Univ., Hsinchu, Taiwan (China); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Knippschild, Bastian [HISKP, Bonn (Germany); Nagy, Attila [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Univ. Berlin (Germany)
2016-12-15
We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility study of our strategy is performed for the pure scalar theory in the weak-coupling regime. Choosing the on-shell renormalisation scheme gives us an advantage to fit the scaling functions against lattice data with only a small number of fit parameters. These formulae can be used to determine the universality of the observed phase transitions, and thus play an essential role in future investigations of Higgs-Yukawa models, in particular in the strong Yukawa coupling region.
Three points of view in transport theory
Energy Technology Data Exchange (ETDEWEB)
Ruben, Panta Pazos [Faculdade de Matematica, PUCRS, Porto Alegre, RS (Brazil); Tilio de Vilhena, M. [Instituto de Matematica, UFRGS, Porto Alegre, RS (Brazil)
2001-07-01
A lot of efforts in Transport Theory is used to develop numerical methods or hybrid numerical-analytical techniques. We present in this work three points of view about transport problems. First the C0 semigroup approach, in which the free transport operator {psi} {yields} {mu} {nabla} generates an strongly continuous semigroup. The operators operator {psi} {yields} {sigma}t and operator {psi} {yields} {integral} {nabla} k(x,{mu},{mu}') {psi}(x,{mu}') d{mu}' are bounded operators, and by perturbation the transport operator {psi} {yields} {mu} {nabla} {psi} + {sigma}t {psi} - K {psi} also generates an strongly continuous semigroup. To prove the convergence of the approximations of a numerical methods to the exact solution we use the approximation theorem of C0 semi-groups in canonical form. In other way, the discrete schemes theory is employed in searching the rate of convergence of numerical techniques in transport theory. For 1D dependent of time transport problem and two-dimensional steady state problem we summarize some estimates, incorporating different boundary conditions. Finally we give a survey about the dynamical behavior of the SN approximations. In order to give a unified approach, some results illustrates the equivalence of the three points of views for the case of the steady-state transport problem for slab geometry. (author)
Three points of view in transport theory
International Nuclear Information System (INIS)
Ruben, Panta Pazos; Tilio de Vilhena, M.
2001-01-01
A lot of efforts in Transport Theory is used to develop numerical methods or hybrid numerical-analytical techniques. We present in this work three points of view about transport problems. First the C0 semigroup approach, in which the free transport operator ψ → μ ∇ generates an strongly continuous semigroup. The operators operator ψ → σt and operator ψ → ∫ ∇ k(x,μ,μ' ψ(x,μ') dμ' are bounded operators, and by perturbation the transport operator ψ → μ ∇ ψ + σt ψ - K ψ also generates an strongly continuous semigroup. To prove the convergence of the approximations of a numerical methods to the exact solution we use the approximation theorem of C0 semi-groups in canonical form. In other way, the discrete schemes theory is employed in searching the rate of convergence of numerical techniques in transport theory. For 1D dependent of time transport problem and two-dimensional steady state problem we summarize some estimates, incorporating different boundary conditions. Finally we give a survey about the dynamical behavior of the SN approximations. In order to give a unified approach, some results illustrates the equivalence of the three points of views for the case of the steady-state transport problem for slab geometry. (author)
Coupled Fixed Point Theorems for Weak Contraction Mappings under F-Invariant Set
Directory of Open Access Journals (Sweden)
Wutiphol Sintunavarat
2012-01-01
Full Text Available We extend the recent results of the coupled fixed point theorems of Cho et al. (2012 by weakening the concept of the mixed monotone property. We also give some examples of a nonlinear contraction mapping, which is not applied to the existence of the coupled fixed point by the results of Cho et al. but can be applied to our results. The main results extend and unify the results of Cho et al. and many results of the coupled fixed point theorems.
An Illusion: “A Suzuki Type Coupled Fixed Point Theorem”
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Hamed H. Alsulami
2014-01-01
Full Text Available We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Ðoric and Lazović (2011] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (α, r-admissible contractions.
Common Fixed Points of Generalized Cocyclic Mappings in Complex Valued Metric Spaces
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Mujahid Abbas
2015-01-01
Full Text Available We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces
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Mujahid Abbas
2015-01-01
Full Text Available The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.
Directory of Open Access Journals (Sweden)
Saewan Siwaporn
2011-01-01
Full Text Available Abstract In this article, we introduce a new hybrid projection iterative scheme based on the shrinking projection method for finding a common element of the set of solutions of the generalized mixed equilibrium problems and the set of common fixed points for a pair of asymptotically quasi-ϕ-nonexpansive mappings in Banach spaces and set of variational inequalities for an α-inverse strongly monotone mapping. The results obtained in this article improve and extend the recent ones announced by Matsushita and Takahashi (Fixed Point Theory Appl. 2004(1:37-47, 2004, Qin et al. (Appl. Math. Comput. 215:3874-3883, 2010, Chang et al. (Nonlinear Anal. 73:2260-2270, 2010, Kamraksa and Wangkeeree (J. Nonlinear Anal. Optim.: Theory Appl. 1(1:55-69, 2010 and many others. AMS Subject Classification: 47H05, 47H09, 47J25, 65J15.
Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems
Directory of Open Access Journals (Sweden)
Zhao-Rong Kong
2012-01-01
Full Text Available We consider and study the modified extragradient methods for finding a common element of the solution set Γ of a split feasibility problem (SFP and the fixed point set Fix(S of a strictly pseudocontractive mapping S in the setting of infinite-dimensional Hilbert spaces. We propose an extragradient algorithm for finding an element of Fix(S∩Γ where S is strictly pseudocontractive. It is proven that the sequences generated by the proposed algorithm converge weakly to an element of Fix(S∩Γ. We also propose another extragradient-like algorithm for finding an element of Fix(S∩Γ where S:C→C is nonexpansive. It is shown that the sequences generated by the proposed algorithm converge strongly to an element of Fix(S∩Γ.
Implementation Considerations for Automotive Vision Systems on a Fixed-Point DSP
Nikolić, Zoran
In this chapter we evaluate numerical requirements for implementation of camera-based lateral position detection algorithms, such as lane keep assistant (LKA) and lane departure warning (LDW) on a fixed-point DSP. We first present methods that address the challenges and requirements of fixed-point design process. The flow proposed is targeted at converting C/C++ code with floating-point operations into C code with integer operations that can then be fed through the native C compiler for a fixed-point DSP. Advanced code optimization and an implementation by DSP-specific, fixed-point C code generation are introduced. We then demonstrate the conversion flow on tracking example (extended Kalman filter) using synthetically generated data, and we analyze trade-offs for algorithm implementation in fixed-point arithmetic. By using the techniques described in this chapter speed can be increased by a factor of up to 10 compared to floating-point emulation on fixed-point hardware.
Fixed point and anomaly mediation in partial {\\boldsymbol{N}}=2 supersymmetric standard models
Yin, Wen
2018-01-01
Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate a partial N = 2 supersymmetric (SUSY) extension of the standard model which has an N = 2 SUSY sector and an N = 1 SUSY sector. We point out that below the scale of the partial breaking of N = 2 to N = 1, the ratio of Yukawa to gauge couplings embedded in the original N = 2 gauge interaction in the N = 2 sector becomes greater due to a fixed point. Since at the partial breaking scale the sfermion masses in the N = 2 sector are suppressed due to the N = 2 non-renormalization theorem, the anomaly mediation effect becomes important. If dominant, the anomaly-induced masses for the sfermions in the N = 2 sector are almost UV-insensitive due to the fixed point. Interestingly, these masses are always positive, i.e. there is no tachyonic slepton problem. From an example model, we show interesting phenomena differing from ordinary MSSM. In particular, the dark matter particle can be a sbino, i.e. the scalar component of the N = 2 vector multiplet of {{U}}{(1)}Y. To obtain the correct dark matter abundance, the mass of the sbino, as well as the MSSM sparticles in the N = 2 sector which have a typical mass pattern of anomaly mediation, is required to be small. Therefore, this scenario can be tested and confirmed in the LHC and may be further confirmed by the measurement of the N = 2 Yukawa couplings in future colliders. This model can explain dark matter, the muon g-2 anomaly, and gauge coupling unification, and relaxes some ordinary problems within the MSSM. It is also compatible with thermal leptogenesis.
Directory of Open Access Journals (Sweden)
Svetoslav Ganchev Nikolov
2015-07-01
Full Text Available The study of the dynamic behavior of a rigid body with one fixed point (gyroscope has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1 to outline the characteristic features of the theory of dynamical systems and 2 to reveal the specific properties of the motion of a rigid body with one fixed point (gyroscope.This article consists of six sections. The first section addresses the main concepts of the theory of dynamical systems. Section two presents the main theoretical results (obtained so far concerning the dynamic behavior of a solid with one fixed point (gyroscope. Section three examines the problem of gyroscopic stabilization. Section four deals with the non-linear (chaotic dynamics of the gyroscope. Section five is a brief analysis of the gyroscope applications in engineering. The final section provides conclusions and generalizations on why the theory of dynamical systems should be used in the study of the movement of gyroscopic systems.
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M. Eshaghi Gordji
2011-01-01
Full Text Available We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation.
Existence of tripled fixed points for a class of condensing operators in Banach spaces.
Karakaya, Vatan; Bouzara, Nour El Houda; Doğan, Kadri; Atalan, Yunus
2014-01-01
We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations.
Fixed point iterations for a class of nonlinear mappings in certain Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.
1991-12-01
It is proved that both the Mann iteration method and the Ishikawa iteration method converge strongly, in real Banach spaces with a certain property, to the unique fixed point of nonlinear mappings belonging to class C. 15 refs
Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations
Directory of Open Access Journals (Sweden)
Bessem Samet
2014-06-01
Full Text Available Recently, Samet et al [24] introduced the concept of alpha-psi contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ciric, Nieto, Lopez, and many others. We prove that alpha-psi contractions unify large classes of contractive type operators, whose fixed points can be obtained by means of the Picard iteration. Finally, we utilize our results to discuss the existence and uniqueness of solutions to a class of quadratic integral equations.
Some common random fixed point theorems for contractive type conditions in cone random metric spaces
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Saluja Gurucharan S.
2016-08-01
Full Text Available In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.
Fixed Point in Topological Vector Space-Valued Cone Metric Spaces
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Muhammad Arshad
2010-01-01
Full Text Available We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.
Latif, Abdul; Mongkolkeha, Chirasak; Sintunavarat, Wutiphol
2014-01-01
We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1993-05-01
It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs
Error tolerance in an NMR implementation of Grover's fixed-point quantum search algorithm
International Nuclear Information System (INIS)
Xiao Li; Jones, Jonathan A.
2005-01-01
We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance quantum computer, searching for either one or two matching items in an unsorted database of four items. In this algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, so that the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored
Directory of Open Access Journals (Sweden)
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
Swinford, Echo
2006-01-01
If you're vexed and perplexed by PowerPoint, pick up a copy of Fixing PowerPoint Annoyances. This funny, and often opinionated, guide is chock full of tools and techniques for eliminating all the problems that drive audiences and presenters crazy. There's nothing more discouraging than an unresponsive audience--or worse, one that snickers at your slides. And there's nothing more maddening than technical glitches that turn your carefully planned slide show into a car wreck. Envious when you see other presenters effectively use nifty features that you've never been able to get to work right?
Common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition
Energy Technology Data Exchange (ETDEWEB)
Abu-Donia, H.M. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)
2007-10-15
Some common fixed point theorems for multi-valued mappings under {phi}-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for {phi}-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding {epsilon} {sup {infinity}}-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the {epsilon} {sup {infinity}}-space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45].
Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition
International Nuclear Information System (INIS)
Abu-Donia, H.M.
2007-01-01
Some common fixed point theorems for multi-valued mappings under φ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for φ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε ∞ -space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45
Extending the Nonlinear-Beam-Dynamics Concept of 1D Fixed Points to 2D Fixed Lines
Franchetti, G.
2015-01-01
The origin of nonlinear dynamics traces back to the study of the dynamics of planets with the seminal work of Poincaré at the end of the nineteenth century: Les Méthodes Nouvelles de la Mécanique Céleste, Vols. 1–3 (Gauthier Villars, Paris, 1899). In his work he introduced a methodology fruitful for investigating the dynamical properties of complex systems, which led to the so-called “Poincaré surface of section,” which allows one to capture the global dynamical properties of a system, characterized by fixed points and separatrices with respect to regular and chaotic motion. For two-dimensional phase space (one degree of freedom) this approach has been extremely useful and applied to particle accelerators for controlling their beam dynamics as of the second half of the twentieth century.We describe here an extension of the concept of 1D fixed points to fixed lines in two dimensions. These structures become the fundamental entities for characterizing the nonlinear motion in the four-dimensional phas...
The Fixed-Point Theory of Strictly Causal Functions
2013-06-09
description languages such as VHDL (see [1]) and SystemC (see [2]), modeling and simulation tools such as Simulink and LabVIEW, network simulation tools such...context is another interesting direction for future work. References [1] IEEE standard VHDL language reference manual. IEEE Std 1076-2000, pages i–290, 2000
Fixed point theory for composite maps on almost dominating ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
ES dominating or more generally almost Schauder admissible dominating (these concepts will be defined in §2). The results in this paper improve those in the literature (see [3–5, 9,. 11] and the references therein). A continuation theorem is also discussed when the maps are between topological vector spaces.
Fixed Point Theory for Lipschitzian-type Mappings with Applications
Sahu, D R; Agarwal, Ravi P
2009-01-01
Offers a systematic presentation of Lipschitzian-type mappings in metric and Banach spaces. This book covers some basic properties of metric and Banach spaces. It also provides background in terms of convexity, smoothness and geometric coefficients of Banach spaces including duality mappings and metric projection mappings.
GUT precursors and fixed points in higher-dimensional theories
Indian Academy of Sciences (India)
Υ gauge bosons associated with the enlarged GUT gauge symmetry, and may also include additional matter particles (such as colored Higgs triplets). There are two basic methods by which GUT symmetries can be broken be- low the scale of unification. The first method is intrinsically field-theoretic: one imagines that a ...
some fixed point theorems for contractive conditions in a g-metric ...
African Journals Online (AJOL)
Global Journal
points for general class of quasicontractive type operators. ... R. U. Kanu, Department of Basic Sciences (Mathematics Unit), Babcock University, Ilishan- Remo, Ogun State, ..... Math.3, 133-181. Giniswamy, G and Maheshwari, P. G., 2014. Some. Common Fixed Point Theorems on G-Metric. Space, Gen. Math. Notes, 21 (2).
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Kang Shin
2011-01-01
Full Text Available Abstract In this paper, the existence, uniqueness and iterative approximations of fixed points for contractive mappings of integral type in complete metric spaces are established. As applications, the existence, uniqueness and iterative approximations of solutions for a class of functional equations arising in dynamic programming are discussed. The results presented in this paper extend and improve essentially the results of Branciari (A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531-536, 2002, Kannan (Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76, 1968 and several known results. Four concrete examples involving the contractive mappings of integral type with uncountably many points are constructed. 2010 Mathematics Subject Classfication: 54H25, 47H10, 49L20, 49L99, 90C39
Some Results of Fixed Points in Generalized Metric Space by Methods of Suzuki and Samet
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Hojjat Afshari
2015-08-01
Full Text Available In 1992 Dhage introduced the notion of generalized metric or D-metric spaces and claimed that D-metric convergence define a Hausdorff topology and that $D$-metric is sequentially continuous in all the three variables. Many authors have taken these claims for granted and used them in proving fixed point theorems in $D$-metric spaces. In 1996 Rhoades generalized Dhages contractive condition by increasing the number of factors and proved the existence of unique fixed point of a self map in $D$-metric space. Recently motivated by the concept of compatibility for metric space. In 2002 Sing and Sharma introduced the concept of $D$-compatibility of maps in $D$-metric space and proved some fixed point theorems using a contractive condition. In this paper ,we prove some fixed point theorems and common fixed point theorems in $D^*$-complete metric spaces under particular conditions among weak compatibility. Also by Using method of Suzuki and Samet we prove some theorems in generalised metric spaces.
Semenov, Alexander; Babikov, Dmitri
2013-11-07
We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.
New PPF Dependent Fixed Point Theorems for Suzuki Type GF-Contractions
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M. A. Kutbi
2015-01-01
Full Text Available We introduce new concepts of an αc-GF-contractive nonself-mapping, a weak αc-GF-contractive nonself-mapping, a generalized αc-GF-contractive nonself-mapping, and Suzuki type GF-contractions and establish the existence of PPF dependent fixed point theorems for such kind of contractive nonself-mappings in the Razumikhin class. As applications of our results, we derive some PPF dependent fixed point theorems for GF-contractive nonself-mappings whenever the range space is endowed with a graph or a partial order. The obtained results generalize, extend, and modify some PPF dependent fixed point results in the literature.
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MANISH JAIN
2017-06-01
Full Text Available Recently, Samet et al. [34], by using the equivalence of the three basic metrics showed that certain coupled fixed point results can be obtained immediately from the well-known fixed point theorems. In the setting of partially ordered metric spaces, we establish a generalization of the recent coupled fixed / coincidence point results under new nonlinear contractive conditions. The signicant feature of the presented work is that, our obtained results are not the immediate consequence of the already existing results in the literature. Presented work generalizes some of the results of Bhaskar and Lakshmikantham [6], Berinde [7], Choudhury et al. [10], Harjani et al. [17], Jain et al. [21] , Karapinar et al. [22], Luong and Thuan [25], and Rasouli and Bahrampour [30].
Eigensolutions of nonviscously damped systems based on the fixed-point iteration
Lázaro, Mario
2018-03-01
In this paper, nonviscous, nonproportional, symmetric vibrating structures are considered. Nonviscously damped systems present dissipative forces depending on the time history of the response via kernel hereditary functions. Solutions of the free motion equation leads to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices, this latter as dependent on frequency. Viscous damping can be considered as a particular case, involving damping forces as function of the instantaneous velocity of the degrees of freedom. In this work, a new numerical procedure to compute eigensolutions is proposed. The method is based on the construction of certain recursive functions which, under a iterative scheme, allow to reach eigenvalues and eigenvectors simultaneously and avoiding computation of eigensensitivities. Eigenvalues can be read then as fixed-points of those functions. A deep analysis of the convergence is carried out, focusing specially on relating the convergence conditions and error-decay rate to the damping model features, such as the nonproportionality and the viscoelasticity. The method is validated using two 6 degrees of freedom numerical examples involving both nonviscous and viscous damping and a continuous system with a local nonviscous damper. The convergence and the sequences behavior are in agreement with the results foreseen by the theory.
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Abdul Latif
2014-01-01
Full Text Available We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011 to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
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Jin Liang
2008-06-01
Full Text Available This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.
Regulator dependence of fixed points in quantum Einstein gravity with R 2 truncation
Nagy, S.; Fazekas, B.; Peli, Z.; Sailer, K.; Steib, I.
2018-03-01
We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the R 2 term.
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Kim JongKyu
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
A regularity result for fixed points, with applications to linear response
Sedro, Julien
2018-04-01
In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition operators acting on spaces of functions with finite regularity. We generalize this approach to higher order differentiability, through the notion of an n-graded family. We then give applications to the fixed point of a nonlinear map, and to linear response in the context of (uniformly) expanding dynamics (theorem 3 and corollary 2), in the spirit of Gouëzel-Liverani.
The Birkhoff-Lewis Fixed Point Theorem and a Conjecture of V. I. Arnold.
1983-09-01
DAAG29 N8 C004 G1/ I 11111. L 28 12.5= 332 1111 L 1. 11.25 1.4 jf1. MiCRCOPY RLSL)LU11N lILr’l CHIARi N-M NAL 1 AN AL AA MRC Technical Summary Report...2569 THE BIRKHOFF-LEWIS FIXED POINT THEOREM AND A CONJECTURE OF V. I. ARNOLD Charles C. Conley and Eduard Zehnder ’Z Mathematics Research Center...UNIVERSITY OF WISCONSIN - MADISON MATHEMATICS RESEARCH CENTER THE BIRKHOFF-LEWIS FIXED POINT THEOREM AND A CONJECTURE OF V. I. ARNOLD Charles C. Conley and
International Nuclear Information System (INIS)
C.E. Chidume; Bashir, Ali
2007-07-01
Let E be a real reflexive Banach space with uniformly Gateaux differentiable norm. Let K be a nonempty closed convex subset of E. Suppose that every nonempty closed convex bounded subset of K has the fixed point property for nonexpansive mappings. Let T 1 , T 2 , ..., T N be a family of nonexpansive self-mappings of K, with F := intersection i=1 N Fix(T i ) ≠ 0, F = Fix(T N T N-1 ... T 1 ) = Fix(T 1 T N ... T 2 ) = ... Fix(T N-1 T N-2 ... T 1 T N ). Let { λ n } be a sequence in (0, 1) satisfying the following conditions: C1 : lim λ n 0; C2 : Σ λ n = ∞ . For a fixed δ element of (0, 1), define S n : K → K by S n x := (1 - δ )x + δT n x for all x element of K where T n = T n mod N . For arbitrary fixed u, x 0 element of K, let B := { x element of K : T N T N-1 ... T 1 x γx+(1- γ)u, for some γ > 1} be bounded and let the sequence {x n } be defined iteratively by x n+1 λ n+1 u + (1 - λ n+1 )S n+1 x n , for n ≥ 0. Assume that lim n →∞ vertical bar vertical bar T n x n - T n+1 x n vertical bar vertical bar = 0. Then, {x n } converges strongly to a common fixed point of the family T 1 , T 2 , ..., T N . Convergence theorem is also proved for non-self maps. (author)
Fixed-point distributions of short-range Ising spin glasses on hierarchical lattices
Almeida, Sebastião T. O.; Nobre, Fernando D.
2015-03-01
Fixed-point distributions for the couplings of Ising spin glasses with nearest-neighbor interactions on hierarchical lattices are investigated numerically. Hierarchical lattices within the Migdal-Kadanoff family with fractal dimensions in the range 2.58 ≤D ≤7 , as well as a lattice of the Wheatstone-Bridge family with fractal dimension D ≈3.58 are considered. Three initial distributions for the couplings are analyzed, namely, the Gaussian, bimodal, and uniform ones. In all cases, after a few iterations of the renormalization-group procedure, the associated probability distributions approached universal fixed shapes. For hierarchical lattices of the Migdal-Kadanoff family, the fixed-point distributions were well fitted either by stretched exponentials, or by q -Gaussian distributions; both fittings recover the expected Gaussian limit as D →∞ . In the case of the Wheatstone-Bridge lattice, the best fit was found by means of a stretched-exponential distribution.
Combined GPS/GLONASS Precise Point Positioning with Fixed GPS Ambiguities
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-01-01
Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF. PMID:25237901
Weak compatibility and fixed point theorems for four self-maps in D-metric spaces
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Bijendra Singh
2005-01-01
Full Text Available This paper establishes one common coincident point theorem and three unique common fixed point theorems for four self-maps in D-metric spaces, which improve and generalize, significantly, the results of Dhage et al. (2003, Dhage (1999, and Rhoades (2003 under weaker assumption using a more general contractive condition. An example, in support of these theorems, has also been constructed. All the results of this paper are new.
Fixed points of contractive mappings in b-metric-like spaces.
Hussain, Nawab; Roshan, Jamal Rezaei; Parvaneh, Vahid; Kadelburg, Zoran
2014-01-01
We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results.
Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph
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Karim Chaira
2018-01-01
Full Text Available We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results.
Some fixed point results in fuzzy metric spaces using a control function
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C. T. Aage
2017-02-01
Full Text Available In this paper, we establish the results on existence and uniqueness of fixed point for φ-contractive and generalized C-contractive mapping in the fuzzy metric space in the sense of George and Veeramani. We use the notion of altering distance for proving the results.
On Quadruple Random Fixed Point Theorems in Partially Ordered Metric Spaces
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R. A. Rashwan
2014-01-01
Full Text Available We prove some quadruple random coincidence and quadruple random fixed point theorems under a set of conditions. We give examples to support our result. Our results are a generalization of the recent paper of Ćirić and Lakshmikantham (2009.
Common fixed point theorems for left reversible and near-commutative semigroups and applications
Directory of Open Access Journals (Sweden)
Kang Shin Min
2005-01-01
Full Text Available We prove some common fixed point theorems for left reversible and near-commutative semigroups in compact and complete metric spaces, respectively. As applications, we get the existence and uniqueness of solutions for a class of nonlinear Volterra integral equations.
Common Fixed Point Theorems for G–Contraction in C∗–Algebra–Valued Metric Spaces
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Akbar Zada
2016-04-01
Full Text Available In this paper we prove the common fixed point theorems for two mappings in complete C∗–valued metric space endowed with the graph G = (V,E, which satisfies G-contractive condition. Also, we provide an example in support of our main result.
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J. Tiammee
2017-01-01
Full Text Available In this paper, we prove some fixed point theorems for multivalued nonself G-almost contractions in Banach spaces with a directed graph and give some examples to illustrate our main results. The main results in this paper extend and generalize many known results in the literature therein.
An application of Darbo\\'s fixed point theorem in the relative ...
African Journals Online (AJOL)
Sufficient conditions for the relative controllability of a class of nonlinear systems with distributed delays in the control are established. Our results are based on the measure of non-compactness of a set and the Darbo's fixed point theorem. Global Jouranl of Mathematical Sciences Vol. 6 (1) 2007: pp. 21-26 ...
Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces
International Nuclear Information System (INIS)
Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi
2009-01-01
In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption
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Xue Zhiqun
2005-01-01
Full Text Available Let E be an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+K⊂K. Assume that T:K→K is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.
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Xiangbing Zhou
2012-01-01
Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.
Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces
Energy Technology Data Exchange (ETDEWEB)
Cho, Yeol Je [Department of Mathematics Education and the RINS, College of Education, Gyeongsang National University, Chinju 660-701 (Korea, Republic of)], E-mail: yjcho@gsnu.ac.kr; Sedghi, Shaban [Department of Mathematics, Islamic Azad University, Ghaemshahr Branch Ghaemshahr P.O. Box 163 (Iran, Islamic Republic of)], E-mail: sedghi_gh@yahoo.com; Shobe, Nabi [Department of Mathematics, Islamic Azad University, Babol Branch (Iran, Islamic Republic of)], E-mail: nabi_shobe@yahoo.com
2009-03-15
In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Operation of internal transmitter control... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be operated...
New versions of the Fan-Browder fixed point theorem and existence of economic equilibria
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Park Sehie
2004-01-01
Full Text Available We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some of recent results of Urai (2000 in more general and efficient forms.
Two fixed point theorems on quasi-metric spaces via mw- distances
Energy Technology Data Exchange (ETDEWEB)
Alegre, C.
2017-07-01
In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)
Strong convergence to common fixed points of a finite family of Z ...
African Journals Online (AJOL)
user
Zhou and Chang introduced the convergence of modified implicit iteration process for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach spaces (Zhou and Chang, 2002). In 2006, Rafiq studied the following implicit iteration process for strong convergence to a common fixed point for a finite ...
Fixed Point Theorems on Spaces Endowed with Vector-Valued Metrics
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Filip Alexandru-Darius
2010-01-01
Full Text Available The purpose of this work is to present some (local and global fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extensions of some theorems given by Perov (1964, Bucur et al. (2009, M. Berinde and V. Berinde (2007, O'Regan et al. (2007, and so forth.
Generalized Hyers-Ulam Stability of Quadratic Functional Equations: A Fixed Point Approach
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Choonkil Park
2008-03-01
Full Text Available Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(2x+y=4f(x+f(y+f(x+yÃ¢ÂˆÂ’f(xÃ¢ÂˆÂ’y in Banach spaces.
A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution
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Lee Zoon-Hee
2008-01-01
Full Text Available Abstract Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation with involution.
A Fixed Point Approach to the Stability of Quadratic Functional Equation with Involution
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Zoon-Hee Lee
2008-06-01
Full Text Available CÃ„Âƒdariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we will adopt the idea of CÃ„Âƒdariu and Radu to prove the Hyers-Ulam-Rassias stability of the quadratic functional equation with involution.
Large deviation tail estimates and related limit laws for stochastic fixed point equations
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE) of the form $V \\stackrel{d}{=} A\\max\\{V, D\\}+B$, where $(A, B, D) \\in (0, \\infty)\\times {\\mathbb R}^2$, for both the stationary and explosive cases. In the stationary case (when ${\\bf E} [\\log \\: A]...
A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem
International Nuclear Information System (INIS)
Prykarpatsky, A.K.
2007-05-01
A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)
An application of a discrete fixed point theorem to the Cournot model
Sato, Junichi
2008-01-01
In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.
Searching for fixed point combinators by using automated theorem proving: A preliminary report
International Nuclear Information System (INIS)
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, Θ must satisfy the equation Θx = x(Θx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs
A preliminary study of the nonlinearity of adhesive point-fixings in structural glass facades
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Jonas Dispersyn
2015-05-01
Full Text Available The recent demand for architectural transparency has drastically increased the use of glass material for structural purpose. However, connections between structural glass members represent one of the most critical aspects of glass engineering, due to the fragile behaviour of this material. In that respect, research activities on adhesive point-fixings are currently on-going. The mechanical behaviour of adhesive point-fixings is affected by large nonlinearities, which are usually investigated by nonlinear Finite Element Analysis (FEA. This paper focuses on the geometrical and the material nonlinearities of adhesive point-fixings for glass structures. Firstly, the nonlinear material behaviour of two selected adhesives are investigated by means of uniaxial tension and compression tests on the bulk material. The production of specimens, test methodology and displacement rate dependency are discussed. Secondly, the nonlinear stress distribution occurring in the adhesive and the joint stiffness is investigated by means of nonlinear FEA. The effects of several parameters on the mechanical behaviour of adhesive point-fixings, such as the connection dimensions and adhesive elastic properties, are studied. The adhesive stress-strain curves resulting from the experimental campaign show that the adhesives exhibit a large nonlinear behaviour. The results show that the stress and strain at failure reduce as the displacement rate is reduced. From the numerical investigations it is concluded that large nonlinearity involves the mechanical behaviour of adhesive point-fixing which cannot be neglected. The stress distribution within the adhesive deviates from uniform nominal stresses, even in case of simple load condition, with stress peaks up to four times higher than nominal stresses.
A preliminary study of the nonlinearity of adhesive point-fixings in structural glass facades
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Jonas Dispersyn
2014-06-01
Full Text Available Corresponding author: Jonas Dispersyn, Laboratory for Research on Structural Models (LMO, Department of Structural Engineering, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium. Tel.: +32 9 264 54 84; Fax: +32 9 264 58 38; E-mail: jonas.dispersyn@UGent.be The recent demand for architectural transparency has drastically increased the use of glass material for structural purpose. However, connections between structural glass members represent one of the most critical aspects of glass engineering, due to the fragile behaviour of this material. In that respect, research activities on adhesive point-fixings are currently on-going. The mechanical behaviour of adhesive point-fixings is affected by large nonlinearities, which are usually investigated by nonlinear Finite Element Analysis (FEA. This paper focuses on the geometrical and the material nonlinearities of adhesive point-fixings for glass structures. Firstly, the nonlinear material behaviour of two selected adhesives are investigated by means of uniaxial tension and compression tests on the bulk material. The production of specimens, test methodology and displacement rate dependency are discussed. Secondly, the nonlinear stress distribution occurring in the adhesive and the joint stiffness is investigated by means of nonlinear FEA. The effects of several parameters on the mechanical behaviour of adhesive point-fixings, such as the connection dimensions and adhesive elastic properties, are studied. The adhesive stress-strain curves resulting from the experimental campaign show that the adhesives exhibit a large nonlinear behaviour. The results show that the stress and strain at failure reduce as the displacement rate is reduced. From the numerical investigations it is concluded that large nonlinearity involves the mechanical behaviour of adhesive point-fixing which cannot be neglected. The stress distribution within the adhesive deviates from uniform nominal stresses
Searching for fixed point combinators by using automated theorem proving: A preliminary report
Energy Technology Data Exchange (ETDEWEB)
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, THETA must satisfy the equation THETAx = x(THETAx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs.
Quantum field theory of point particles and strings
Hatfield, Brian
1992-01-01
The purpose of this book is to introduce string theory without assuming any background in quantum field theory. Part I of this book follows the development of quantum field theory for point particles, while Part II introduces strings. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Thus, Part I presents the main framework of quantum field theory and provides for a coherent development of the generalization and application of quantum field theory for point particles to strings.Part II emphasizes the quantization of the bosonic string.
Comment on “Common Fixed Point Theorems for Commutating Mappings in Fuzzy Metric Spaces”
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Yonghong Shen
2012-01-01
Full Text Available In the recent paper “common fixed point theorems for commutating mappings in fuzzy metric spaces,” the authors proved that a common fixed point theorem for commutating mappings in G-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of G-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed by Zheng and Lian actually holds in an M-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.
Dermíšek, Radovan; McGinnis, Navin
2018-03-01
We use the IR fixed point predictions for gauge couplings and the top Yukawa coupling in the minimal supersymmetric model (MSSM) extended with vectorlike families to infer the scale of vectorlike matter and superpartners. We quote results for several extensions of the MSSM and present results in detail for the MSSM extended with one complete vectorlike family. We find that for a unified gauge coupling αG>0.3 vectorlike matter or superpartners are expected within 1.7 TeV (2.5 TeV) based on all three gauge couplings being simultaneously within 1.5% (5%) from observed values. This range extends to about 4 TeV for αG>0.2 . We also find that in the scenario with two additional large Yukawa couplings of vectorlike quarks the IR fixed point value of the top Yukawa coupling independently points to a multi-TeV range for vectorlike matter and superpartners. Assuming a universal value for all large Yukawa couplings at the grand unified theory scale, the measured top quark mass can be obtained from the IR fixed point for tan β ≃4 . The range expands to any tan β >3 for significant departures from the universality assumption. Considering that the Higgs boson mass also points to a multi-TeV range for superpartners in the MSSM, adding a complete vectorlike family at the same scale provides a compelling scenario where the values of gauge couplings and the top quark mass are understood as a consequence of the particle content of the model.
Existence of fixed points on compact epilipschitz sets without invariance conditions
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Quincampoix Marc
2005-01-01
Full Text Available We provide a new result of existence of equilibria of a single-valued Lipschitz function on a compact set of which is locally the epigraph of a Lipschitz functions (such a set is called epilipschitz set. Equivalently this provides existence of fixed points of the map . The main point of our result lies in the fact that we do not impose that is an "inward vector" for all point of the boundary of . Some extensions of the existence of equilibria result are also discussed for continuous functions and set-valued maps.
Dmitrović, Lana Horvat
2017-01-01
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is, the orbits near the hyperbolic fixed point in one-dimensional discrete dynamical system has the box dimension equal to zero and the orbits near nonhyperbolic fixed point has positive box dimension. In the process of studying box dimensions, we use the stable,...
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Rafa Espínola
2010-01-01
Full Text Available We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
Rigorous high-precision enclosures of fixed points and their invariant manifolds
Wittig, Alexander N.
The well established concept of Taylor Models is introduced, which offer highly accurate C0 enclosures of functional dependencies, combining high-order polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly non-linear dynamical systems. A method is proposed to extend the existing implementation of Taylor Models in COSY INFINITY from double precision coefficients to arbitrary precision coefficients. Great care is taken to maintain the highest efficiency possible by adaptively adjusting the precision of higher order coefficients in the polynomial expansion. High precision operations are based on clever combinations of elementary floating point operations yielding exact values for round-off errors. An experimental high precision interval data type is developed and implemented. Algorithms for the verified computation of intrinsic functions based on the High Precision Interval datatype are developed and described in detail. The application of these operations in the implementation of High Precision Taylor Models is discussed. An application of Taylor Model methods to the verification of fixed points is presented by verifying the existence of a period 15 fixed point in a near standard Henon map. Verification is performed using different verified methods such as double precision Taylor Models, High Precision intervals and High Precision Taylor Models. Results and performance of each method are compared. An automated rigorous fixed point finder is implemented, allowing the fully automated search for all fixed points of a function within a given domain. It returns a list of verified enclosures of each fixed point, optionally verifying uniqueness within these enclosures. An application of the fixed point finder to the rigorous analysis of beam transfer maps in accelerator physics is presented. Previous work done by
Cryostat for Fixed-Point Calibration of Capsule-Type SPRTs
Yang, I.; Song, C. H.; Kim, Y.-G.; Gam, K. S.
2011-12-01
A cryostat for fixed-point calibration of capsule-type SPRTs (standard platinum resistance thermometers) was developed. Using this system, cryogenic fixed points defined on the International Temperature Scale of 1990 (ITS-90) were realized. The cryogenic cells were argon, oxygen, neon, and two equilibrium-hydrogen (e-H2) cells, made by INRiM, Italy. The uncertainty of the realization of each fixed point was estimated to range from 0.53 mK to 0.43 mK ( k = 2). The realizations of the triple point of e-H2 using two sealed cells coincided within 0.1 mK. Therefore, we are able to calibrate capsule-type SPRTs down to 24.5561 K within an uncertainty of 1 mK ( k = 2) by this system. A closed-cycle helium gas refrigerator was used for the cryostat. Each sealed cell was designed so that it could accommodate three sealed cells in the thermometer wells made within the cell. Therefore, the cryostat was designed to accommodate only one sealed cell at a time. The base temperature of this liquid-free cryostat, when one sealed cell and three capsule-type SPRTs were attached for calibration, was ~17 K. For the realization of the triple point of e-H2, we used liquid helium for additional cooling. Adiabatic melting of the triple point was realized by controlling the inner-most radiation shield at a temperature very close to that of the triple point, and by applying a heat pulse by a heater directly wound to the cell. The amount of the heater power and the waiting time for the thermal equilibrium after each heat pulse were chosen in a way that the adiabatic melting could be finished within ~6 h for each cell. The triple point of each cryogenic fixed point was deduced from the equilibrium temperatures between the heat pulses and subsequent extrapolation to the liquidus point. For the oxygen cell, temperatures of two solid-solid transitions ( α- β and β- γ transitions) were also measured, and the results were consistent with values reported in the literature within the designated
Theory of Single Point Incremental Forming
DEFF Research Database (Denmark)
Martins, P.A.F.; Bay, Niels; Skjødt, Martin
2008-01-01
This paper presents a closed-form theoretical analysis modelling the fundamentals of single point incremental forming and explaining the experimental and numerical results available in the literature for the past couple of years. The model is based on membrane analysis with bi-directional in-plan...
An extragradient-like approximation method for variational inequalities and fixed point problems
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Wong Ngai-Ching
2011-01-01
Full Text Available Abstract The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and the modified Mann iteration process. We establish a strong convergence theorem for two sequences generated by this extragradient-like iterative algorithm. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings. 1991 MSC: 47H09; 47J20.
Computing fixed points of nonexpansive mappings by $\\alpha$-dense curves
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G. García
2017-08-01
Full Text Available Given a multivalued nonexpansive mapping defined on a convex and compact set of a Banach space, with values in the class of convex and compact subsets of its domain, we present an iteration scheme which (under suitable conditions converges to a fixed point of such mapping. This new iteration provides us another method to approximate the fixed points of a singlevalued nonexpansive mapping, defined on a compact and convex set into itself. Moreover, the conditions for the singlevalued case are less restrictive than for the multivalued case. Our main tool will be the so called $\\alpha$-dense curves, which will allow us to construct such iterations. Some numerical examples are provided to illustrate our results.
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Hao Tao
2012-01-01
analysis of real estate asset securitization by using the generalized fixed point theorem for weakly contractive mappings in partially ordered sets. Based on the analysis for the existence and uniqueness of the solution and scientific numerical calculation of the solution, in further study, some optimization schemes for traditional risk control process will be obtained, and then the main results of this paper can be applied to the forefront of research of real estate asset securitization.
da Silva, Rodrigo; Pearce, Jonathan V.; Machin, Graham
2017-06-01
The fixed points of the International Temperature Scale of 1990 (ITS-90) are the basis of the calibration of standard platinum resistance thermometers (SPRTs). Impurities in the fixed point material at the level of parts per million can give rise to an elevation or depression of the fixed point temperature of order of millikelvins, which often represents the most significant contribution to the uncertainty of SPRT calibrations. A number of methods for correcting for the effect of impurities have been advocated, but it is becoming increasingly evident that no single method can be used in isolation. In this investigation, a suite of five aluminium fixed point cells (defined ITS-90 freezing temperature 660.323 °C) have been constructed, each cell using metal sourced from a different supplier. The five cells have very different levels and types of impurities. For each cell, chemical assays based on the glow discharge mass spectroscopy (GDMS) technique have been obtained from three separate laboratories. In addition a series of high quality, long duration freezing curves have been obtained for each cell, using three different high quality SPRTs, all measured under nominally identical conditions. The set of GDMS analyses and freezing curves were then used to compare the different proposed impurity correction methods. It was found that the most consistent corrections were obtained with a hybrid correction method based on the sum of individual estimates (SIE) and overall maximum estimate (OME), namely the SIE/Modified-OME method. Also highly consistent was the correction technique based on fitting a Scheil solidification model to the measured freezing curves, provided certain well defined constraints are applied. Importantly, the most consistent methods are those which do not depend significantly on the chemical assay.
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Tomar Anita
2017-11-01
Full Text Available The aim of this paper is to introduce generalized condition (B in a quasi-partial metric space acknowledging the notion of Künzi et al. [Künzi H.-P. A., Pajoohesh H., Schellekens M. P., Partial quasi-metrics, Theoret. Comput. Sci., 2006, 365, 237-246] and Karapinar et al. [Karapinar E., Erhan M.,Öztürk A., Fixed point theorems on quasi-partial metric spaces, Math. Comput.Modelling, 2013, 57, 2442-2448] and to establish coincidence and common fixed point theorems for twoweakly compatible pairs of self mappings. In the sequelwe also answer affirmatively two open problems posed by Abbas, Babu and Alemayehu [Abbas M., Babu G. V. R., Alemayehu G. N., On common fixed points of weakly compatible mappings satisfying generalized condition (B, Filomat, 2011, 25(2, 9-19]. Further in the setting of a quasi-partial metric space, the results obtained are utilized to establish the existence and uniqueness of a solution of the integral equation and the functional equation arising in dynamic programming. Our results are also justified by explanatory examples supported with pictographic validations to demonstrate the authenticity of the postulates.
Solutions to second order non-homogeneous multi-point BVPs using a fixed-point theorem
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Yuji Liu
2008-07-01
Full Text Available In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs of second order differential equations with the one-dimensional p-Laplacian. These problems have a common equation (in different function domains and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several known ones and are illustrated by examples. It is also shown that the approach for getting three positive solutions by using multi-fixed-point theorems can be extended to nonhomogeneous BVPs. The emphasis is on the nonhomogeneous boundary conditions and the nonlinear term involving first order derivative of the unknown. Some open problems are also proposed.
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Malte Baesler
2013-01-01
and decimal formats, for instance, commercial, financial, and insurance applications. In this paper we present five different radix-10 digit recurrence dividers for FPGA architectures. The first one implements a simple restoring shift-and-subtract algorithm, whereas each of the other four implementations performs a nonrestoring digit recurrence algorithm with signed-digit redundant quotient calculation and carry-save representation of the residuals. More precisely, the quotient digit selection function of the second divider is implemented fully by means of a ROM, the quotient digit selection function of the third and fourth dividers are based on carry-propagate adders, and the fifth divider decomposes each digit into three components and requires neither a ROM nor a multiplexer. Furthermore, the fixed-point divider is extended to support IEEE 754-2008 compliant decimal floating-point division for decimal64 data format. Finally, the algorithms have been synthesized on a Xilinx Virtex-5 FPGA, and implementation results are given.
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Maryam A. Alghamdi
2014-01-01
Full Text Available We introduce the notion of generalized weaker (α-ϕ-φ-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.
International Nuclear Information System (INIS)
Vidossich, G.
1979-01-01
The paper presents a proof of two fixed-point theorems, which unify previous results on periodic solutions of second-order ordinary differential equations, in the sense that the existence part of these solutions become a corollay of the fixed-point theorems. (author)
A Class of Fan-Browder Type Fixed-Point Theorem and Its Applications in Topological Space
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Yi-An Chen
2010-01-01
Full Text Available A fixed-point theorem is proved under noncompact setting of general topological spaces. By applying the fixed-point theorem, several new existence theorems of solutions for equilibrium problems are proved under noncompact setting of topological spaces. These theorems improve and generalize the corresponding results in related literature.
Surface field theories of point group symmetry protected topological phases
Huang, Sheng-Jie; Hermele, Michael
2018-02-01
We identify field theories that describe the surfaces of three-dimensional bosonic point group symmetry protected topological (pgSPT) phases. The anomalous nature of the surface field theories is revealed via a dimensional reduction argument. Specifically, we study three different surface field theories. The first field theory is quantum electrodynamics in three space-time dimensions (QED3) with four flavors of fermions. We show this theory can describe the surfaces of a majority of bosonic pgSPT phases protected by a single mirror reflection, or by Cn v point group symmetry for n =2 ,3 ,4 ,6 . The second field theory is a variant of QED3 with charge-1 and charge-3 Dirac fermions. This field theory can describe the surface of a reflection symmetric pgSPT phase built by placing an E8 state on the mirror plane. The third field theory is an O (4 ) nonlinear sigma model with a topological theta term at θ =π , or, equivalently, a noncompact CP1 model. Using a coupled wire construction, we show this is a surface theory for bosonic pgSPT phases with U (1 ) ×Z2P symmetry. For the latter two field theories, we discuss the connection to gapped surfaces with topological order. Moreover, we conjecture that the latter two field theories can describe surfaces of more general bosonic pgSPT phases with Cn v point group symmetry.
Ford, Derek R.
2014-01-01
Over the last two decades, educational theory has begun to incorporate analyses of space where formerly temporal considerations dominated. In this article, Marxist educational theory is spatialized by considering the school as (1) a form of fixed capital, (2) a crucial aspect of the built environment and (3) a relational space. The author begins…
Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure
International Nuclear Information System (INIS)
Hardy, Lucien
2007-01-01
General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper, we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. We adopt an operational methodology for the purposes of theory construction (though without committing to operationalism as a fundamental philosophy). The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for a composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. The third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate everything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity
Reliability of High-Temperature Fixed-Point Installations over 8 Years
Elliott, C. J.; Ford, T.; Ongrai, O.; Pearce, J. V.
2017-12-01
At NPL, high-temperature metal-carbon eutectic fixed points have been set up for thermocouple calibration purposes since 2006, for realising reference temperatures above the highest point specified in the International Temperature Scale of 1990 for contact thermometer calibrations. Additionally, cells of the same design have been provided by NPL to other national measurement institutes (NMIs) and calibration laboratories over this period, creating traceable and ISO 17025 accredited facilities around the world for calibrating noble metal thermocouples at 1324 {°}C (Co-C) and 1492 {°}C (Pd-C). This paper shows collections of thermocouple calibration results obtained during use of the high-temperature fixed-point cells at NPL and, as further examples, the use of cells installed at CCPI Europe (UK) and NIMT (Thailand). The lifetime of the cells can now be shown to be in excess of 7 years, whether used on a weekly or monthly basis, and whether used in an NMI or industrial calibration laboratory.
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U. A. Sychou
2014-01-01
Full Text Available In this article, the problem of the practical realization of nonlinear systems with chaotic dynam-ics for targeted generation of chaotic sequences in digital devices is considered. The possible applica-tion in this task with using fixed-point arithmetic to ensure the identity of the obtained results on dif-ferent hardware and software platforms is studied. The implementation of logistic mapping is described; carry out the analysis of the results. This article proposes using the obtained results for the various tasks of the field of mobile robotics.
Random fixed point equations and inverse problems using "collage method" for contraction mappings
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2007-10-01
In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations T(w,x(w))=x(w) where is a given operator, [Omega] is a probability space and X is a Polish metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations, and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.
1988-01-01
Let K be a subset of a real Banach space X. A mapping T:K → X is called pseudo-contractive if the inequality ||x-y|| ≤ ||(1+r)(x-y)-r(Tx-Ty)|| holds for all x,y in K and r > 0. Fixed points of Lipschitz pseudo-contractive maps are approximated under appropriate conditions, by an iteration process of the type introduced by W.R. Mann. This gives an affirmative answer to the problem stated by T.L. Hicks and J.R. Rubicek (J. Math. Anal. Appl. 59 (1977) 504). (author). 28 refs
Standard map in magnetized relativistic systems: fixed points and regular acceleration.
de Sousa, M C; Steffens, F M; Pakter, R; Rizzato, F B
2010-08-01
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.
Schauder’s fixed-point theorem in approximate controllability problems
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Babiarz Artur
2016-06-01
Full Text Available The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions, impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
Isotopic effects in the neon fixed point: uncertainty of the calibration data correction
Steur, Peter P. M.; Pavese, Franco; Fellmuth, Bernd; Hermier, Yves; Hill, Kenneth D.; Seog Kim, Jin; Lipinski, Leszek; Nagao, Keisuke; Nakano, Tohru; Peruzzi, Andrea; Sparasci, Fernando; Szmyrka-Grzebyk, Anna; Tamura, Osamu; Tew, Weston L.; Valkiers, Staf; van Geel, Jan
2015-02-01
The neon triple point is one of the defining fixed points of the International Temperature Scale of 1990 (ITS-90). Although recognizing that natural neon is a mixture of isotopes, the ITS-90 definition only states that the neon should be of ‘natural isotopic composition’, without any further requirements. A preliminary study in 2005 indicated that most of the observed variability in the realized neon triple point temperatures within a range of about 0.5 mK can be attributed to the variability in isotopic composition among different samples of ‘natural’ neon. Based on the results of an International Project (EUROMET Project No. 770), the Consultative Committee for Thermometry decided to improve the realization of the neon fixed point by assigning the ITS-90 temperature value 24.5561 K to neon with the isotopic composition recommended by IUPAC, accompanied by a quadratic equation to take the deviations from the reference composition into account. In this paper, the uncertainties of the equation are discussed and an uncertainty budget is presented. The resulting standard uncertainty due to the isotopic effect (k = 1) after correction of the calibration data is reduced to (4 to 40) μK when using neon of ‘natural’ isotopic composition or to 30 μK when using 20Ne. For comparison, an uncertainty component of 0.15 mK should be included in the uncertainty budget for the neon triple point if the isotopic composition is unknown, i.e. whenever the correction cannot be applied.
The implementation of matrix free Newton /Krylov methods based on a fixed point iteration
International Nuclear Information System (INIS)
Downar, Y.X.T.
2005-01-01
A generalized approach is presented for coupling subsystems with Matrix Free Newton /Krylov (MFNK) methods. A system of nonlinear equations is defined based on a Fixed Point Iteration (FPI) scheme which does not require the reformulation of the coupled subsystems into a larger system of equations. This makes it possible for each of the subsystems to retain their respective solvers for the individual field equations. The MFNK method is applied to the new nonlinear system related to the FPI in order to find the fixed point. Convergence of both the FPI and the MFNK were analyzed and the convergence of the MFNK was shown to be dominated by the residual of linearized system. The residuals for the solution of the Newton linear system with the Matrix Free Krylov method consist of two parts, the residual due to the iteration which can be easily monitored and controlled in the Krylov iteration, and the residual introduced by the finite difference approximation of the matrix fee method. An algorithm is proposed to estimate the optimal perturbation size for MFNK which is based on balance of the truncation error and the round off error introduced by the finite difference approximation. It is shown that even for the cases in which the corresponding FPI diverges, the MFNK can achieve at least local q-linear and even q-quadratic convergence for most problems. (authors)
Acoustic resonator providing fixed points of temperature between 0.1 and 2 K
International Nuclear Information System (INIS)
Salmela, Anssi; Tuoriniemi, Juha; Pentti, Elias; Sebedash, Alexander; Rysti, Juho
2009-01-01
Below 2 K the speed of second sound in mixtures of liquid 3 He and 4 He first increases to a maximum of 30-40 m/s at about 1 K and then decreases again at lower temperatures to values below 15 m/s. The exact values depend on the concentration and pressure of the mixture. This can be exploited to provide fixed points in temperature by utilizing a resonator with appropriate dimensions and frequency to excite standing waves in the resonator cavity filled with helium mixture. We demonstrate that commercially mass produced quartz tuning forks can be used for this purpose. They are meant for frequency standards operating at 32 kHz. Their dimensions are typically of order 1 mm matching the wavelength of the second sound in helium mixtures at certain values of temperature. Due to the complicated geometry, we observe some 20 sharp acoustic resonances in the range 0.1l 2 K having temperature resolution of order 1 μK. The quartz resonators are cheap, compact, simple to implement, easy to measure with great accuracy, and, above all, they are not sensitive to magnetic field, which is a great advantage compared to fixed point devices based on superconductivity transitions. The reproducibility of the resonance pattern upon thermal cycling remains to be verified.
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Wilson Rodríguez Calderón
2015-04-01
Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.
A fixed point Kanade Lucas Tomasi tracker implementation for smart cameras
Rosner, M.
2007-09-01
This work presents the implementation of the Kanade-Lucas-Tomasi tracking algorithm on a Digital Signal Processor with a 40-bit fixed-point Arithmetic Logic Unit built into a smart camera. The main goal of this work was to obtain realtime frame processing performance while loosing as little tracking accuracy as possible. This task was motivated by increasing demand for the application of smart cameras as main data processing units in large surveillance systems, where factors like cost and demand of space are excluding PCs from this role. In a first effort the modification of the Kanade-Lucas-Tomasi to integer numbers was performed and then in the next step the influence on stability and accuracy of this modification was investigated. It is demonstrated how changing the numeric data type of intermediate results within the algorithm from float to integer, and decreasing the number of bits used to store variables, affects tracking accuracy. Nevertheless the DSP implementation can be used where the computation of optical flow based on a tracking algorithm needs to be done in real-time on an embedded platform where limited subpixel accuracy can be tolerated. As a further result of this implementation we can conclude that a DSP with a fixed-point arithmetic logic unit can be very effectively applied for complex computer vision tasks and is able deliver good performance even compared to high-end PC architectures.
Lampitt, Richard; Cristini, Luisa
2014-05-01
The Fixed point Open Ocean Observatory network (FixO3) seeks to integrate the 23 European open ocean fixed point observatories and to improve access to these key installations for the broader community. These will provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Coordinated by the National Oceanography Centre, UK, FixO3 builds on the significant advances achieved through the previous Europe-funded FP7 programmes EuroSITES, ESONET and CARBOOCEAN. Started in September 2013 with a budget of 7 Million Euros over 4 years the project has 29 partners drawn from academia, research institutions and SME's. In addition 12 international experts from a wide range of disciplines comprise an Advisory Board. On behalf of the FixO3 Consortium, we present the programme that will be achieved through the activities of 12 Work Packages: 1. Coordination activities to integrate and harmonise the current procedures and processes. Strong links will be fostered with the wider community across academia, industry, policy and the general public through outreach, knowledge exchange and training. 2. Support actions to offer a) free access to observatory infrastructures to those who do not have such access, and b) free and open data services and products. 3. Joint research activities to innovate and enhance the current capability for multidisciplinary in situ ocean observation. Support actions include Transnational Access (TNA) to FixO3 infrastructure, meaning that European organizations can apply to free-of-charge access to the observatories for research and testing in two international calls during the project lifetime. The first call for TNA opens in summer 2014. More information can be found on FixO3 website (www.fixo3.eu/). Open ocean observation is currently a high priority for European marine and maritime activities. FixO3 will provide important data on environmental products and services to address the Marine Strategy
Point splitting regularization of classical string field theory
International Nuclear Information System (INIS)
Strominger, A.
1987-01-01
We regulate Witten's star algebra using point splitting and conformal field theory techniques. Certain products of nonassociative operators and states are defined. This involves a refinement of star that exists in cases where Witten's star is ill-defined. A simple derivation of a recently discovered associativity anomaly is given. It is shown that there is no anomaly obstructing the equivalence of Witten's string theory action and the cubic action for string fields in the open string Fock space. (orig.)
Three Point Tree Level Amplitude in Superstring Theory
Hatefi, Ehsan
2011-01-01
In order to check the definite amplitude and the exact zero result of the amplitude of three massless points $(CAA)$ in both string theory and field theory side for $p=n$ case and to find all gauge field couplings to R-R closed string, we investigate the disk level S-matrix element of one Ramond-Ramond field and two gauge field vertex operators in the world volume of BPS branes.
Fixed Points and Fuzzy Stability of Functional Equations Related to Inner Product
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Hassan Azadi Kenary
2012-04-01
Full Text Available In , Th.M. Rassias introduced the following equality sum_{i,j=1}^m |x_i - x_j |^2 = 2m sum_{i=1}^m|x_i|^2, qquad sum_{i=1}^m x_i =0 for a fixed integer $m ge 3$. Let $V, W$ be real vector spaces. It is shown that if a mapping $f : V ightarrow W$ satisfies sum_{i,j=1}^m f(x_i - x_j = 2m sum_{i=1}^m f(x_i for all $x_1, ldots, x_{m} in V$ with $sum_{i=1}^m x_i =0$, then the mapping $f : V ightarrow W$ is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equation f(x-y +f(2x+y + f(x+2y= 3f(x+ 3f(y + 3f(x+y , which is called a {it quadratic functional equation}. Every solution of the quadratic functional equation is said to be a {it quadratic mapping}. Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation ( in fuzzy Banach spaces.
Fixed Points of Wegner-Wilson Flows and Many-Body Localization
Pekker, David; Clark, Bryan K.; Oganesyan, Vadim; Refael, Gil
2017-08-01
Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner-Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a Gaussian white-noise-like distribution in the ergodic phase, a 1 /f law inside the MBL phase, and scale-free distributions in the transition regime.
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Phayap Katchang
2010-01-01
Full Text Available The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008, Peng et al. (2008, Peng and Yao (2009, as well as Plubtieng and Sriprad (2009 and some well-known results in the literature.
Fixed point property for nonexpansive mappings and nonexpansive semigroups on the unit disk
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Luis Benítez-Babilonia
2015-06-01
Full Text Available For closed convex subsets D of a Banach spaces, in 2009, Tomonari Suzuki [11] proved that the fixed point property (FPP for nonexpansive mappings and the FPP for nonexpansive semigroups are equivalent. In this paper some relations between the aforementioned properties for mappings and semigroups defined on D, a closed convex subset of the hyperbolic metric space (D, ρ, are studied. This work arises as a generalization to the space (D, ρ of the study made by Suzuki. Resumen. Para subconjuntos D cerrados y convexos de espacios de Banach, Tomonari Suzuki [11] demostró en 2009 que la propiedad del punto fijo (PPF para funciones no expansivas y la PPF para semigrupos de funciones no expansivas son equivalentes. En este trabajo se estudian algunas relaciones entre dichas propiedades, cuando D es un subconjunto del espacio mético (D, ρ. Este trabajo surge como una generalización al espacio (D, ρ de los resultados de Suzuki.
On the fixed points of monotonic operators in the critical case
International Nuclear Information System (INIS)
Engibaryan, N B
2006-01-01
We consider the problem of constructing positive fixed points x of monotonic operators φ acting on a cone K in a Banach space E. We assume that ||φx||≤||x||+γ, γ>0, for all x element of K. In the case when φ has a so-called non-trivial dissipation functional we construct a solution in an extension of E, which is a Banach space or a Frechet space. We consider examples in which we prove the solubility of a conservative integral equation on the half-line with a sum-difference kernel, and of a non-linear integral equation of Urysohn type in the critical case
Point and Fixed Plot Sampling Inventory Estimates at the Savannah River Site, South Carolina.
Energy Technology Data Exchange (ETDEWEB)
Parresol, Bernard, R.
2004-02-01
This report provides calculation of systematic point sampling volume estimates for trees greater than or equal to 5 inches diameter breast height (dbh) and fixed radius plot volume estimates for trees < 5 inches dbh at the Savannah River Site (SRS), Aiken County, South Carolina. The inventory of 622 plots was started in March 1999 and completed in January 2002 (Figure 1). Estimates are given in cubic foot volume. The analyses are presented in a series of Tables and Figures. In addition, a preliminary analysis of fuel levels on the SRS is given, based on depth measurements of the duff and litter layers on the 622 inventory plots plus line transect samples of down coarse woody material. Potential standing live fuels are also included. The fuels analyses are presented in a series of tables.
Infrared cameras are potential traceable "fixed points" for future thermometry studies.
Yap Kannan, R; Keresztes, K; Hussain, S; Coats, T J; Bown, M J
2015-01-01
The National physical laboratory (NPL) requires "fixed points" whose temperatures have been established by the International Temperature Scale of 1990 (ITS 90) be used for device calibration. In practice, "near" blackbody radiators together with the standard platinum resistance thermometer is accepted as a standard. The aim of this study was to report the correlation and limits of agreement (LOA) of the thermal infrared camera and non-contact infrared temporal thermometer against each other and the "near" blackbody radiator. Temperature readings from an infrared thermography camera (FLIR T650sc) and a non-contact infrared temporal thermometer (Hubdic FS-700) were compared to a near blackbody (Hyperion R blackbody model 982) at 0.5 °C increments between 20-40 °C. At each increment, blackbody cavity temperature was confirmed with the platinum resistance thermometer. Measurements were taken initially with the thermal infrared camera followed by the infrared thermometer, with each device mounted in turn on a stand at a fixed distance of 20 cm and 5 cm from the blackbody aperture, respectively. The platinum thermometer under-estimated the blackbody temperature by 0.015 °C (95% LOA: -0.08 °C to 0.05 °C), in contrast to the thermal infrared camera and infrared thermometer which over-estimated the blackbody temperature by 0.16 °C (95% LOA: 0.03 °C to 0.28 °C) and 0.75 °C (95% LOA: -0.30 °C to 1.79 °C), respectively. Infrared thermometer over-estimates thermal infrared camera measurements by 0.6 °C (95% LOA: -0.46 °C to 1.65 °C). In conclusion, the thermal infrared camera is a potential temperature reference "fixed point" that could substitute mercury thermometers. However, further repeatability and reproducibility studies will be required with different models of thermal infrared cameras.
The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
Energy Technology Data Exchange (ETDEWEB)
Gliozzi, Ferdinando [Dipartimento di Fisica, Università di Torino andIstituto Nazionale di Fisica Nucleare - sezione di Torino,Via P. Giuria 1, I-10125 Torino (Italy); Guerrieri, Andrea L. [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); I.N.F.N. Sezione di Roma Tor Vergata,Via della Ricerca Scientifica, I-00133 Roma (Italy); Petkou, Anastasios C. [Institute of Theoretical Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece); Wen, Congkao [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Mani L. Bhaumik Institute for Theoretical Physics,Department of Physics and Astronomy, UCLA,Los Angeles, CA 90095 (United States)
2017-04-11
We describe in detail the method used in our previous work https://arxiv.org/abs/1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.
New Approach in Filling of Fixed-Point Cells: Case Study of the Melting Point of Gallium
Bojkovski, J.; Hiti, M.; Batagelj, V.; Drnovšek, J.
2008-02-01
The typical way of constructing fixed-point cells is very well described in the literature. The crucible is loaded with shot, or any other shape of pure metal, inside an argon-filled glove box. Then, the crucible is carefully slid into a fused-silica tube that is closed at the top with an appropriate cap. After that, the cell is removed from the argon glove box and melted inside a furnace while under vacuum or filled with an inert gas like argon. Since the metal comes as shot, or in some other shape such as rods of various sizes, and takes more volume than the melted material, it is necessary to repeat the procedure until a sufficient amount of material is introduced into the crucible. With such a procedure, there is the possibility of introducing additional impurities into the pure metal with each cycle of melting the material and putting it back into the glove box to fill the cell. Our new approach includes the use of a special, so-called dry-box system, which is well known in chemistry. The atmosphere inside the dry box contains less than 20 ppm of water and less than 3 ppm of oxygen. Also, the size of the dry box allows it to contain a furnace for melting materials, not only for gallium but for higher-temperature materials as well. With such an approach, the cell and all its parts (pure metal, graphite, fused-silica tube, and cap) are constantly inside the controlled atmosphere, even while melting the material and filling the crucible. With such a method, the possibility of contaminating the cell during the filling process is minimized.
Spectral properties of a two-orbital Anderson impurity model across anon-Fermi-liquid fixed point
Leo, Lorenzo De; Fabrizio, Michele
2004-06-01
We study by Wilson numerical renormalization group the spectral properties of a two-orbital Anderson impurity model in the presence of an exchange splitting that follows either regular or inverted Hund’s rules. The phase diagram contains a non-Fermi-liquid fixed point separating a screened phase, where conventional Kondo effect occurs, from an unscreened one, where the exchange splitting takes care of quenching the impurity degrees of freedom. On the Kondo screened side close to this fixed point the impurity density of states shows a narrow Kondo peak on top of a broader resonance. This narrow peak transforms in the unscreened phase into a narrow pseudogap inside the broad resonance. Right at the fixed point only the latter survives. The fixed point is therefore identified by a jump of the density of states at the chemical potential. We also consider the effect of several particle-hole symmetry-breaking terms. We show that particle-hole perturbations that simply shift the orbital energies do not wash out the fixed point, unlike those perturbations that hybridize the two orbitals. Consequently the density-of-state jump at the chemical potential remains finite even away from particle-hole symmetry. In other words, the pseudogap stays pinned at the chemical potential, although it is partially filled in. We also discuss the relevance of these results for lattice models that map onto this Anderson impurity model in the limit of large lattice coordination. Upon approaching the Mott metal-insulator transition, these lattice models necessarily enter a region with a local criticality that reflects the impurity non-Fermi-liquid fixed point. However, unlike the impurity, the lattice can get rid of the single-impurity fixed-point instability by spontaneously developing bulk coherent symmetry-broken phases, which we identify for different lattice models.
General theory of spontaneous emission near exceptional points.
Pick, Adi; Zhen, Bo; Miller, Owen D; Hsu, Chia W; Hernandez, Felipe; Rodriguez, Alejandro W; Soljačić, Marin; Johnson, Steven G
2017-05-29
We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes.
Two-point function of a d =2 quantum critical metal in the limit kF→∞ , Nf→0 with NfkF fixed
Säterskog, Petter; Meszena, Balazs; Schalm, Koenraad
2017-10-01
We show that the fermionic and bosonic spectrum of d =2 fermions at finite density coupled to a critical boson can be determined nonperturbatively in the combined limit kF→∞ ,Nf→0 with NfkF fixed. In this double scaling limit, the boson two-point function is corrected but only at one loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched Nf→0 result. For ω →0 with k fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory.
Development of large-area high-temperature fixed-point blackbodies for photometry and radiometry
Khlevnoy, Boris; Grigoryeva, Irina; Anhalt, Klaus; Waehmer, Martin; Ivashin, Evgeniy; Otryaskin, Denis; Solodilov, Maxim; Sapritsky, Victor
2018-04-01
Large-area high-temperature fixed-point (HTFP) blackbodies with working temperatures of approximately 2748 K and 3021 K, based on an Re-C eutectic and a WC-C peritectic respectively, have been developed and investigated. The blackbodies have an emissivity of 0.9997, show high-quality phase-transition plateaus and have high repeatability of the melting temperatures, but demonstrate temperature differences (from 0.2 K to 0.6 K) compared with small-cell blackbodies of the same HTFP. We associate these temperature differences with the temperature drop effect, which may differ from cell to cell. The large radiating cavity diameter of 14 mm allows developed HTFP blackbodies to be used for photometric and radiometric applications in irradiance mode with uncertainties as small as 0.12% (k = 1) in the visible. A photometer and an irradiance-mode filter radiometer (visible range), previously calibrated at VNIIOFI, were used to measure illuminance and irradiance of the HTFP blackbodies equipped with a precise outer aperture. The values measured by the detectors agreed with those based on the blackbody calculation to within 0.2%. The large-area HTFP blackbodies will be used in a joint PTB-VNIIOFI experiment on measuring thermodynamic temperature.
Directory of Open Access Journals (Sweden)
Ibrahim Karahan
2016-04-01
Full Text Available Let C be a nonempty closed convex subset of a real Hilbert space H. Let {T_{n}}:C›H be a sequence of nearly nonexpansive mappings such that F:=?_{i=1}^{?}F(T_{i}?Ø. Let V:C›H be a ?-Lipschitzian mapping and F:C›H be a L-Lipschitzian and ?-strongly monotone operator. This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem. It is shown that under certain approximate assumptions on the operators and parameters, the modified iterative sequence {x_{n}} converges strongly to x^{*}?F which is also the unique solution of the following variational inequality: ?0, ?x?F. As a special case, this projection method can be used to find the minimum norm solution of above variational inequality; namely, the unique solution x^{*} to the quadratic minimization problem: x^{*}=argmin_{x?F}?x?². The results here improve and extend some recent corresponding results of other authors.
Higgs and supersymmetric particle signals at the infrared fixed point of the top quark mass
International Nuclear Information System (INIS)
Carena, M.; Wagner, C.E.M.
1995-01-01
We study the properties of the Higgs and supersymmetric particle spectrum, associated with the infrared fixed point solution of the top quark mass in the Minimal Supersymmetric Standard Model. We concentrate on the possible detection of these particles, analysing the deviations from the Standard Model predictions for the leptonic and hadronic variables measured at LEP and for the b→sγ decay rate. We consider the low and moderate tan β regime, imposing the constraints derived from a proper radiative SU(2) L xU(1) Y symmetry breaking, and we study both the cases of universal and non-universal soft supersymmetry-breaking parameters at high energies. In the first case, for any given value of the top quark mass, the Higgs and supersymmetric particle spectrum is completely determined as a function of only two soft supersymmetry-breaking parameters, implying very definite experimental signatures. In the case of non-universal mass parameters at M GUT , instead, the strong correlations between the sparticle masses are relaxed, allowing a richer structure for the precision data variables. As a general feature, whenever a significant deviation from the Standard Model value of the precision data parameters is predicted, a light sparticle, which should be visible at LEP2, appears in the model. (orig.)
CPN-1 models with a θ term and fixed point action
International Nuclear Information System (INIS)
Burkhalter, Rudolf; Imachi, Masahiro; Shinno, Yasuhiko; Yoneyama, Hiroshi
2001-01-01
The topological charge distribution P(Q) is calculated for lattice CP N-1 models. In order to suppress lattice cutoff effects, we employ a fixed point (FP) action. Through transformation of P(Q), we calculate the free energy F(θ) as a function of the θ parameter. For N=4, scaling behavior is observed for P(Q) and F(θ), as well as the correlation lengths ξ(Q). For N=2, however, scaling behavior is not observed, as expected. For comparison, we also make a calculation for the CP 3 model with a standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For this purpose, we carefully consider the behavior of γ eff , which is an effective power of P(Q) (∼exp (-CQ γeff )), and reflects the local behavior of P(Q) as a function of Q. We study γ eff for two cases, the dilute gas approximation based on the Poisson distribution of instantons and the Debye-Hueckel approximation of instanton quarks. In both cases, we find behavior similar to that observed in numerical simulations. (author)
Point sources and multipoles in inverse scattering theory
Potthast, Roland
2001-01-01
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.With interest in extracting information about an object through scattered waves at an all-ti...
Einstein gravity 3-point functions from conformal field theory
Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan; Tajdini, Amirhossein
2017-12-01
We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories in this class are expected to have local holographic duals, so effective field theory in anti-de Sitter suggests that the stress tensor sector should exhibit universal, gravity-like behavior. At the linearized level, the hallmark of locality in the emergent geometry is that stress tensor three-point functions 〈 T T T 〉, normally specified by three constants, should approach a universal structure controlled by a single parameter as the gap to higher spin operators is increased. We demonstrate this phenomenon by a direct CFT calculation. Stress tensor exchange, by itself, violates causality and unitarity unless the three-point functions are carefully tuned, and the unique consistent choice exactly matches the prediction of Einstein gravity. Under some assumptions about the other potential contributions, we conclude that this structure is universal, and in particular, that the anomaly coefficients satisfy a ≈ c as conjectured by Camanho et al. The argument is based on causality of a four-point function, with kinematics designed to probe bulk locality, and invokes the chaos bound of Maldacena, Shenker, and Stanford.
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Xue-song Li
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
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Kamonrat Sombut
2013-01-01
Full Text Available The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP and systems of equilibrium problems (SEP in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012 and many others.
Zero-point energy in early quantum theory
International Nuclear Information System (INIS)
Milonni, P.W.; Shih, M.-L.
1991-01-01
In modern physics the vacuum is not a tranquil void but a quantum state with fluctuations having observable consequences. The present concept of the vacuum has its roots in the zero-point energy of harmonic oscillators and the electromagnetic field, and arose before the development of the formalism of quantum mechanics. This article discusses these roots in the blackbody research of Planck and Einstein in 1912--1913, and the relation to Bose--Einstein statistics and the first indication of wave--particle duality uncovered by Einstein's fluctuation formula. Also considered are the Einstein--Stern theory of specific heats, which invoked zero-point energy in a way which turned out to be incorrect, and the experimental implications of zero-point energy recognized by Mulliken and Debye in vibrational spectroscopy and x-ray diffraction
Ragay-Enot, Monalisa; Lee, Young Hee; Kim, Yong-Gyoo
2017-07-01
A mini multi-fixed-point cell (length 118 mm, diameter 33 mm) containing three materials (In-Zn eutectic (mass fraction 3.8% Zn), Sn and Pb) in a single crucible was designed and fabricated for the easy and economical fixed-point calibration of industrial platinum resistance thermometers (IPRTs) for use in industrial temperature measurements. The melting and freezing behaviors of the metals were investigated and the phase transition temperatures were determined using a commercial dry-block calibrator. Results showed that the melting plateaus are generally easy to realize and are reproducible, flatter and of longer duration. On the other hand, the freezing process is generally difficult, especially for Sn, due to the high supercooling required to initiate freezing. The observed melting temperatures at optimum set conditions were 143.11 °C (In-Zn), 231.70 °C (Sn) and 327.15 °C (Pb) with expanded uncertainties (k = 2) of 0.12 °C, 0.10 °C and 0.13 °C, respectively. This multi-fixed-point cell can be treated as a sole reference temperature-generating system. Based on the results, the realization of melting points of the mini multi-fixed-point cell can be recommended for the direct calibration of IPRTs in industrial applications without the need for a reference thermometer.
Co-C and Pd-C Eutectic Fixed Points for Radiation Thermometry and Thermocouple Thermometry
Wang, L.
2017-12-01
Two Co-C and Pd-C eutectic fixed point cells for both radiation thermometry and thermocouple thermometry were constructed at NMC. This paper describes details of the cell design, materials used, and fabrication of the cells. The melting curves of the Co-C and Pd-C cells were measured with a reference radiation thermometer realized in both a single-zone furnace and a three-zone furnace in order to investigate furnace effect. The transition temperatures in terms of ITS-90 were determined to be 1324.18 {°}C and 1491.61 {°}C with the corresponding combined standard uncertainty of 0.44 {°}C and 0.31 {°}C for Co-C and Pd-C, respectively, taking into account of the differences of two different types of furnaces used. The determined ITS-90 temperatures are also compared with that of INRIM cells obtained using the same reference radiation thermometer and the same furnaces with the same settings during a previous bilateral comparison exercise (Battuello et al. in Int J Thermophys 35:535-546, 2014). The agreements are within k=1 uncertainty for Co-C cell and k = 2 uncertainty for Pd-C cell. Shapes of the plateaus of NMC cells and INRIM cells are compared too and furnace effects are analyzed as well. The melting curves of the Co-C and Pd-C cells realized in the single-zone furnace are also measured by a Pt/Pd thermocouple, and the preliminary results are presented as well.
Castro, P.; Machin, G.; Bloembergen, P.; Lowe, D.; Whittam, A.
2014-07-01
This study forms part of the European Metrology Research Programme project implementing the New Kelvin to assign thermodynamic temperatures to a selected set of high-temperature fixed points (HTFPs), Cu, Co-C, Pt-C, and Re-C. A realistic thermal model of these HTFPs, developed in finite volume software ANSYS FLUENT, was constructed to quantify the uncertainty associated with the temperature drop across the back wall of the cell. In addition, the widely applied software package, STEEP3 was used to investigate the influence of cell emissivity. The temperature drop, , relates to the temperature difference due to the net loss of heat from the aperture of the cavity between the back wall of the cavity, viewed by the thermometer, defining the radiance temperature, and the solid-liquid interface of the alloy, defining the transition temperature of the HTFP. The actual value of can be used either as a correction (with associated uncertainty) to thermodynamic temperature evaluations of HTFPs, or as an uncertainty contribution to the overall estimated uncertainty. In addition, the effect of a range of furnace temperature profiles on the temperature drop was calculated and found to be negligible for Cu, Co-C, and Pt-C and small only for Re-C. The effective isothermal emissivity is calculated over the wavelength range from 450 nm to 850 nm for different assumed values of surface emissivity. Even when furnace temperature profiles are taken into account, the estimated emissivities change only slightly from the effective isothermal emissivity of the bare cell. These emissivity calculations are used to estimate the uncertainty in the temperature assignment due to the uncertainty in the emissivity of the blackbody.
Péli, Zoltán; Nagy, Sándor; Sailer, Kornel
2018-02-01
The effect of the O(partial4) terms of the gradient expansion on the anomalous dimension η and the correlation length's critical exponent ν of the Wilson-Fisher fixed point has been determined for the Euclidean 3-dimensional O( N) models with N≥ 2 . Wetterich's effective average action renormalization group method is used with field-independent derivative couplings and Litim's optimized regulator. It is shown that the critical theory is well approximated by the effective average action preserving O( N) symmetry with an accuracy of O(η).
Nieto, John
2007-04-01
Since their introduction in 1993, turbo codes have received a significant amount of attention in the communications theory field due to their Shannon-capacity approaching performance. In recent years, the cellular systems market has embraced turbo code technology and made it part of the latest standards. This paper will review the effects of scale factors, fixed-point precision, soft decisions and hard decisions on the performance of the turbo codes defined in the UMTS third-generation cellular system. In addition, a new scale factor estimation technique which provides improved performance at low signal to noise ratios will be presented.
Energy Technology Data Exchange (ETDEWEB)
Kijima, K.; Murata, W.; Furukawa, Y. [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1997-10-01
The control system for keeping the fixed-point of ships against disturbance was designed by applying an ILQ (Inverse Linear Quadratic) control (possible to specify the response of controlled systems with time constant) theory, to study the effect of different time constants as design parameter on a fixed-point keeping performance. It was assumed that the controlled ship is equipped with two bow thrusters and one stern thruster of 30ton in output to generate a control force. For fixed-point keeping control, the state equation was derived to slave the controlled system to a target input. The ILQ design method uses the result of the inverse problem of optimum regulators. For designing control systems by using the ILQ control theory, the smallest time constant should be selected according to the most severe disturbance condition considering the response performance of controllers, to achieve fixed-point keeping of ships. In fixed-point keeping, it is also essential to put the initial position as close as possible to the target point. 2 refs., 6 figs., 2 tabs.
2010-05-11
leading to some of the ideas presented in Section 4 and David Baelde for technical discussions on proof rules for fixed-points. References [1] M. S...sites. In Proceedings of the 5th International Conference on Electronic Commerce, pages 326–338, 2003. [16] R. Chadha, D. Macedonio, and V. Sassone . A
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Yazheng Dang
2013-01-01
Full Text Available Inspired by the Moudafi (2010, we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.
DEFF Research Database (Denmark)
Beltran, H.; Perez, E.; Chen, Zhe
2009-01-01
This paper describes a Fixed Maximum Power Point analog control used in a step-down Pulse Width Modulated power converter. The DC/DC converter drives a DC motor used in small water pumping installations, without any electric storage device. The power supply is provided by PV panels working around...
M. Aamri; A. Bassou; S. Bennani; D. El Moutawakil
2007-01-01
The main purpose of this paper is to give some common fixed point theorems of mappings and set-valued mappings of a symmetric space with some applications to probabilistic spaces. In order to get these results, we define the concept of E-weak compatibility between set-valued and single-valued mappings of a symmetric space.
International Nuclear Information System (INIS)
Jesic, Sinisa N.; Babacev, Natasa A.
2008-01-01
The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given
International Nuclear Information System (INIS)
Sharma, Sushil; Deshpande, Bhavana
2009-01-01
The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces. Our results extend, generalize and intuitionistic fuzzify several known results in fuzzy metric spaces. We give an example and also give formulas for total number of commutativity conditions for finite number of mappings.
Some Common Fixed Point Theorems for F-Contraction Type Mappings in 0-Complete Partial Metric Spaces
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Satish Shukla
2013-01-01
Full Text Available We prove some common fixed point theorems for F-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.
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Urriza I
2010-01-01
Full Text Available Abstract This paper presents a word length selection method for the implementation of digital controllers in both fixed-point and floating-point hardware on FPGAs. This method uses the new types defined in the VHDL-2008 fixed-point and floating-point packages. These packages allow customizing the word length of fixed and floating point representations and shorten the design cycle simplifying the design of arithmetic operations. The method performs bit-true simulations in order to determine the word length to represent the constant coefficients and the internal signals of the digital controller while maintaining the control system specifications. A mixed-signal simulation tool is used to simulate the closed loop system as a whole in order to analyze the impact of the quantization effects and loop delays on the control system performance. The method is applied to implement a digital controller for a switching power converter. The digital circuit is implemented on an FPGA, and the simulations are experimentally verified.
Saddle-points of a two dimensional random lattice theory
International Nuclear Information System (INIS)
Pertermann, D.
1985-07-01
A two dimensional random lattice theory with a free massless scalar field is considered. We analyse the field theoretic generating functional for any given choice of positions of the lattice sites. Asking for saddle-points of this generating functional with respect to the positions we find the hexagonal lattice and a triangulated version of the hypercubic lattice as candidates. The investigation of the neighbourhood of a single lattice site yields triangulated rectangles and regular polygons extremizing the above generating functional on the local level. (author)
Theory of Nonlocal Point Transformations in General Relativity
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Massimo Tessarotto
2016-01-01
Full Text Available A discussion of the functional setting customarily adopted in General Relativity (GR is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs. While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern (1 a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; (2 the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; (3 the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and (4 the diagonalization of nondiagonal metric tensors.
Use of cooperative game theory in power system fixed-cost allocation
International Nuclear Information System (INIS)
Stamtsis, G.C.; Erlich, I.
2004-01-01
The use of cooperative game theory in power system fixed-cost allocation is investigated. The implementation of the allocation game in a bilateral transaction electricity market as well as in a pool market is discussed and the use of two well-known solution methods, nucleolus and the Shapley value, is explored. Conclusions are drawn which show that the Shapley value is a more preferable method when it is in the core of the game. For all the cases, results are illustrated in the IEEE 14-bus system. (author)
Poor textural image tie point matching via graph theory
Yuan, Xiuxiao; Chen, Shiyu; Yuan, Wei; Cai, Yang
2017-07-01
Feature matching aims to find corresponding points to serve as tie points between images. Robust matching is still a challenging task when input images are characterized by low contrast or contain repetitive patterns, occlusions, or homogeneous textures. In this paper, a novel feature matching algorithm based on graph theory is proposed. This algorithm integrates both geometric and radiometric constraints into an edge-weighted (EW) affinity tensor. Tie points are then obtained by high-order graph matching. Four pairs of poor textural images covering forests, deserts, bare lands, and urban areas are tested. For comparison, three state-of-the-art matching techniques, namely, scale-invariant feature transform (SIFT), speeded up robust features (SURF), and features from accelerated segment test (FAST), are also used. The experimental results show that the matching recall obtained by SIFT, SURF, and FAST varies from 0 to 35% in different types of poor textures. However, through the integration of both geometry and radiometry and the EW strategy, the recall obtained by the proposed algorithm is better than 50% in all four image pairs. The better matching recall improves the number of correct matches, dispersion, and positional accuracy.
Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
Tóth, Gábor Zsolt
2017-07-01
We extend the standard construction of conserved currents for matter fields in general relativity to general gauge theories. In the original construction, the conserved current associated with a spacetime symmetry generated by a Killing field hμ is given by √{-g }Tμ νhν , where Tμ ν is the energy-momentum tensor of the matter. We show that if in a Lagrangian field theory that has gauge symmetry in the general Noetherian sense some of the elementary fields are fixed and are invariant under a particular infinitesimal gauge transformation, then there is a current Bμ that is analogous to √{-g }Tμ νhν and is conserved if the nonfixed fields satisfy their Euler-Lagrange equations. The conservation of Bμ can be seen as a consequence of an identity that is a generalization of ∇μTμ ν=0 and is a consequence of the gauge symmetry of the Lagrangian. This identity holds in any configuration of the fixed fields if the nonfixed fields satisfy their Euler-Lagrange equations. We also show that Bμ differs from the relevant canonical Noether current by the sum of an identically conserved current and a term that vanishes if the nonfixed fields are on shell. For an example, we discuss the case of general, possibly fermionic, matter fields propagating in fixed gravitational and Yang-Mills background. We find that in this case the generalization of ∇μTμ ν=0 is the Lorentz law ∇μTμ ν-Fa ν λJa λ=0 , which holds as a consequence of the diffeomorphism, local Lorentz and Yang-Mills gauge symmetry of the matter Lagrangian. For a second simple example, we consider the case of general fields propagating in a background that consists of a gravitational and a real scalar field.
Merzlikin, Boris S.; Shapiro, Ilya L.; Wipf, Andreas; Zanusso, Omar
2017-12-01
Using covariant methods, we construct and explore the Wetterich equation for a nonminimal coupling F (ϕ )R of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered nonminimal coupling ξ ϕ2R as a special case. We consider the truncations without and with scale- and field-dependent wave-function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the nonminimal coupling in the symmetric and spontaneously broken phases with vanishing and nonvanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension d =4 .
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R. A. Rashwan
2013-01-01
Full Text Available We prove some strong convergence of a new random iterative scheme with errors to common random fixed points for three and then N nonself asymptotically quasi-nonexpansive-type random mappings in a real separable Banach space. Our results extend and improve the recent results in Kiziltunc, 2011, Thianwan, 2008, Deng et al., 2012, and Zhou and Wang, 2007 as well as many others.
Energy Technology Data Exchange (ETDEWEB)
Laurie, M.; Vlahovic, L.; Rondinella, V.V. [European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, D-76125 Karlsruhe, (Germany); Sadli, M.; Failleau, G. [Laboratoire Commun de Metrologie, LNE-Cnam, Saint-Denis, (France); Fuetterer, M.; Lapetite, J.M. [European Commission, Joint Research Centre, Institute for Energy and Transport, P.O. Box 2, NL-1755 ZG Petten, (Netherlands); Fourrez, S. [Thermocoax, 8 rue du pre neuf, F-61100 St Georges des Groseillers, (France)
2015-07-01
Temperature measurements in the nuclear field require a high degree of reliability and accuracy. Despite their sheathed form, thermocouples subjected to nuclear radiations undergo changes due to radiation damage and transmutation that lead to significant EMF drift during long-term fuel irradiation experiment. For the purpose of a High Temperature Reactor fuel irradiation to take place in the High Flux Reactor Petten, a dedicated fixed-point cell was jointly developed by LNE-Cnam and JRC-IET. The developed cell to be housed in the irradiation rig was tailor made to quantify the thermocouple drift during the irradiation (about two year duration) and withstand high temperature (in the range 950 deg. C - 1100 deg. C) in the presence of contaminated helium in a graphite environment. Considering the different levels of temperature achieved in the irradiation facility and the large palette of thermocouple types aimed at surveying the HTR fuel pebble during the qualification test both copper (1084.62 deg. C) and gold (1064.18 deg. C) fixed-point materials were considered. The aim of this paper is to first describe the fixed-point mini-cell designed to be embedded in the reactor rig and to discuss the preliminary results achieved during some out of pile tests as much as some robustness tests representative of the reactor scram scenarios. (authors)
Directory of Open Access Journals (Sweden)
Sadli Mohamed
2014-01-01
Full Text Available Among the activities of the European Metrology Research Programme (EMRP project HiTeMS one work package is devoted to the development and testing of industrial solutions for long-standing temperature measurement problems at the highest temperatures. LNE-Cnam, NPL, TUBITAK-UME have worked on the design of high temperature fixed points (HTFP suitable for in-situ temperature monitoring to be implemented in the facilities of CEA (Commissariat à l’énergie atomique et aux énergies alternatives. Several high temperature fixed point cells were constructed in these three national metrology institutes (NMIs using a rugged version of cells based on the hybrid design of the laboratory HTFP developed and continuously improved at LNE-Cnam during the last years. The fixed points of interest were Co-C, Ru-C and Re-C corresponding to melting temperatures of 1324 °C, 1953 °C and 2474 °C respectively. The cells were characterised at the NMIs after their construction. Having proved robust enough, they were transported to CEA and tested in an induction furnace and cycled from room temperature to temperatures much above the melting temperatures (> +400 °C with extremely high heating and cooling rates (up to 10 000 K/h. All the cells withstood the tests and the melting plateaus could be observed in all cases.
The EuroSITES network: Integrating and enhancing fixed-point open ocean observatories around Europe
Lampitt, Richard S.; Larkin, Kate E.; EuroSITES Consortium
2010-05-01
EuroSITES is a 3 year (2008-2011) EU collaborative project (3.5MEuro) with the objective to integrate and enhance the nine existing open ocean fixed point observatories around Europe (www.eurosites.info). These observatories are primarily composed of full depth moorings and make multidisciplinary in situ observations within the water column as the European contribution to the global array OceanSITES (www.oceansites.org). In the first 18 months, all 9 observatories have been active and integration has been significant through the maintenance and enhancement of observatory hardware. Highlights include the enhancement of observatories with sensors to measure O2, pCO2, chlorophyll, and nitrate in near real-time from the upper 1000 m. In addition, some seafloor missions are also actively supported. These include seafloor platforms currently deployed in the Mediterranean, one for tsunami detection and one to monitor fluid flow related to seismic activity and slope stability. Upcoming seafloor science missions in 2010 include monitoring benthic biological communities and associated biogeochemistry as indicators of climate change in both the Northeast Atlantic and Mediterranean. EuroSITES also promotes the development of innovative sensors and samplers in order to progress capability to measure climate-relevant properties of the ocean. These include further developing current technologies for autonomous long-term monitoring of oxygen consumption in the mesopelagic, pH and mesozooplankton abundance. Many of these science missions are directly related to complementary activities in other European projects such as EPOCA, HYPOX and ESONET. In 2010 a direct collaboration including in situ field work will take place between ESONET and EuroSITES. The demonstration mission MODOO (funded by ESONET) will be implemented in 2010 at the EuroSITES PAP observatory. Field work will include deployment of a seafloor lander system with various sensors which will send data to shore in real
Kuyper, Brett; Palmer, Carl J.; Labuschagne, Casper; Reason, Chris J. C.
2018-04-01
Bromoform mixing ratios in marine air were measured at Cape Point Global Atmospheric Watch Station, South Africa. This represents the first such bromoform data set recorded at this location. Manual daily measurements were made during a month-long field campaign (austral spring 2011) using a gas chromatograph-electron capture detector (GC-ECD) with a custom-built front end thermal desorption trap. The measured concentrations ranged between 4.4 and 64.6 (± 22.2 %) ppt with a mean of 24.8 ± 14.8 ppt. The highest mixing ratios recorded here occurred at, or shortly after, low tide. The diurnal cycle exhibited a morning and evening maximum with lower concentrations throughout the rest of the day. Initial analysis of the data presented indicates that the local kelp beds were the dominant source of the bromoform reported. A concentration-weighted trajectory analysis of the bromoform measurements suggests that two offshore source areas may exist. These source areas appear to be centred on the Agulhas retroflection and extend from St Helena Bay to the southwest.
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B. Kuyper
2018-04-01
Full Text Available Bromoform mixing ratios in marine air were measured at Cape Point Global Atmospheric Watch Station, South Africa. This represents the first such bromoform data set recorded at this location. Manual daily measurements were made during a month-long field campaign (austral spring 2011 using a gas chromatograph-electron capture detector (GC-ECD with a custom-built front end thermal desorption trap. The measured concentrations ranged between 4.4 and 64.6 (± 22.2 % ppt with a mean of 24.8 ± 14.8 ppt. The highest mixing ratios recorded here occurred at, or shortly after, low tide. The diurnal cycle exhibited a morning and evening maximum with lower concentrations throughout the rest of the day. Initial analysis of the data presented indicates that the local kelp beds were the dominant source of the bromoform reported. A concentration-weighted trajectory analysis of the bromoform measurements suggests that two offshore source areas may exist. These source areas appear to be centred on the Agulhas retroflection and extend from St Helena Bay to the southwest.
Comparative performance of fixed-film biological filters: Application of reactor theory
Watten, B.J.; Sibrell, P.L.
2006-01-01
Nitrification is classified as a two-step consecutive reaction where R1 represents the rate of formation of the intermediate product NO2-N and R2 represents the rate of formation of the final product NO3-N. The relative rates of R1 and R2 are influenced by reactor type characterized hydraulically as plug-flow, plug-flow with dispersion and mixed-flow. We develop substrate conversion models for fixed-film biofilters operating in the first-order kinetic regime based on application of chemical reactor theory. Reactor type, inlet conditions and the biofilm kinetic constants Ki (h-1) are used to predict changes in NH4-N, NO2-N, NO3-N and BOD5. The inhibiting effects of the latter on R1 and R2 were established based on the ?? relation, e.g.:{A formula is presented}where BOD5,max is the concentration that causes nitrification to cease and N is a variable relating Ki to increasing BOD5. Conversion models were incorporated in spreadsheet programs that provided steady-state concentrations of nitrogen and BOD5 at several points in a recirculating aquaculture system operating with input values for fish feed rate, reactor volume, microscreen performance, make-up and recirculating flow rates. When rate constants are standardized, spreadsheet use demonstrates plug-flow reactors provide higher rates of R1 and R2 than mixed-flow reactors thereby reducing volume requirements for target concentrations of NH4-N and NO2-N. The benefit provided by the plug-flow reactor varies with hydraulic residence time t as well as the effective vessel dispersion number, D/??L. Both reactor types are capable of providing net increases in NO2-N during treatment but the rate of decrease in the mixed-flow case falls well behind that predicted for plug-flow operation. We show the potential for a positive net change in NO2-N increases with decreases in the dimensionless ratios K2, (R2 )/K1,( R1 ) and [NO2-N]/[NH4-N] and when the product K1, (R1) t provides low to moderate NH4-N conversions. Maintaining
Gradient flow and IR fixed point in SU(2) with Nf=8 flavors
DEFF Research Database (Denmark)
Leino, Viljami; Karavirta, Tuomas; Rantaharju, Jarno
2015-01-01
We study the running of the coupling in SU(2) gauge theory with 8 massless fundamental representation fermion flavours, using the gradient flow method with the Schr\\"odinger functional boundary conditions. Gradient flow allows us to measure robust continuum limit for the step scaling function...
Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
2012-01-01
of pure supersymmetric Yang-Mills. We can therefore determine the exact nonperturbative fermion condensate and deduce relevant properties of the nonperturbative spectrum of the theory. We also show that the intrinsic scale of super Yang-Mills is exponentially smaller than the scale associated...
Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory
International Nuclear Information System (INIS)
Chen, G.-H.; Wu, Y.-S.
2002-01-01
A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level
Carretero, L; Perez-Molina, M; Blaya, S; Madrigal, R; Acebal, P; Fimia, A
2005-10-31
A method based in the application of Fixed Point Theorem (FPT) techniques to the solution of the 1D wave equation at normal incidence for materials that present a continuous (real or complex) dielectric constant is presented. As an example, the method is applied for the calculation of the electric field, reflection and transmission spectra in volume holographic gratings. It is shown that the solution obtained using this method agrees with the exact Mathieu solutions also obtained in this paper for volume holographic reflection gratings.
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Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
Stabilities of Cubic Mappings in Various Normed Spaces: Direct and Fixed Point Methods
Directory of Open Access Journals (Sweden)
H. Azadi Kenary
2012-01-01
Full Text Available In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber (1978 this kind of stability problems are of the particular interest in probability theory and in the case of functional equations of different types. In 1981, Skof was the first author to solve the Ulam problem for quadratic mappings. In 1982–2011, J. M. Rassias solved the above Ulam problem for linear and nonlinear mappings and established analogous stability problems even on restricted domains. The purpose of this paper is the generalized Hyers-Ulam stability for the following cubic functional equation: (++(−=(++(−+2(3−(,≥2 in various normed spaces.
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Eleonora Pantano
2013-05-01
Full Text Available The current advances in information and communications technologies developed new tools for retailers to innovate. In fact, the increasing computing capacity and the advancements in networking systems provided a new ubiquitous scenario that can be adapted for retailing in order to develop innovative shopping environments. The aim of this paper is to deeply understand the emergence of the ubiquitous retailing phenomenon and the possible shift from the physical point of sale to a ubiquitous one, by analysing this radical innovation and the main consequences for frms and market.
Slamnoiu, G.; Radu, O.; Surdu, G.; Roşca, V.; Damian, R.; Pascu, C.; Curcă, E.; Rădulescu, A.
2016-08-01
The paper has as its main objectives the presentation and the analysis of the numerical analysis results for the study of a fixed point anchoring system for a hydroacoustic sensor when measuring the hydroacoustic signature of divers and ships in real sea conditions. The study of the mechanical behavior of this system has as main objectives the optimization of the shape and weight of the anchorage ballast for the metallic structure while considering the necessity to maintain the sensor in a fixed point and the analysis of the sensor movements and the influences on the measurements caused by the sea current streams. The study was focused on the 3D model of metallic structure design; numerical modeling of the water flow around the sensor anchoring structure using volume of fluid analysis and the analysis of the forces and displacements using FEM when needed for the study. In this paper we have used data for the sea motion dynamics and in particular the velocity of the sea current streams as determined by experimental measurements that have been conducted for the western area of the Black Sea.
Inflection point inflation and time dependent potentials in string theory
International Nuclear Information System (INIS)
Itzhaki, Nissan; Kovetz, Ely D.
2007-01-01
We consider models of inflection point inflation. The main drawback of such models is that they suffer from the overshoot problem. Namely the initial condition should be fine tuned to be near the inflection point for the universe to inflate. We show that stringy realizations of inflection point inflation are common and offer a natural resolution to the overshoot problem
Typical Orbits of Quadratic Polynomials with a Neutral Fixed Point: Brjuno Type
Cheraghi, Davoud
2013-09-01
We describe the topological behavior of typical orbits of complex quadratic polynomials {P_{α}(z) = e^{2 π α {i}} z + z2}, with α of high return type. Here we prove that for such Brjuno values of α the closure of the critical orbit, which is the measure theoretic attractor of the map, has zero area. Then we show that the limit set of the orbit of a typical point in the Julia set of P α is equal to the closure of the critical orbit. Our method is based on the near parabolic renormalization of Inou-Shishikura, and a uniform optimal estimate on the derivative of the Fatou coordinate that we prove here.
Cancer Theory from Systems Biology Point of View
Wang, Gaowei; Tang, Ying; Yuan, Ruoshi; Ao, Ping
In our previous work, we have proposed a novel cancer theory, endogenous network theory, to understand mechanism underlying cancer genesis and development. Recently, we apply this theory to hepatocellular carcinoma (HCC). A core endogenous network of hepatocyte was established by integrating the current understanding of hepatocyte at molecular level. Quantitative description of the endogenous network consisted of a set of stochastic differential equations which could generate many local attractors with obvious or non-obvious biological functions. By comparing with clinical observation and experimental data, the results showed that two robust attractors from the model reproduced the main known features of normal hepatocyte and cancerous hepatocyte respectively at both modular and molecular level. In light of our theory, the genesis and progression of cancer is viewed as transition from normal attractor to HCC attractor. A set of new insights on understanding cancer genesis and progression, and on strategies for cancer prevention, cure, and care were provided.
De la Sen, M.
2015-01-01
In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilistic α-fuzzy fixed points under some types of probabilistic contractive conditions.
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Sunny Chauhan
2013-11-01
Full Text Available In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature.
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Tong-Huei Chang
2009-01-01
Full Text Available We use a concept of abstract convexity to define the almost S-KKM𝒞 property, al-S-KKM𝒞(X,Y family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors.
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Marwan Amin Kutbi
2014-01-01
weakly compatible mappings in symmetric spaces satisfying generalized (ψ,φ-contractive conditions employing the common limit range property. We furnish some interesting examples which support our main theorems. Our results generalize and extend some recent results contained in Imdad et al. (2013 to symmetric spaces. Consequently, a host of metrical common fixed theorems are generalized and improved. In the process, we also derive a fixed point theorem for four finite families of mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings.
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Jose Ernie C. Lope
2013-12-01
Full Text Available In their 2012 work, Lope, Roque, and Tahara considered singular nonlinear partial differential equations of the form tut = F(t; x; u; ux, where the function F is assumed to be continuous in t and holomorphic in the other variables. They have shown that under some growth conditions on the coefficients of the partial Taylor expansion of F as t 0, the equation has a unique solution u(t; x with the same growth order as that of F(t; x; 0; 0. Koike considered systems of partial differential equations using the Banach fixed point theorem and the iterative method of Nishida and Nirenberg. In this paper, we prove the result obtained by Lope and others using the method of Koike, thereby avoiding the repetitive step of differentiating a recursive equation with respect to x as was done by the aforementioned authors.
DEFF Research Database (Denmark)
Filipiuk, Piotr; Nielson, Flemming; Nielson, Hanne Riis
2012-01-01
are a Moore Family result and a parametrized worst case time complexity result. We show that the logic and the associated solver can be used for rapid prototyping of analyses and illustrate a wide variety of applications within Static Analysis, Constraint Satisfaction Problems and Model Checking. In all cases...
Kray, Laura J; Howland, Laura; Russell, Alexandra G; Jackman, Lauren M
2017-01-01
Four studies (n = 1199) tested support for the idea that implicit theories about the fixedness versus malleability of gender roles (entity vs. incremental theories) predict differences in the degree of gender system justification, that is, support for the status quo in relations between women and men in society. Relative to an incremental theory, the holding of an entity theory correlated with more system-justifying attitudes and self-perceptions (Study 1) for men and women alike. We also found that strength of identification with one's gender in-group was a stronger predictor of system justification for men than it was for women, suggesting men's defense of the status quo may be motivated by their membership in a high status group in the social hierarchy. In 3 experiments, we then tested whether exposure to a fixed gender role theory would lead men to identify more with masculine characteristics and their male gender group, thus increasing their defense of the gender system as fair and just. We did not expect a fixed gender role theory to trigger these identity-motivated responses in women. Overall, we found that, by increasing the degree of psychological investment in their masculine identity, adopting a fixed gender role theory increased men's rationalization of the gender status quo compared with when gender roles were perceived to be changeable. This suggests that, when men are motivated to align with their masculine identity, they are more likely to endorse the persistence of gender inequality as a way of affirming their status as "real men." (PsycINFO Database Record (c) 2016 APA, all rights reserved).
Simulating water distribution patterns for fixed spray plate sprinkler using the ballistic theory
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Sofiane Ouazaa
2014-07-01
Full Text Available Ballistic simulation of the spray sprinkler for self-propelled irrigation machines requires the incorporation of the effect of the jet impact with the deflecting plate. The kinetic energy losses produced by the jet impact with the spray plate were experimentally characterized for different nozzle sizes and two working pressures for fixed spray plate sprinklers (FSPS. A technique of low speed photography was used to determine drop velocity at the point where the jet is broken into droplets. The water distribution pattern of FSPS for different nozzle sizes, working at two pressures and under different wind conditions were characterized in field experiments. The ballistic model was calibrated to simulate water distribution in different technical and meteorological conditions. Field experiments and the ballistic model were used to obtain the model parameters (D50, n, K1and K2. The results show that kinetic energy losses decrease with nozzle diameter increments; from 80% for the smallest nozzle diameter (2 mm to 45% for nozzle diameters larger than 5.1 mm, and from 80% for the smallest nozzle diameter (2 mm to 34.7% for nozzle diameters larger than 6.8 mm, at 138 kPa and 69 kPa working pressures, respectively. The results from the model compared well with field observations. The calibrated model has reproduced accurately the water distribution pattern in calm (r=0.98 and high windy conditions (r=0.76. A new relationship was found between the corrector parameters (K1’ and K2’ and the wind speed. As a consequence, model simulation will be possible for untested meteorological conditions.
THEORY OF DISPERSED FIXED-DELAY INTERFEROMETRY FOR RADIAL VELOCITY EXOPLANET SEARCHES
International Nuclear Information System (INIS)
Van Eyken, Julian C.; Ge Jian; Mahadevan, Suvrath
2010-01-01
The dispersed fixed-delay interferometer (DFDI) represents a new instrument concept for high-precision radial velocity (RV) surveys for extrasolar planets. A combination of a Michelson interferometer and a medium-resolution spectrograph, it has the potential for performing multi-object surveys, where most previous RV techniques have been limited to observing only one target at a time. Because of the large sample of extrasolar planets needed to better understand planetary formation, evolution, and prevalence, this new technique represents a logical next step in instrumentation for RV extrasolar planet searches, and has been proven with the single-object Exoplanet Tracker (ET) at Kitt Peak National Observatory, and the multi-object W. M. Keck/MARVELS Exoplanet Tracker at Apache Point Observatory. The development of the ET instruments has necessitated fleshing out a detailed understanding of the physical principles of the DFDI technique. Here we summarize the fundamental theoretical material needed to understand the technique and provide an overview of the physics underlying the instrument's working. We also derive some useful analytical formulae that can be used to estimate the level of various sources of error generic to the technique, such as photon shot noise when using a fiducial reference spectrum, contamination by secondary spectra (e.g., crowded sources, spectroscopic binaries, or moonlight contamination), residual interferometer comb, and reference cross-talk error. Following this, we show that the use of a traditional gas absorption fiducial reference with a DFDI can incur significant systematic errors that must be taken into account at the precision levels required to detect extrasolar planets.
Ciaran Driver; Katsushi Imai; Paul Temple; Giovanni Urga
2002-01-01
This paper reports estimation of investment equations for two classes of fixed assets: plant & machinery and building for a large sample of UK manufacturing industries. It exploits the different degree of irreversibility that characterises these assets to test the power of real options theory to explain investment under uncertainty. Additionally, the paper uses a specially constructed industry-specific measure of irreversibility for plant and machinery investment to test for real options effe...
Dong, W.; Machin, G.; Bloembergen, P.; Lowe, D.; Wang, T.
2016-11-01
Extensive studies of platinum-carbon eutectic alloy based high temperature fixed point cells have shown that this alloy has extremely good metrological potential as a temperature reference. However, it’s possible adoption as an accepted reference standard means that its eutectic temperature value will soon be agreed with an uncertainty less than most radiation thermometry scales at that temperature. Thus it will lack credibility if used as a future scale comparison artefact. To avoid this, the fixed-point cell can be deliberately doped with an impurity to change its transition temperature by an amount sufficient to test the accuracy of the scales of the institutes, involved in the comparison. In this study dopants of palladium and iridium were added to platinum-carbon to produce ternary alloy and quaternary alloy fixed-point cells. The stability of these artefacts was demonstrated and the fixed-point cells were used to compare the ITS-90 scales of NIM and NPL. It was found that the fixed point temperatures could be changed by an appreciable amount while retaining the stability and repeatability required for comparison artefacts.
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Douglas Scott C
2007-01-01
Full Text Available We derive new fixed-point algorithms for the blind separation of complex-valued mixtures of independent, noncircularly symmetric, and non-Gaussian source signals. Leveraging recently developed results on the separability of complex-valued signal mixtures, we systematically construct iterative procedures on a kurtosis-based contrast whose evolutionary characteristics are identical to those of the FastICA algorithm of Hyvarinen and Oja in the real-valued mixture case. Thus, our methods inherit the fast convergence properties, computational simplicity, and ease of use of the FastICA algorithm while at the same time extending this class of techniques to complex signal mixtures. For extracting multiple sources, symmetric and asymmetric signal deflation procedures can be employed. Simulations for both noiseless and noisy mixtures indicate that the proposed algorithms have superior finite-sample performance in data-starved scenarios as compared to existing complex ICA methods while performing about as well as the best of these techniques for larger data-record lengths.
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Kutbi Marwan Amin
2016-01-01
Full Text Available The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.
International Nuclear Information System (INIS)
Singh, Vimal
2007-01-01
In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters
Graviton n-point functions for UV-complete theories in Anti-de Sitter space
Brustein, Ram
2012-01-01
We calculate graviton n-point functions in an anti-de Sitter black brane background for effective gravity theories whose linearized equations of motion have at most two time derivatives. We compare the n-point functions in Einstein gravity to those in theories whose leading correction is quadratic in the Riemann tensor. The comparison is made for any number of gravitons and for all physical graviton modes in a kinematic region for which the leading correction can significantly modify the Einstein result. We find that the n-point functions of Einstein gravity depend on at most a single angle, whereas those of the corrected theories may depend on two angles. For the four-point functions, Einstein gravity exhibits linear dependence on the Mandelstam variable s versus a quadratic dependence on s for the corrected theory.
Three- and two-point one-loop integrals in heavy particle effective theories
International Nuclear Information System (INIS)
Bouzas, A.O.
2000-01-01
We give a complete analytical computation of three- and two-point loop integrals occurring in heavy particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta. (orig.)
Yang, Chen; Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue
2017-06-24
With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array-application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.
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Chen Yang
2017-06-01
Full Text Available With the development of satellite load technology and very large scale integrated (VLSI circuit technology, onboard real-time synthetic aperture radar (SAR imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT, which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array−application-specific integrated circuit (FPGA-ASIC hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.
Hahl, Sayuri K.; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
G. J. Jordan; M. J. Ducey; J. H. Gove
2004-01-01
We present the results of a timed field trial comparing the bias characteristics and relative sampling efficiency of line-intersect, fixed-area, and point relascope sampling for downed coarse woody material. Seven stands in a managed northern hardwood forest in New Hampshire were inventoried. Significant differences were found among estimates in some stands, indicating...
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Quynh Anh NguyenThi
2011-01-01
Full Text Available We introduce a new implicit iteration method for finding a solution for a variational inequality involving Lipschitz continuous and strongly monotone mapping over the set of common fixed points for a finite family of nonexpansive mappings on Hilbert spaces.
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
International Nuclear Information System (INIS)
Boyer, T.H.
1975-01-01
The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and distinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory. (U.S.)
Growing Fixed With Age: Lay Theories of Malleability Are Target Age-Specific.
Neel, Rebecca; Lassetter, Bethany
2015-11-01
Beliefs about whether people can change ("lay theories" of malleability) are known to have wide-ranging effects on social motivation, cognition, and judgment. Yet rather than holding an overarching belief that people can or cannot change, perceivers may hold independent beliefs about whether different people are malleable-that is, lay theories may be target-specific. Seven studies demonstrate that lay theories are target-specific with respect to age: Perceivers hold distinct, uncorrelated lay theories of people at different ages, and younger targets are considered to be more malleable than older targets. Both forms of target-specificity are consequential, as target age-specific lay theories predict policy support for learning-based senior services and the rehabilitation of old and young drug users. The implications of target age-specific lay theories for a number of psychological processes, the social psychology of aging, and theoretical frameworks of malleability beliefs are discussed. © 2015 by the Society for Personality and Social Psychology, Inc.
La, Moonwoo; Park, Sang Min; Kim, Dong Sung
2015-01-01
In this study, a multiple sample dispenser for precisely metered fixed volumes was successfully designed, fabricated, and fully characterized on a plastic centrifugal lab-on-a-disk (LOD) for parallel biochemical single-end-point assays. The dispenser, namely, a centrifugal multiplexing fixed-volume dispenser (C-MUFID) was designed with microfluidic structures based on the theoretical modeling about a centrifugal circumferential filling flow. The designed LODs were fabricated with a polystyrene substrate through micromachining and they were thermally bonded with a flat substrate. Furthermore, six parallel metering and dispensing assays were conducted at the same fixed-volume (1.27 μl) with a relative variation of ±0.02 μl. Moreover, the samples were metered and dispensed at different sub-volumes. To visualize the metering and dispensing performances, the C-MUFID was integrated with a serpentine micromixer during parallel centrifugal mixing tests. Parallel biochemical single-end-point assays were successfully conducted on the developed LOD using a standard serum with albumin, glucose, and total protein reagents. The developed LOD could be widely applied to various biochemical single-end-point assays which require different volume ratios of the sample and reagent by controlling the design of the C-MUFID. The proposed LOD is feasible for point-of-care diagnostics because of its mass-producible structures, reliable metering/dispensing performance, and parallel biochemical single-end-point assays, which can identify numerous biochemical.
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Tian Zhou Xu
2010-01-01
Full Text Available Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation f(x+ky+f(x−ky=k2f(x+y+k2f(x−y+2(1−k2f(x+((k4−k2/12[f(2y+f(−2y−4f(y−4f(−y] for a fixed integer k with k≠0,±1 in non-Archimedean normed spaces.
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L. I. Katelnitskaya
2008-01-01
Full Text Available Calcium antagonists (CA therapy of patients with arterial hypertension is focused on the base of current recommendations. Results of some large clinical trials confirm high antihypertensive efficacy of this therapeutic class. Special attention is devoted to implementation of fixed combinations on the basis of CA. Advantages of these combinations in hypertension therapy are discussed.
Magnetic point sources in three dimensional Brans-Dicke gravity theories
Dias, Oscar J. C.; Lemos, Jose' P. S.
2002-01-01
We obtain geodesically complete spacetimes generated by static and rotating magnetic point sources in an Einstein-Maxwell-Dilaton theory of the Brans-Dicke type in three dimensions (3D). The theory is specified by three fields, the dilaton, the graviton and the electromagnetic field, and two parameters, the cosmological constant and the Brans-Dicke parameter, w. When the Brans-Dicke parameter is infinity, our solution reduces to the magnetic counterpart of the BTZ solution, while the w=0 case...
Analysis of the stochastic channel model by Saleh & Valenzuela via the theory of point processes
DEFF Research Database (Denmark)
Jakobsen, Morten Lomholt; Pedersen, Troels; Fleury, Bernard Henri
2012-01-01
In this paper we revisit the classical channel model by Saleh & Valenzuela via the theory of spatial point processes. By reformulating this model as a particular point process and by repeated application of Campbell’s Theorem we provide concise and elegant access to its overall structure and unde......In this paper we revisit the classical channel model by Saleh & Valenzuela via the theory of spatial point processes. By reformulating this model as a particular point process and by repeated application of Campbell’s Theorem we provide concise and elegant access to its overall structure...... to define, analyze, and compare most channel models already suggested in literature and that the powerful tools of this framework have not been fully exploited in this context yet....
Complex source point theory of paraxial and nonparaxial cosine-Gauss and Bessel-Gauss beams.
Sheppard, Colin J R
2013-02-15
It shown how cosine-Gauss and Bessel-Gauss beams can be generated using the complex source point theory. Paraxial beams are treated first. An analytic expression is derived for the nonparaxial cosine-Gaussian beam, based on the complex source point approach, and numerical results are presented to illustrate its behavior. A way to generate nonparaxial Bessel-Gauss beams is also indicated.
Open superstring field theory I: gauge fixing, ghost structure, and propagator
Czech Academy of Sciences Publication Activity Database
Kroyter, M.; Okawa, Y.; Schnabl, Martin; Torii, S.; Zwiebach, B.
2012-01-01
Roč. 2012, č. 3 (2012), 1-34 ISSN 1126-6708 R&D Projects: GA MŠk(CZ) LH11106 Grant - others:EUROHORC and ESF(XE) EYI/07/E010 Institutional research plan: CEZ:AV0Z10100502 Keywords : superstrings and heterotic strings * string field theory Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 5.618, year: 2012 http://link.springer.com/article/10.1007%2FJHEP03%282012%29030
Deng, Bin-Chao; Chen, Tong; Xin, Baogui
2012-01-01
We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the pap...
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Manish Jain
2013-01-01
Full Text Available We establish the existence and uniqueness of coupled common fixed point for symmetric (φ,ψ-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011, Nashine (2012, and Mohiuddine and Alotaibi (2012, thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.
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Jing Zhao
2012-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-ϕ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.
Shimamoto, Akira; Yamashita, Keitaro; Inoue, Hirofumi; Yang, Sung-Mo; Iwata, Masahiro; Ike, Natsuko
2013-04-01
Destructive tests are generally applied to evaluate the fixed strength of spot-welding nuggets of zinc-plated steel (which is a widely used primary structural material for automobiles). These destructive tests, however, are expensive and time-consuming. This paper proposes a nondestructive method for evaluating the fixed strength of the welded joints using surface electrical resistance. A direct current nugget-tester and probes have been developed by the authors for this purpose. The proposed nondestructive method uses the relative decrease in surface electrical resistance, α . The proposed method also considers the effect of the corona bond. The nugget diameter is estimated by two factors: R Quota , which is calculated from variation of resistance, and a constant that represents the area of the corona bond. Since the maximum tensile strength is correlated with the nugget diameter, it can be inferred from the estimated nugget diameter. When appropriate measuring conditions for the surface electrical resistance are chosen, the proposed method can effectively evaluate the fixed strength of the spot-welded joints even if the steel sheet is zinc-plated.
Asymptotic distribution theory for break point estimators in models estimated via 2SLS
Boldea, O.; Hall, A.R.; Han, S.
2012-01-01
In this paper, we present a limiting distribution theory for the break point estimator in a linear regression model with multiple structural breaks obtained by minimizing a Two Stage Least Squares (2SLS) objective function. Our analysis covers both the case in which the reduced form for the
On the factorization of universal poles in a theory of gravitating point particles.
Hooft, G. 't
1988-01-01
A theory is considered in which point-like particles scatter only gravitationally and electromagnetically but no other exchanges are taken into account. The two-particle amplitude at high s, low t, as computed before, has universal poles at s values whose imaginary parts are integer positive numbers
The critical points of the multimatrix model as the theories of 2-d W-gravity
International Nuclear Information System (INIS)
Awada, M.A.; Qiu, Zongan.
1990-03-01
We further explore the connections between the generalized KdV hierarchy, the multimatrix model and W n -gravity. We show that the Lax-pair formulation of the generalized KdV hierarchy is nothing but the Hamiltonian equations of W-gravity. Thus we demonstrate that the multicritical points of the multimatrix model are W-gravity theories. 16 refs
Point Defects in 2D and 3D Nanomaterials: A Density Functional Theory Exploration
Li, W.F.
2017-01-01
In this thesis, a large number of point defects was studied in both 2D and 3D nanomaterials that are of utmost importance to nanoscience by means of first principles density functional theory calculations. First, we focused on the lead chalcogenide family: PbS, PbSe, and PbTe that are frequently
Theory of finite-entanglement scaling at one-dimensional quantum critical points.
Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M; Moore, Joel E
2009-06-26
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.
Hierarchical path planning and control of a small fixed-wing UAV: Theory and experimental validation
Jung, Dongwon
2007-12-01
problem is formulated by setting up geometric linear constraints as well as boundary conditions. Subsequently, we construct B-spline path templates by solving a set of distinct optimization problems. For application in UAV motion planning, the path templates are incorporated to replace parts of the entire path by the smooth B-spline paths. Each path segment is stitched together while preserving continuity to obtain a final smooth reference path to be used for path following control. The path following control for a small fixed-wing UAV to track the prescribed smooth reference path is also addressed. Assuming the UAV is equipped with an autopilot for low level control, we adopt a kinematic error model with respect to the moving Serret-Frenet frame attached to a path for tracking controller design. A kinematic path following control law that commands heading rate is presented. Backstepping is applied to derive the roll angle command by taking into account the approximate closed-loop roll dynamics. A parameter adaptation technique is employed to account for the inaccurate time constant of the closed-loop roll dynamics during actual implementation. Finally, we implement the proposed hierarchical path control of a small UAV on the actual hardware platform, which is based on an 1/5 scale R/C model airframe (Decathlon) and the autopilot hardware and software. Based on the hardware-in-the-loop (HIL) simulation environment, the proposed hierarchical path control algorithm has been validated through on-line, real-time implementation on a small micro-controller. By a seamless integration of the control algorithms for path planning, path smoothing, and path following, it has been demonstrated that the UAV equipped with a small autopilot having limited computational resources manages to accomplish the path control objective to reach the goal while avoiding obstacles with minimal human intervention.
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
Dixon, Lance J.; Henn, Johannes M.
2012-01-01
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two function...
Directory of Open Access Journals (Sweden)
Saud M. Alsulami
2014-01-01
Full Text Available We prove that every map satisfying the g-weakly C-contractive inequality in partial metric space has a unique coincidence point. Our results generalize several well-known existing results in the literature.
Fujita, Masahiko
2013-06-01
A new supervised learning theory is proposed for a hierarchical neural network with a single hidden layer of threshold units, which can approximate any continuous transformation, and applied to a cerebellar function to suppress the end-point variability of saccades. In motor systems, feedback control can reduce noise effects if the noise is added in a pathway from a motor center to a peripheral effector; however, it cannot reduce noise effects if the noise is generated in the motor center itself: a new control scheme is necessary for such noise. The cerebellar cortex is well known as a supervised learning system, and a novel theory of cerebellar cortical function developed in this study can explain the capability of the cerebellum to feedforwardly reduce noise effects, such as end-point variability of saccades. This theory assumes that a Golgi-granule cell system can encode the strength of a mossy fiber input as the state of neuronal activity of parallel fibers. By combining these parallel fiber signals with appropriate connection weights to produce a Purkinje cell output, an arbitrary continuous input-output relationship can be obtained. By incorporating such flexible computation and learning ability in a process of saccadic gain adaptation, a new control scheme in which the cerebellar cortex feedforwardly suppresses the end-point variability when it detects a variation in saccadic commands can be devised. Computer simulation confirmed the efficiency of such learning and showed a reduction in the variability of saccadic end points, similar to results obtained from experimental data.
Five-loop four-point amplitude of N=4 super-Yang-Mills theory.
Bern, Z; Carrasco, J J M; Johansson, H; Roiban, R
2012-12-14
Using the method of maximal cuts, we construct the complete D-dimensional integrand of the five-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions. In the critical dimension where this amplitude becomes ultraviolet divergent, we present a compact explicit expression for the nonvanishing ultraviolet divergence in terms of three vacuum integrals. This construction provides a crucial step towards obtaining the corresponding amplitude of N=8 supergravity required to resolve the general ultraviolet behavior of supergravity theories.
Lee, Jongtae; Jeon, Sangil; Hong, Taegon; Han, Seunghoon; Yim, Dong-Seok
2015-11-01
This study aimed to determine the effect of PET scan timings on the reliability of occupancy parameter estimates and to identify the scan timing design that gives the most reliable occupancy parameter estimates. We compared the performance of designs with various sets of sampling time points using the stochastic simulation and estimation method in Perl-speaks-NONMEM. Biases, relative standard errors, relative estimation errors, and root mean square errors were used to compare the performance of designs. Unlike the results of a previous report, we found that rather complicated designs where each subject or group of subjects are allocated to different scan timings were not superior to the simple, conventional fixed-time designs regardless of whether effect compartment or receptor binding models were used. We conclude that the conventional fixed-time designs that have been used so far may give robust PD parameter estimates for occupancy data obtained from human PET studies of CNS drugs.
Disk one-point function for a family of non-rational conformal theories
Babaro, Juan Pablo; Giribet, Gaston
2010-09-01
We consider an infinite family of non-rational conformal field theories in the presence of a conformal boundary. These theories, which have been recently proposed in [1], are parameterized by two real numbers ( b, m) in such a way that the corresponding central charges c ( b, m) are given by c ( b, m) = 3 + 6( b + b -1(1 - m))2. For the disk geometry, we explicitly compute the expectation value of a bulk vertex operator in the case m in mathbb{Z} , such that the result reduces to the Liouville one-point function when m = 0. We perform the calculation of the disk one-point function in two different ways, obtaining results in perfect agreement, and giving the details of both the path integral and the free field derivations.
Four-point correlation function of stress-energy tensors in N=4 superconformal theories
Korchemsky, G P
2015-01-01
We derive the explicit expression for the four-point correlation function of stress-energy tensors in four-dimensional N=4 superconformal theory. We show that it has a remarkably simple and suggestive form allowing us to predict a large class of four-point correlation functions involving the stress-energy tensor and other conserved currents. We then apply the obtained results on the correlation functions to computing the energy-energy correlations, which measure the flow of energy in the final states created from the vacuum by a source. We demonstrate that they are given by a universal function independent of the choice of the source. Our analysis relies only on N=4 superconformal symmetry and does not use the dynamics of the theory.
Mobile point sensors and actuators in the controllability theory of partial differential equations
Khapalov, Alexander Y
2017-01-01
This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.
Point-like bounding chains in open Gromov-Witten theory
Solomon, Jake P.; Tukachinsky, Sara B.
2016-01-01
We use $A_\\infty$ algebras to define open Gromov-Witten invariants with both boundary and interior constraints, associated to a Lagrangian submanifold $L\\subset X$ of arbitrary odd dimension. The boundary constraints are bounding chains, which are shown to behave like points. The interior constraints are arbitrary even degree classes in the cohomology of $X$ relative to $L.$ We show the invariants satisfy analogs of the axioms of closed Gromov-Witten theory. Our definition of invariants depen...
Directory of Open Access Journals (Sweden)
SATISH SHUKLA
2016-12-01
Full Text Available In this paper, the notion of G-(F; -contractions in the context of partial rectangular metric spaces endowed with a graph is introduced. Some xed point theorems for G-(F; -contractions are also proved. The results of this paper generalize, extend, and unify some known results. Some examples are provided to illustrate the results proved herein.
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Kiêu, K
1994-01-01
Unbiased stereological estimators of d-dimensional volume in R(n) are derived, based on information from an isotropic random r-slice through a specified point. The content of the slice can be subsampled by means of a spatial grid. The estimators depend only on spatial distances. As a fundamental...
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u , [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
Directory of Open Access Journals (Sweden)
Zhaoli Ma
2012-01-01
Full Text Available We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.
Directory of Open Access Journals (Sweden)
V. S. Serov
2010-01-01
Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.
Directory of Open Access Journals (Sweden)
Liu Min
2010-01-01
Full Text Available In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
Jones, Caroline H D; Glogowska, Margaret; Locock, Louise; Lasserson, Daniel S
2016-10-19
Many point of care diagnostic technologies are available which produce results within minutes, and offer the opportunity to deliver acute care out of hospital settings. Increasing access to diagnostics at the point of care could increase the volume and scope of acute ambulatory care. Yet these technologies are not routinely used in many settings. We aimed to explore how point of care testing is used in a setting where it has become 'normalized' (embedded in everyday practice), in order to inform future adoption and implementation in other settings. We used normalization process theory to guide our case study approach. We used a single case study design, choosing a community based ambulatory care unit where point of care testing is used routinely. A focused ethnographic approach was taken, including non-participant observation of all activities related to point of care testing, and semi-structured interviews, with all clinical staff involved in point of care testing at the unit. Data were analysed thematically, guided by normalization process theory. Fourteen days of observation and six interviews were completed. Staff had a shared understanding of the purpose, value and benefits of point of care testing, believing it to be integral to the running of the unit. They organised themselves as a team to ensure that point of care testing worked effectively; and one key individual led a change in practice to ensure more consistency and trust in procedures. Staff assessed point of care testing as worthwhile for the unit, their patients, and themselves in terms of job satisfaction and knowledge. Potential barriers to adoption of point of care testing were evident (including lack of trust in the accuracy of some results compared to laboratory testing; and lack of ease of use of some aspects of the equipment); but these did not prevent point of care testing from becoming embedded, because the importance and value attributed to it were so strong. This case study offers insights
Directory of Open Access Journals (Sweden)
Yasser A. Abdel-Aziz
2009-12-01
Full Text Available This paper reports the realization and stability of the freezing point of high purity copper (99.9999% Cu (1084.62 °C in a sealed cell by noble metal thermocouples of Pt-l0%Rh/Pt (type S and Pt-30%Rh/Pt-6%Rh (type B, using a three zone heating furnace. The graphite crucible in the sealed cell is made of ultra high purity carbon to contain 99.9999 % purity Cu metal. The individual difference at Cu freezing point, measured by each thermocouple at the National Institute for Standards (NIS with respect to the value as stated in the ITS-90, is lying within the overall uncertainty of measurements. The expanded uncertainty of measurements was evaluated and expressed as 95% confidence level. The Cu freezing point as measured with type-S thermocouple was found to be 1084.62 °C ± 0.666 °C and that with type B thermocouple was found to be 1084.62 °C ± 0.532 °C.
The resolution of point sources of light as analyzed by quantum detection theory
Helstrom, C. W.
1972-01-01
The resolvability of point sources of incoherent light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.
Resolution of point sources of light as analyzed by quantum detection theory.
Helstrom, C. W.
1973-01-01
The resolvability of point sources of incoherent thermal light is analyzed by quantum detection theory in terms of two hypothesis-testing problems. In the first, the observer must decide whether there are two sources of equal radiant power at given locations, or whether there is only one source of twice the power located midway between them. In the second problem, either one, but not both, of two point sources is radiating, and the observer must decide which it is. The decisions are based on optimum processing of the electromagnetic field at the aperture of an optical instrument. In both problems the density operators of the field under the two hypotheses do not commute. The error probabilities, determined as functions of the separation of the points and the mean number of received photons, characterize the ultimate resolvability of the sources.
International Nuclear Information System (INIS)
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of the modulus of angular velocity ω. The equivalence between this plane construction and the well-known Poinsot's three-dimensional graphical procedure is also shown. From this equivalence, analogies have been found between the general plane wave equation (relation of dispersion) in anisotropic media and basic equations of torque-free motion of a rigid body about a fixed point. These analogies allow reciprocal transfer of results between optics and mechanics and, as an example, reinterpretation of the internal conical refraction phenomenon in biaxial media is carried out. This paper is intended as an interdisciplinary application of analogies for students and teachers in the context of intermediate physics courses at university level
Matter fields near quantum critical point in (2+1)-dimensional U(1) gauge theory
International Nuclear Information System (INIS)
Liu Guozhu; Li Wei; Cheng Geng
2010-01-01
We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, r=0, defines a quantum critical point between the Higgs phase and the Coulomb phase. We consider only the critical point r=0 and the Coulomb phase with r>0. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value N f c , which depends quantitatively on the flavor N b and the scalar boson mass r. When N f f c , the matter fields carrying internal gauge charge are all confined if r≠0 but are deconfined at the quantum critical point r=0. The system has distinct low-energy elementary excitations at the critical point r=0 and in the Coulomb phase with r≠0. We calculate the specific heat and susceptibility of the system at r=0 and r≠0, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.
Merli, Marcello; Pavese, Alessandro
2018-03-01
The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non-degenerate critical points, i.e. such that ∇ρ(x c ) = 0 and λ 1 , λ 2 , λ 3 ≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at x c ], towards degenerate critical points, i.e. ∇ρ(x c ) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of x c and allows one to rationalize the occurrence of instability in terms of electron-density topology and Gibbs energy. The phase/state transitions that TiO 2 (rutile structure), MgO (periclase structure) and Al 2 O 3 (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3-5% is observed between the theoretical model and experimental pressure/temperature of transformation.
A density functional theory based approach for predicting melting points of ionic liquids.
Chen, Lihua; Bryantsev, Vyacheslav S
2017-02-01
Accurate prediction of melting points of ILs is important both from the fundamental point of view and from the practical perspective for screening ILs with low melting points and broadening their utilization in a wider temperature range. In this work, we present an ab initio approach to calculate melting points of ILs with known crystal structures and illustrate its application for a series of 11 ILs containing imidazolium/pyrrolidinium cations and halide/polyatomic fluoro-containing anions. The melting point is determined as a temperature at which the Gibbs free energy of fusion is zero. The Gibbs free energy of fusion can be expressed through the use of the Born-Fajans-Haber cycle via the lattice free energy of forming a solid IL from gaseous phase ions and the sum of the solvation free energies of ions comprising IL. Dispersion-corrected density functional theory (DFT) involving (semi)local (PBE-D3) and hybrid exchange-correlation (HSE06-D3) functionals is applied to estimate the lattice enthalpy, entropy, and free energy. The ions solvation free energies are calculated with the SMD-generic-IL solvation model at the M06-2X/6-31+G(d) level of theory under standard conditions. The melting points of ILs computed with the HSE06-D3 functional are in good agreement with the experimental data, with a mean absolute error of 30.5 K and a mean relative error of 8.5%. The model is capable of accurately reproducing the trends in melting points upon variation of alkyl substituents in organic cations and replacement one anion by another. The results verify that the lattice energies of ILs containing polyatomic fluoro-containing anions can be approximated reasonably well using the volume-based thermodynamic approach. However, there is no correlation of the computed lattice energies with molecular volume for ILs containing halide anions. Moreover, entropies of solid ILs follow two different linear relationships with molecular volume for halides and polyatomic fluoro
Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
International Nuclear Information System (INIS)
Martin, C. P.; Tamarit, C.
2009-01-01
We show at one loop and first order in the noncommutativity parameters that in any noncommutative GUT inspired theory the total contribution to the fermionic four point functions coming only from the interaction between fermions and gauge bosons, though not UV finite by power counting, is UV finite at the end of the day. We also show that this is at odds with the general case for noncommutative gauge theories - chiral or otherwise - defined by means of Seiberg-Witten maps that are the same - barring the gauge group representation - for left-handed spinors as for right-handed spinors. We believe that the results presented in this paper tilt the scales to the side of noncommutative GUTS and noncommutative GUT inspired versions of the standard model.
Analytic Result for the Two-loop Six-point NMHV Amplitude in N = 4 Super Yang-Mills Theory
Energy Technology Data Exchange (ETDEWEB)
Dixon, Lance J.; /SLAC; Drummond, James M.; /CERN /Annecy, LAPTH; Henn, Johannes M.; /Humboldt U., Berlin /Princeton, Inst. Advanced Study
2012-02-15
We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behavior, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral {Omega}{sup (2)}, also plays a key role in a new representation of the remainder function R{sub 6}{sup (2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) x (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) x (parity even) part. The second non-polylogarithmic function, the loop integral {tilde {Omega}}{sup (2)}, characterizes this sector. Both {Omega}{sup (2)} and {tilde {Omega}}{sup (2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.
Algebraic and analyticity properties of the n-point function in quantum field theory
International Nuclear Information System (INIS)
Bros, Jacques
1970-01-01
The general theory of quantized fields (axiomatic approach) is investigated. A systematic study of the algebraic properties of all the Green functions of a local field, which generalize the ordinary retarded and advanced functions, is presented. The notion emerges of a primitive analyticity domain of the n-point function, and of the existence of auxiliary analytic functions into which the various Green functions can be decomposed. Certain processes of analytic completion are described, and then applied to enlarging the primitive domain, particularly for the case n = 4; among the results the crossing property for all scattering amplitudes which involve two incoming and two outgoing particles is proved. (author) [fr
Fifty years of Yang-Mills Theories: a phenomenological point of view
De Rújula, Alvaro
2005-01-01
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds for nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
FIFTY YEARS OF YANG-MILLS THEORIES: A Phenomenological Point of View
de Rújula, Alvaro
On the occasion of the celebration of the first half-century of Yang-Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds form nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
Quantum integrability for three-point functions of maximally supersymmetric Yang-Mills theory.
Gromov, Nikolay; Vieira, Pedro
2013-11-22
Quantum corrections to three-point functions of scalar single trace operators in planar N=4 Super-Yang-Mills theory are studied using integrability. At one loop, we find new algebraic structures that not only govern all two-loop corrections to the mixing of the operators but also automatically incorporate all one-loop diagrams correcting the tree-level Wick contractions. Speculations about possible extensions of our construction to all loop orders are given. We also match our results with the strong coupling predictions in the classical (Frolov-Tseytlin) limit.
Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations
Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.; Woodard, Mark A.
2013-01-01
Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.
[Discussion on the key points of building modern theory of acupuncture treatment].
Yang, Guang
2013-10-01
Acupuncture treatment is different from treatment of materia medica. However, syndrome differentiation system of internal medicine is adopted all the time for the present acupuncture textbooks. It is held that the characteristics of acupuncture can not be fully reflexed, and advantages of acupuncture can not be brought into full play. Therefore, it's urgent to build up a modem theory on acupuncture treatment which is fit for the clinical practice of acupuncture and can give a better play for the treatment of acupuncture. A clear target is one of the characteristics of acupuncture treatment. And it is based on the understanding of the location of disease, therefore, disease differentiation is held as the basis of acupuncture treatment. The aim of meridian differentiation is to select distal effective points on the base of diseases differentiation, which is also taken as the characteristics of acupuncture treatment. Syndrome differentiation is a process of understanding the general pathological states of the human body, it is an important process to enhance the therapeutic effect of acupuncture. Thus, the key point for establishing the modern acupuncture theory is clarifying the values of disease differentiation, meridian differentiation and syndrome differentiation.
A Fixed Point, A Point of Interruption
Directory of Open Access Journals (Sweden)
Mark Hewson
2006-10-01
Full Text Available A review of Alain Badiou, emInfinite Thought: Truth and the Return to Philosophy/em, ed. and trans. Justin Clemens and Oliver Feltham, New Edition, London, Continuum, 2005. ISBN: 0826479294.br /
On the 'area to point' flow problem based on constructal theory
International Nuclear Information System (INIS)
Wu Wenjun; Chen Lingen; Sun Fengrui
2007-01-01
The study of the 'area to point' flow problem, which generates heat uniformly, is conducted based on constructal theory in this paper. Bejan [Bejan A. Constructal-theory network of conducting path for cooling a heat generating volume. Int J Heat Mass Transfer 1997;40(4):799-816] analyzed the problem using an effective thermal conductivity, which simplified the optimization greatly, and deduced an approximate result. Ghodoossi and Egrican [Ghodoossi L, Egrican N. Exact solution for cooling of electronics using constructal theory. J Appl Phys 2003;93(8):4922-9] analyzed the problem without the simplification of an effective conductivity, obtained an exact result, found a great deviation from Bejan's approximate result and stated that the simplification is the cause of the deviation in the approximate solution. It is proved in this paper that the cause of the deviation in the approximate solution is not the reasonable simplification of an effective conductivity but the mistakenly derived effective thermal conductivity. The approximate solution is revised, and the corresponding result, which is consistent with the exact solution, is obtained
Brown, Jonathan M.; Petersen, Jeremy D.
2014-01-01
NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.
Complete conformal field theory solution of a chiral six-point correlation function
Simmons, Jacob J. H.; Kleban, Peter
2011-08-01
Using conformal field theory, we perform a complete analysis of the chiral six-point correlation function C(z)=\\langle \\phi _{1,2}\\phi _{1,2} \\Phi _{1/2,0}(z, \\bar{z}) \\phi _{1,2}\\phi _{1,2} \\rangle, with the four phi1, 2 operators at the corners of an arbitrary rectangle, and the point z = x + iy in the interior. We calculate this for arbitrary central charge (equivalently, SLE parameter κ > 0). C is of physical interest because for percolation (κ = 6) and many other two-dimensional critical points, it specifies the density at z of critical clusters conditioned to touch either or both vertical ends of the rectangle, with these ends 'wired', i.e. constrained to be in a single cluster, and the horizontal ends free. The correlation function may be written as the product of an algebraic prefactor f and a conformal block G, where f = f(x, y, m), with m a cross-ratio specified by the corners (m determines the aspect ratio of the rectangle). By appropriate choice of f and using coordinates that respect the symmetry of the problem, the conformal block G is found to be independent of either y or x, and given by an Appell function.
Chang Tong-Huei; Chen Chi-Ming; Huang Yueh-Hung
2009-01-01
We use a concept of abstract convexity to define the almost - property, al- - family, and almost -spaces. We get some new approximate fixed point theorems and fixed point theorems in almost -spaces. Our results extend some results of other authors.
Infrared Fixed Point Physics in ${\\rm SO}(N_c)$ and ${\\rm Sp}(N_c)$ Gauge Theories
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2017-01-01
, and rank-2 symmetric and antisymmetric tensor fermion representations are considered. We present scheme-independent calculations of the anomalous dimensions of (gauge-invariant) fermion bilinear operators $\\gamma_{\\bar\\psi\\psi,IR}$ to $O(\\Delta_f^4)$ and of the derivative of the beta function at $\\alpha...
End-Point Contact Force Control with Quantitative Feedback Theory for Mobile Robots
Directory of Open Access Journals (Sweden)
Shuhuan Wen
2012-12-01
Full Text Available Robot force control is an important issue for intelligent mobile robotics. The end-point stiffness of a robot is a key and open problem in the research community. The control strategies are mostly dependent on both the specifications of the task and the environment of the robot. Due to the limited stiffness of the end-effector, we may adopt inherent torque to feedback the oscillations of the controlled force. This paper proposes an effective control strategy which contains a controller using quantitative feedback theory. The nested loop controllers take into account the physical limitation of the system's inner variables and harmful interference. The biggest advantage of the method is its simplicity in both the design process and the implementation of the control algorithm in engineering practice. Taking the one-link manipulator as an example, numerical experiments are carried out to verify the proposed control method. The results show the satisfactory performance.
Directory of Open Access Journals (Sweden)
Houzeng Han
2016-07-01
Full Text Available Precise Point Positioning (PPP makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC algorithm is implemented by integrating PPP with inertial navigation system (INS using an Extended Kalman filter (EKF. The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies
Feng, Shengchuang; Ye, Xiang; Mao, Lihua; Yue, Xiaodong
2014-04-03
The mind-reading hypothesis of humor and the inner eye theory of laughter both claim that readers' mentalizing about characters in jokes is essential for perceiving humor. On the basis of this notion, we hypothesized that point-to-other verbal jokes (in which one character said funny things about the other character) induced more theory of mind (ToM) processing than point-to-self verbal jokes (in which one character said funny things about him/herself to the other character). Our hypothesis was tested by comparing percent signal changes of these two conditions in six core components of the ToM neural network. A whole-brain analysis was also conducted. Results from both the region of interest (ROI) analysis and the whole-brain analysis show that theory of mind network is more activated when subjects read point-to-other jokes than when they read point-to-self jokes. Moreover, the whole-brain results provide support for the viewpoint that the right hemisphere, especially the right frontal lobe, is important in ToM and humor processing. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Siegel, J.; Siegel, Edward Carl-Ludwig
2011-03-01
Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!
Darrason, Marie
2013-08-01
In the contemporary biomedical literature, every disease is considered genetic. This extension of the concept of genetic disease is usually interpreted either in a trivial or genocentrist sense, but it is never taken seriously as the expression of a genetic theory of disease. However, a group of French researchers defend the idea of a genetic theory of infectious diseases. By identifying four common genetic mechanisms (Mendelian predisposition to multiple infections, Mendelian predisposition to one infection, and major gene and polygenic predispositions), they attempt to unify infectious diseases from a genetic point of view. In this article, I analyze this explicit example of a genetic theory, which relies on mechanisms and is applied only to a specific category of diseases, what we call "a regional genetic theory." I have three aims: to prove that a genetic theory of disease can be devoid of genocentrism, to consider the possibility of a genetic theory applied to every disease, and to introduce two hypotheses about the form that such a genetic theory could take by distinguishing between a genetic theory of diseases and a genetic theory of Disease. Finally, I suggest that network medicine could be an interesting framework for a genetic theory of Disease.
Turning points in nonlinear business cycle theories, financial crisis and the 2007-2008 downturn.
Dore, Mohammed H I; Singh, Ragiv G
2009-10-01
This paper reviews three nonlinear dynamical business cycle theories of which only one (The Goodwin model) reflects the stylized facts of observed business cycles and has a plausible turning point mechanism. The paper then examines the US (and now global) financial crisis of 2008 and the accompanying downturn in the US. The paper argues that a skewed income distribution could not sustain effective demand and that over the 2001-2006 expansion demand was maintained through massive amounts of credit, with more than 50 percent of sales in the US being maintained through credit. A vector autoregression model confirms the crucial role played by credit. However legislative changes that dismantled the restrictions placed on the financial sector after the crash of 1929 and the consequent structural changes in the financial sector after 1980 enabled the growth of new debt instruments and credit. But overexpansion of credit when profits and house prices were declining in 2005/06 led to a nonlinear shift due to a new realization of the poor quality of some of this debt, namely mortgage backed securities. Bankruptcies, followed by retrenchment at the banks, then led to the bursting of the credit bubble, with the possibility of a severe recession.
Directory of Open Access Journals (Sweden)
Kazimierz Włodarczyk
2015-01-01
Full Text Available Let C={Cα}α∈A∈[1;∞A, A-index set. A quasi-triangular space (X,PC;A is a set X with family PC;A={pα:X2→[0,∞, α∈A} satisfying ∀α∈A ∀u,v,w∈X {pα(u,w≤Cα[pα(u,v+pα(v,w]}. For any PC;A, a left (right family JC;A generated by PC;A is defined to be JC;A={Jα:X2→[0,∞, α∈A}, where ∀α∈A ∀u,v,w∈X {Jα(u,w≤Cα[Jα(u,v+Jα(v,w]} and furthermore the property ∀α∈A {limm→∞pα(wm,um=0} (∀α∈A {limm→∞pα(um,wm=0} holds whenever two sequences (um:m∈N and (wm:m∈N in X satisfy ∀α∈A {limm→∞supn>mJα(um,un=0 and limm→∞Jα(wm,um=0} (∀α∈A {limm→∞supn>mJα(un,um=0 and limm→∞Jα(um,wm=0}. In (X,PC;A, using the left (right families JC;A generated by PC;A (PC;A is a special case of JC;A, we construct three types of Pompeiu-Hausdorff left (right quasi-distances on 2X; for each type we construct of left (right set-valued quasi-contraction T:X→2X, and we prove the convergence, existence, and periodic point theorem for such quasi-contractions. We also construct two types of left (right single-valued quasi-contractions T:X→X and we prove the convergence, existence, approximation, uniqueness, periodic point, and fixed point theorem for such quasi-contractions. (X,PC;A generalize ultra quasi-triangular and partiall quasi-triangular spaces (in particular, generalize metric, ultra metric, quasi-metric, ultra quasi-metric, b-metric, partial metric, partial b-metric, pseudometric, quasi-pseudometric, ultra quasi-pseudometric, partial quasi-pseudometric, topological, uniform, quasi-uniform, gauge, ultra gauge, partial gauge, quasi-gauge, ultra quasi-gauge, and partial quasi-gauge spaces.
International Nuclear Information System (INIS)
Bakasov, A.A.; Govorkov, B.B. Jr.
1990-08-01
The critical case in stability theory is the case when it is impossible to study the stability of solutions over the linear part of ordinary differential equations. This situation is usual at the bifurcation points. There exists a powerful and constructive approach to investigate the stability - the theory of critical cases created by Lyapunov. The famous Lorenz model is used in this article as an illustration of the power of the method (new results). (author). 27 refs
Nagai, Satoshi; Hida, Kohsuke; Urushizaki, Shingo; Onitsuka, Goh; Yasuike, Motoshige; Nakamura, Yoji; Fujiwara, Atushi; Tajimi, Seisuke; Kimoto, Katsunori; Kobayashi, Takanori; Gojobori, Takashi; Ototake, Mitsuru
2016-02-01
In this study, we investigated the influence of diurnal sampling bias on the community structure of plankton by comparing the biodiversity among seawater samples (n=9) obtained every 3h for 24h by using massively parallel sequencing (MPS)-based plankton monitoring at a fixed point conducted at Himedo seaport in Yatsushiro Sea, Japan. The number of raw operational taxonomy units (OTUs) and OTUs after re-sampling was 507-658 (558 ± 104, mean ± standard deviation) and 448-544 (467 ± 81), respectively, indicating high plankton biodiversity at the sampling location. The relative abundance of the top 20 OTUs in the samples from Himedo seaport was 48.8-67.7% (58.0 ± 5.8%), and the highest-ranked OTU was Pseudo-nitzschia species (Bacillariophyta) with a relative abundance of 17.3-39.2%, followed by Oithona sp. 1 and Oithona sp. 2 (Arthropoda). During seawater sampling, the semidiurnal tidal current having an amplitude of 0.3ms(-1) was dominant, and the westward residual current driven by the northeasterly wind was continuously observed during the 24-h monitoring. Therefore, the relative abundance of plankton species apparently fluctuated among the samples, but no significant difference was noted according to G-test (p>0.05). Significant differences were observed between the samples obtained from a different locality (Kusuura in Yatsushiro Sea) and at different dates, suggesting that the influence of diurnal sampling bias on plankton diversity, determined using the MPS-based survey, was not significant and acceptable. Copyright © 2015 Elsevier B.V. All rights reserved.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, Claudio, E-mail: claudio.dappiaggi@unipv.it; Nosari, Gabriele [Università degli Studi di Pavia, Dipartimento di Fisica (Italy); Pinamonti, Nicola [Università di Genova, Dipartimento di Matematica (Italy)
2016-06-15
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
Equivalences from tilting theory and commutative algebra from the adjoint functor point of view
DEFF Research Database (Denmark)
Celikbas, Olgur; Holm, Henrik
2017-01-01
We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen Macaulay modules in the sense of Hellus, Schenzel, and Z argar....
Cornelissen, Jeremy C; Obeng, Samuel; Rice, Kenner C; Zhang, Yan; Negus, S Stevens; Banks, Matthew L
2018-04-01
Receptor theory predicts that fixed-proportion mixtures of a competitive, reversible agonist (e.g., fentanyl) and antagonist (e.g., naltrexone) at a common receptor [e.g., mu-opioid receptors (MORs)] will result in antagonist proportion-dependent decreases in apparent efficacy of the agonist/antagonist mixtures and downward shifts in mixture dose-effect functions. The present study tested this hypothesis by evaluating behavioral effects of fixed-proportion fentanyl/naltrexone mixtures in a warm-water tail-withdrawal procedure in rhesus monkeys ( n = 4). Fentanyl (0.001-0.056 mg/kg) alone, naltrexone (0.032-1.0 mg/kg, i.m.) alone, and fixed-proportion mixtures of fentanyl/naltrexone (1:0.025, 1:0.074, and 1:0.22) were administered in a cumulative-dosing procedure, and the proportions were based on published fentanyl and naltrexone K d values at MOR in monkey brain. Fentanyl alone produced dose-dependent antinociception at both 50 and 54°C thermal intensities. Up to the largest dose tested, naltrexone alone did not alter nociception. Consistent with receptor theory predictions, naltrexone produced a proportion-dependent decrease in the effectiveness of fentanyl/naltrexone mixtures to produce antinociception. The maximum effects of fentanyl, naltrexone, and each mixture were also used to generate an efficacy-effect scale for antinociception at each temperature, and this scale was evaluated for its utility in quantifying 1) efficacy requirements for antinociception at 50 and 54°C and 2) relative efficacy of six MOR agonists that vary in their efficacies to produce agonist-stimuated GTP γ S binding in vitro (from lowest to highest efficacy: 17-cyclopropylmethyl-3,14 β -dihyroxy-4,5 α -epoxy-6 α -[(3'-isoquinolyl)acetamindo]morphine, nalbuphine, buprenorphine, oxycodone, morphine, and methadone). These results suggest that fixed-proportion agonist/antagonist mixtures may offer a useful strategy to manipulate apparent drug efficacy for basic research or therapeutic
Chapman, Craig T; Cheng, Xiaolu; Cina, Jeffrey A
2011-04-28
A recently framed quantum/semiclassical treatment for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium (Chapman, C. T.; Cina, J. A. J. Chem. Phys.2007,127, 114502) is further analyzed and subjected to initial tests of its numerical implementation. In the illustrative context of a 1D system interacting with a 1D medium, we rederive the fixed vibrational basis/gaussian bath (FVB/GB) equations of motion for the parameters defining the gaussian bath wave packet accompanying each of the energy eigenkets of the quantum mechanical system. The conditions of validity for the gaussian-bath approximation are shown to coincide with those supporting approximate population conservation. We perform initial numerical tests of the FVB/GB scheme and illustrate the semiclassical description it provides of coherent motion in the medium by comparing its predictions with the exact results for a high-frequency system harmonic oscillator bilinearly coupled to a lower-frequency bath oscillator. Linear vibronic absorption spectra or, equivalently, ultrafast wave packet interferometry signals are shown to be readily and accurately calculable within the FVB/GB framework.
Jones, Caroline H. D.; Glogowska, Margaret; Locock, Louise; Lasserson, Daniel S.
2016-01-01
Background Many point of care diagnostic technologies are available which produce results within minutes, and offer the opportunity to deliver acute care out of hospital settings. Increasing access to diagnostics at the point of care could increase the volume and scope of acute ambulatory care. Yet these technologies are not routinely used in many settings. We aimed to explore how point of care testing is used in a setting where it has become ?normalized? (embedded in everyday practice), in o...
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ewerz, Carlo [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany). ExtreMe Matter Institute EMMI; Bielefeld Univ. (Germany). Fakultaet fuer Physik; European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy)
2009-12-15
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N{sub c}. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria
2009-12-01
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N c . We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Theory and computerized simulation of interaction of point defects with grain boundaries
International Nuclear Information System (INIS)
Bojko, V.S.
1987-01-01
The issued results on mathematical simulation at the atomic level of formation and migration of point defects arising under radiation (of intrinsic point defects, helium atoms) in the region of grain boundary are analyzed. Simulation data on impurity atom interaction with grain boundaries are also considered
Singularity structure of the two-point function in quantum field theory in curved spacetime, II
International Nuclear Information System (INIS)
Fulling, S.A.; Narcowich, F.J.; Wald, R.M.
1981-01-01
We prove that, for a massive, scalar, quantum field in a wide class of static spacetimes, the two-point function has singularity structure of the Hadamard form. In particular, this implies that the point-splitting renormalization prescription is well defined in these spacetimes. As a corollary of this result and a previous result of Fulling, Sweeny, and Wald, we show that in an arbitrary globally hyperbolic spacetime there always exists a large class of states for which the singular part of the two-point function has the Hadamard form. In addition, we prove that, for a closed universe which is both initially and finally static, the S-matrix exists
Elnoby, Rasha M.; Mourad, M. Hussein; Elnaby, Salah L. Hassab; Abou Kana, Maram T. H.
2018-05-01
Solar based cells coated by nanoparticles (NPs) acknowledge potential utilizing as a part of photovoltaic innovation. The acquired silicon solar cells (Si-SCs) coated with different sizes of silver nanoparticles (Ag NPs) as well as uncoated were fabricated in our lab. The sizes and optical properties of prepared NPs were characterized by spectroscopic techniques and Mie theory respectively. The reflectivity of Si-SCs showed reduction of this property as the size of NPs increased. Electrical properties as open circuit current, fill factor and output power density were assessed and discussed depending on point of view of Mie theory for the optical properties of NPs. Also, photostabilities of SCs were assessed using diode laser of wavelength 450 nm and power 300 mW. Coated SCs with the largest Ag NPs size showed the highest Photostability due to its highest scattering efficiency according to Mie theory concept.
On the two-loop divergences of the 2-point hypermultiplet supergraphs for 6D, N = (1 , 1) SYM theory
Buchbinder, I. L.; Ivanov, E. A.; Merzlikin, B. S.; Stepanyantz, K. V.
2018-03-01
We consider 6D, N = (1 , 1) supersymmetric Yang-Mills theory formulated in N = (1 , 0) harmonic superspace and analyze the structure of the two-loop divergences in the hypermultiplet sector. Using the N = (1 , 0) superfield background field method we study the two-point supergraphs with the hypermultiplet legs and prove that their total contribution to the divergent part of effective action vanishes off shell.
Vosmaer, J.
2010-01-01
In this dissertation we discuss three subjects: canonical extensions of lattice-based algebras, Stone duality for distributive lattices with operators, and a generalization of the point-free Vietoris powerlocale construction.
Some exact results for the two-point function of an integrable quantum field theory
International Nuclear Information System (INIS)
Creamer, D.B.; Thacker, H.B.; Wilkinson, D.
1981-02-01
The two point correlation function for the quantum nonlinear Schroedinger (delta-function gas) model is studied. An infinite series representation for this function is derived using the quantum inverse scattering formalism. For the case of zero temperature, the infinite coupling (c → infinity) result of Jimbo, Miwa, Mori and Sato is extended to give an exact expression for the order 1/c correction to the two point function in terms of a Painleve transcendent of the fifth kind
Singularity theory and N = 2 superconformal field theories
International Nuclear Information System (INIS)
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs
On Best Proximity Points under the -Property on Partially Ordered Metric Spaces
Directory of Open Access Journals (Sweden)
Mohamed Jleli
2013-01-01
Full Text Available Very recently, Abkar and Gabeleh (2013 observed that some best proximity point results under the -property can be obtained from the same results in fixed-point theory. In this paper, motivated by this mentioned work, we show that the most best proximity point results on a metric space endowed with a partial order (under the -property can be deduced from existing fixed-point theorems in the literature. We present various model examples to illustrate this point of view.
Directory of Open Access Journals (Sweden)
María Jesús Algar
2013-01-01
Full Text Available An efficient approach for the analysis of surface conformed reflector antennas fed arbitrarily is presented. The near field in a large number of sampling points in the aperture of the reflector is obtained applying the Geometrical Theory of Diffraction (GTD. A new technique named Master Points has been developed to reduce the complexity of the ray-tracing computations. The combination of both GTD and Master Points reduces the time requirements of this kind of analysis. To validate the new approach, several reflectors and the effects on the radiation pattern caused by shifting the feed and introducing different obstacles have been considered concerning both simple and complex geometries. The results of these analyses have been compared with the Method of Moments (MoM results.
Some exact results for the two-point function of an integrable quantum field theory
International Nuclear Information System (INIS)
Creamer, D.B.; Thacker, H.B.; Wilkinson, D.
1981-01-01
The two-point correlation function for the quantum nonlinear Schroedinger (one-dimensional delta-function gas) model is studied. An infinite-series representation for this function is derived using the quantum inverse-scattering formalism. For the case of zero temperature, the infinite-coupling (c→infinity) result of Jimbo, Miwa, Mori, and Sato is extended to give an exact expression for the order-1/c correction to the two-point function in terms of a Painleve transcendent of the fifth kind
López-Rosa, Sheila; Molina-Espíritu, Moyocoyani; Esquivel, Rodolfo O; Soriano-Correa, Catalina; Dehesa, Jésus S
2016-12-05
The relative structural location of a selected group of 27 sulfonamide-like molecules in a chemical space defined by three information theory quantities (Shannon entropy, Fisher information, and disequilibrium) is discussed. This group is composed of 15 active bacteriostatic molecules, 11 theoretically designed ones, and para-aminobenzoic acid. This endeavor allows molecules that share common chemical properties through the molecular backbone, but with significant differences in the identity of the chemical substituents, which might result in bacteriostatic activity, to be structurally classified and characterized. This is performed by quantifying the structural changes on the electron density distribution due to different functional groups and number of electrons. The macroscopic molecular features are described by means of the entropy-like notions of spatial electronic delocalization, order, and uniformity. Hence, an information theory three-dimensional space (IT-3D) emerges that allows molecules with common properties to be gathered. This space witnesses the biological activity of the sulfonamides. Some structural aspects and information theory properties can be associated, as a result of the IT-3D chemical space, with the bacteriostatic activity of these molecules. Most interesting is that the active bacteriostatic molecules are more similar to para-aminobenzoic acid than to the theoretically designed analogues. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Indentations and Starting Points in Traveling Sales Tour Problems: Implications for Theory
MacGregor, James N.
2012-01-01
A complete, non-trivial, traveling sales tour problem contains at least one "indentation", where nodes in the interior of the point set are connected between two adjacent nodes on the boundary. Early research reported that human tours exhibited fewer such indentations than expected. A subsequent explanation proposed that this was because…
Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.
2018-02-01
The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.
Grech, Victor
2018-01-01
PowerPoint™ and other slideware have the potential to be overused and abused. Presentations should be tailored using scientifically derived principles in order to maximise teaching potential. This paper applies the Mayer Multimedia Learning Theory (with its twelve evidence-based principles of multimedia design) to medical slide show presentations. The best way to avoid audience boredom or mortification is to adhere to these precepts. Presentations stand or fall on the quality, relevance, and integrity of the content. Slide shows should supplement a presentation, and not substitute for it. The key principles are brevity, cogency and clarity.
Ana Stefanova
2012-01-01
Humour theories describe different parts of humour as a phenomenon, obtained on the personal and community level, so difficult to be explained. The analytical psychology of Carl Gustav Jung may help in the explanation of why the search for the “Holy Grail of Humour” is as if trying to catch a shadow. The archetype of the trickster in folklore may help us describe some common and different parts of the universal phenomenon of humour and the specific ethno-psychological traits.The paper present...
On the space of solutions of the Hořava theory at the kinetic-conformal point
Bellorín, Jorge; Restuccia, Alvaro
2017-10-01
The nonprojectable Hořava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multipliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.
2008-01-01
Ansambel Fix peab 13. detsembril Tallinnas Saku Suurhallis oma 40. sünnipäeva. Kontserdi erikülaline on ansambel Apelsin, kaastegevad Jassi Zahharov ja HaleBopp Singers. Õhtut juhib Tarmo Leinatamm
Bayesian change-point analysis reveals developmental change in a classic theory of mind task.
Baker, Sara T; Leslie, Alan M; Gallistel, C R; Hood, Bruce M
2016-12-01
Although learning and development reflect changes situated in an individual brain, most discussions of behavioral change are based on the evidence of group averages. Our reliance on group-averaged data creates a dilemma. On the one hand, we need to use traditional inferential statistics. On the other hand, group averages are highly ambiguous when we need to understand change in the individual; the average pattern of change may characterize all, some, or none of the individuals in the group. Here we present a new method for statistically characterizing developmental change in each individual child we study. Using false-belief tasks, fifty-two children in two cohorts were repeatedly tested for varying lengths of time between 3 and 5 years of age. Using a novel Bayesian change point analysis, we determined both the presence and-just as importantly-the absence of change in individual longitudinal cumulative records. Whenever the analysis supports a change conclusion, it identifies in that child's record the most likely point at which change occurred. Results show striking variability in patterns of change and stability across individual children. We then group the individuals by their various patterns of change or no change. The resulting patterns provide scarce support for sudden changes in competence and shed new light on the concepts of "passing" and "failing" in developmental studies. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
Two-Point Incremental Forming with Partial Die: Theory and Experimentation
Silva, M. B.; Martins, P. A. F.
2013-04-01
This paper proposes a new level of understanding of two-point incremental forming (TPIF) with partial die by means of a combined theoretical and experimental investigation. The theoretical developments include an innovative extension of the analytical model for rotational symmetric single point incremental forming (SPIF), originally developed by the authors, to address the influence of the major operating parameters of TPIF and to successfully explain the differences in formability between SPIF and TPIF. The experimental work comprised the mechanical characterization of the material and the determination of its formability limits at necking and fracture by means of circle grid analysis and benchmark incremental sheet forming tests. Results show the adequacy of the proposed analytical model to handle the deformation mechanics of SPIF and TPIF with partial die and demonstrate that neck formation is suppressed in TPIF, so that traditional forming limit curves are inapplicable to describe failure and must be replaced by fracture forming limits derived from ductile damage mechanics. The overall geometric accuracy of sheet metal parts produced by TPIF with partial die is found to be better than that of parts fabricated by SPIF due to smaller elastic recovery upon unloading.
Chen, Yuntian; Zhang, Yan; Femius Koenderink, A
2017-09-04
We study semi-analytically the light emission and absorption properties of arbitrary stratified photonic structures with embedded two-dimensional magnetoelectric point scattering lattices, as used in recent plasmon-enhanced LEDs and solar cells. By employing dyadic Green's function for the layered structure in combination with the Ewald lattice summation to deal with the particle lattice, we develop an efficient method to study the coupling between planar 2D scattering lattices of plasmonic, or metamaterial point particles, coupled to layered structures. Using the 'array scanning method' we deal with localized sources. Firstly, we apply our method to light emission enhancement of dipole emitters in slab waveguides, mediated by plasmonic lattices. We benchmark the array scanning method against a reciprocity-based approach to find that the calculated radiative rate enhancement in k-space below the light cone shows excellent agreement. Secondly, we apply our method to study absorption-enhancement in thin-film solar cells mediated by periodic Ag nanoparticle arrays. Lastly, we study the emission distribution in k-space of a coupled waveguide-lattice system. In particular, we explore the dark mode excitation on the plasmonic lattice using the so-called array scanning method. Our method could be useful for simulating a broad range of complex nanophotonic structures, i.e., metasurfaces, plasmon-enhanced light emitting systems and photovoltaics.
De Grandi, C.; Polkovnikov, A.
Dynamics in closed systems recently attracted a lot of theoretical interest largely following experimental developments in cold atom systems (see e.g., [1] for a review). Several spectacular experiments already explored different aspects of non-equilibrium dynamics in interacting many-particle systems [2-8]. Recent theoretical works in this context focused on various topics, for instance: connection of dynamics and thermodynamics [9-11 M. Rigol, unpublished], dynamics following a sudden quench in low dimensional systems [11-23, L. Mathey and A. Polkovnikov, unpublished; A. Iucci and M.A. Cazalilla,unpublished], adiabatic dynamics near quantum critical points [24-37, D. Chowdhury et al., unpublished; K. Sengupta and D. Sen, unpublished; A.P. Itin and P. Törmä, unpublished; F. Pollmann et al., unpublished] and others. Though there is still very limited understanding of the generic aspects of non-equilibrium quantum dynamics, it has been recognized that such issues as integrability, dimensionality, universality (near critical points) can be explored to understand the non-equilibrium behavior of many-particle systems in various specific situations.
Mehr, Ali Farhang; Tumer, Irem
2005-01-01
In this paper, we will present a new methodology that measures the "worth" of deploying an additional testing instrument (sensor) in terms of the amount of information that can be retrieved from such measurement. This quantity is obtained using a probabilistic model of RLV's that has been partially developed in the NASA Ames Research Center. A number of correlated attributes are identified and used to obtain the worth of deploying a sensor in a given test point from an information-theoretic viewpoint. Once the information-theoretic worth of sensors is formulated and incorporated into our general model for IHM performance, the problem can be formulated as a constrained optimization problem where reliability and operational safety of the system as a whole is considered. Although this research is conducted specifically for RLV's, the proposed methodology in its generic form can be easily extended to other domains of systems health monitoring.
Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps
Keller, Gerhard; Nowicki, Tomasz
1992-09-01
We study unimodal interval maps T with negative Schwarzian derivative satisfying the Collet-Eckmann condition | DT n ( Tc)|≧ Kλ {c/n} for some constants K>0 and λc>1 ( c is the critical point of T). We prove exponential mixing properties of the unique invariant probability density of T, describe the long term behaviour of typical (in the sense of Lebesgue measure) trajectories by Central Limit and Large Deviations Theorems for partial sum processes of the formS_n = Σ _{i = 0}^{n - 1} f(T^i x), and study the distribution of “typical” periodic orbits, also in the sense of a Central Limit Theorem and a Large Deviations Theorem. This is achieved by proving quasicompactness of the Perron Frobenius operator and of similar transfer operators for the Markov extension of T and relating the isolated eigenvalues of these operators to the poles of the corresponding Ruelle zeta functions.
Linear response theory for one point statistics in the log-law region of wall bounded turbulence
Kaneda, Yukio; Yamamoto, Yoshinobu; Tsuji, Yoshiyuki
2017-11-01
The idea of linear response theory developed in statistical mechanics for irreversible phenomena is applied to one-point statistics in the so-called log-law region, or strictly speaking the constant Reynolds stress region, of wall bounded turbulence. The one-point statistics include the Reynolds stress and the r.m.s's of the velocity fluctuations in the stream wise, span wise and wall normal directions. In the application of the idea, a similarity between (i) the Karman-Howarth equation for homogeneous isotropic turbulence and (ii) the conservation equation of the Reynolds averaged momentum in turbulence with parallel mean flow plays a key role. Both of (i) and (ii) are exact, and they respectively represent the energy-transfer from large to small scales, and the momentum-transfer in the wall normal direction. In the limit of infinite Reynolds number, (i) reduces to Kolmogorov's 4/5-law in the inertial subrange, while (ii) results in the constancy of the Reynolds stress in a certain range. The theory gives an estimate on the influence of finite Reynolds number on the statistics. The theoretical conjectures are compared with data of a series of direct numerical simulations of turbulent channel flow with Reτ up to 8000. This study was partly supported by JSPS KAKENHI Grant Numbers (S)16H06339 and (C)26400410.
Nuclear Quantum Effects in Water at the Triple Point: Using Theory as a Link Between Experiments.
Cheng, Bingqing; Behler, Jörg; Ceriotti, Michele
2016-06-16
One of the most prominent consequences of the quantum nature of light atomic nuclei is that their kinetic energy does not follow a Maxwell-Boltzmann distribution. Deep inelastic neutron scattering (DINS) experiments can measure this effect. Thus, the nuclear quantum kinetic energy can be probed directly in both ordered and disordered samples. However, the relation between the quantum kinetic energy and the atomic environment is a very indirect one, and cross-validation with theoretical modeling is therefore urgently needed. Here, we use state of the art path integral molecular dynamics techniques to compute the kinetic energy of hydrogen and oxygen nuclei in liquid, solid, and gas-phase water close to the triple point, comparing three different interatomic potentials and validating our results against equilibrium isotope fractionation measurements. We will then show how accurate simulations can draw a link between extremely precise fractionation experiments and DINS, therefore establishing a reliable benchmark for future measurements and providing key insights to increase further the accuracy of interatomic potentials for water.
R-current three-point functions in 4d $\\mathcal{N}=1$ superconformal theories arXiv
Manenti, Andrea; Vichi, Alessandro
In 4d $\\mathcal{N}=1$ superconformal field theories (SCFTs) the R-symmetry current, the stress-energy tensor, and the supersymmetry currents are grouped into a single object, the Ferrara--Zumino multiplet. In this work we study the most general form of three-point functions involving two Ferrara--Zumino multiplets and a third generic multiplet. We solve the constraints imposed by conservation in superspace and show that non-trivial solutions can only be found if the third multiplet is R-neutral and transforms in suitable Lorentz representations. In the process we give a prescription for counting independent tensor structures in superconformal three-point functions. Finally, we set the Grassmann coordinates of the Ferrara--Zumino multiplets to zero and extract all three-point functions involving two R-currents and a third conformal primary. Our results pave the way for bootstrapping the correlation function of four R-currents in 4d $\\mathcal{N}=1$ SCFTs.
Lisano, Michael E.
2007-01-01
Recent literature in applied estimation theory reflects growing interest in the sigma-point (also called unscented ) formulation for optimal sequential state estimation, often describing performance comparisons with extended Kalman filters as applied to specific dynamical problems [c.f. 1, 2, 3]. Favorable attributes of sigma-point filters are described as including a lower expected error for nonlinear even non-differentiable dynamical systems, and a straightforward formulation not requiring derivation or implementation of any partial derivative Jacobian matrices. These attributes are particularly attractive, e.g. in terms of enabling simplified code architecture and streamlined testing, in the formulation of estimators for nonlinear spaceflight mechanics systems, such as filter software onboard deep-space robotic spacecraft. As presented in [4], the Sigma-Point Consider Filter (SPCF) algorithm extends the sigma-point filter algorithm to the problem of consider covariance analysis. Considering parameters in a dynamical system, while estimating its state, provides an upper bound on the estimated state covariance, which is viewed as a conservative approach to designing estimators for problems of general guidance, navigation and control. This is because, whether a parameter in the system model is observable or not, error in the knowledge of the value of a non-estimated parameter will increase the actual uncertainty of the estimated state of the system beyond the level formally indicated by the covariance of an estimator that neglects errors or uncertainty in that parameter. The equations for SPCF covariance evolution are obtained in a fashion similar to the derivation approach taken with standard (i.e. linearized or extended) consider parameterized Kalman filters (c.f. [5]). While in [4] the SPCF and linear-theory consider filter (LTCF) were applied to an illustrative linear dynamics/linear measurement problem, in the present work examines the SPCF as applied to
Renormalized G-convolution of n-point functions in quantum field theory. I. The Euclidean case
International Nuclear Information System (INIS)
Bros, Jacques; Manolessou-Grammaticou, Marietta.
1977-01-01
The notion of Feynman amplitude associated with a graph G in perturbative quantum field theory admits a generalized version in which each vertex v of G is associated with a general (non-perturbative) nsub(v)-point function Hsup(nsub(v)), nsub(v) denoting the number of lines which are incident to v in G. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle's G-convolution procedure. The authors propose a generalization of G-convolution which includes the case when the functions Hsup(nsub(v)) are not integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of the G-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. The case of Euclidean four-momentum configurations is only treated
Density functional theory calculations of point defects and hydrogen isotopes in Li4SiO4
Directory of Open Access Journals (Sweden)
Xiaogang Xiang
2015-10-01
Full Text Available The Li4SiO4 is a promising breeder material for future fusion reactors. Radiation induced vacancies and hydrogen isotope related impurities are the major types of point defects in this breeder material. In present study, various kinds of vacancies and hydrogen isotopes related point defects in Li4SiO4 are investigated through density functional theory (DFT calculations. The band gap of Li4SiO4 is determined by UV-Vis diffuse reflectance spectroscopy experiments. Formation energies of all possible charge states of Li, Si and O vacancies are calculated using DFT methods. Formation energies of possible charge states of hydrogen isotopes substitution for Li and O are also calculated. We found that Li-vacancies will dominate among all vacancies in neutral charge state under radiation conditions and the O, Li, and Si vacancies (VO,VLi,VSi are stable in charge states +2, -1, -4 for most of the range of Fermi level, respectively. The interstitial hydrogen isotopes (Hi and substitutional HLi are stable in the charge states +1, 0 for most of the range of Fermi level, respectively. Moreover, substitutional HO are stable in +1 charge states. We also investigated the process of tritium recovery by discussing the interaction between interstitial H and Li-vacancy, O-vacancy, and found that H O + and H Li 0 are the most common H related defects during radiation process.
Infrared behaviors of SU(2 gauge theory
Directory of Open Access Journals (Sweden)
Tuominen Kimmo
2017-01-01
Full Text Available We will discuss some recent results in the determination of the location of the conformal window in SU(2 gauge theory with Nf fermions in the fundamental representation of the gauge group. In particular, we will demonstrate that the long distance behavior of the continuum theory with Nf = 6 is governed by an infrared stable fixed point.
Karriem, Veronica V.
Nuclear reactor design incorporates the study and application of nuclear physics, nuclear thermal hydraulic and nuclear safety. Theoretical models and numerical methods implemented in computer programs are utilized to analyze and design nuclear reactors. The focus of this PhD study's is the development of an advanced high-fidelity multi-physics code system to perform reactor core analysis for design and safety evaluations of research TRIGA-type reactors. The fuel management and design code system TRIGSIMS was further developed to fulfill the function of a reactor design and analysis code system for the Pennsylvania State Breazeale Reactor (PSBR). TRIGSIMS, which is currently in use at the PSBR, is a fuel management tool, which incorporates the depletion code ORIGEN-S (part of SCALE system) and the Monte Carlo neutronics solver MCNP. The diffusion theory code ADMARC-H is used within TRIGSIMS to accelerate the MCNP calculations. It manages the data and fuel isotopic content and stores it for future burnup calculations. The contribution of this work is the development of an improved version of TRIGSIMS, named TRIGSIMS-TH. TRIGSIMS-TH incorporates a thermal hydraulic module based on the advanced sub-channel code COBRA-TF (CTF). CTF provides the temperature feedback needed in the multi-physics calculations as well as the thermal hydraulics modeling capability of the reactor core. The temperature feedback model is using the CTF-provided local moderator and fuel temperatures for the cross-section modeling for ADMARC-H and MCNP calculations. To perform efficient critical control rod calculations, a methodology for applying a control rod position was implemented in TRIGSIMS-TH, making this code system a modeling and design tool for future core loadings. The new TRIGSIMS-TH is a computer program that interlinks various other functional reactor analysis tools. It consists of the MCNP5, ADMARC-H, ORIGEN-S, and CTF. CTF was coupled with both MCNP and ADMARC-H to provide the
International Nuclear Information System (INIS)
Aharony, Ofer; Komargodski, Zohar; Yankielowicz, Shimon
2016-01-01
We consider Euclidean Conformal Field Theories perturbed by quenched disorder, namely by random fluctuations in their couplings. Such theories are relevant for second-order phase transitions in the presence of impurities or other forms of disorder. Theories with quenched disorder often flow to new fixed points of the renormalization group. We begin with disorder in free field theories. Imry and Ma showed that disordered free fields can only exist for d>4. For d>4 we show that disorder leads to new fixed points which are not scale-invariant. We then move on to large-N theories (vector models or gauge theories in the ‘t Hooft limit). We compute exactly the beta function for the disorder, and the correlation functions of the disordered theory. We generalize the results of Imry and Ma by showing that such disordered theories exist only when disorder couples to operators of dimension Δ>d/4. Sometimes the disordered fixed points are not scale-invariant, and in other cases they have unconventional dependence on the disorder, including non-trivial effects due to irrelevant operators. Holography maps disorder in conformal theories to stochastic differential equations in a higher dimensional space. We use this dictionary to reproduce our field theory results. We also study the leading 1/N corrections, both by field theory methods and by holography. These corrections are particularly important when disorder scales with the number of degrees of freedom.
International Nuclear Information System (INIS)
Aref'eva, I.Ya.; Slavnov, A.A.
1981-01-01
This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks [ru
Alarm points for fixed oxygen monitors
International Nuclear Information System (INIS)
Miller, G.C.
1987-05-01
Oxygen concentration monitors were installed in a vault where numerous pipes carried inert cryogens and gases to the Mirror Fusion Test Facility (MFTF-B) experimental vessel at Lawrence Livermore National Laboratory (LLNL). The problems associated with oxygen-monitoring systems and the reasons why such monitors were installed were reviewed. As a result of this review, the MFTF-B monitors were set to sound an evacuation alarm when the oxygen concentration fell below 18%. We chose the 18% alarm criterion to minimize false alarms and to allow time for personnel to escape in an oxygen-deficient environment
On Fixed Points of Strictly Causal Functions
2013-04-08
languages such as VHDL (see [1]) and SystemC (see [2]), modeling and simulation tools such as Simulink and LabVIEW, network simulation tools such as ns-2/ns...interesting direction for future 49 work. References [1] IEEE standard VHDL language reference manual. IEEE Std 1076-2000, pages i–290, 2000. [2] IEEE
Common fixed points for weakly compatible maps
Indian Academy of Sciences (India)
Proceedings – Mathematical Sciences. Current Issue : Vol. 127, Issue 5. Current Issue Volume 127 | Issue 5. November 2017. Home · Volumes & Issues · Special Issues · Forthcoming Articles · Search · Editorial Board · Information for Authors · Subscription ...
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Karlin, Anna R
2016-01-01
This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields, such as computer science, economics, social choice, biology, and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. Game theory's influence is felt in a wide range of disciplines, and the authors deliver masterfully on the challenge of presenting both the breadth and coherence of its underlying ...
Branes and Six Dimensional Supersymmetric Theories
Hanany, Amihay; Hanany, Amihay; Zaffaroni, Alberto
1998-01-01
We consider configurations of sixbranes, fivebranes and eightbranes in various superstring backgrounds. These configurations give rise to $(0,1)$ supersymmetric theories in six dimensions. The condition for RR charge conservation of a brane configuration translates to the condition that the corresponding field theory is anomaly free. Sets of infinitely many models with non trivial RG fixed points at strong coupling are demonstrated. Some of them reproduce and generalise the world-volume theories of SO(32) and $E_8\\times E_8$ small instantons. All the models are shown to be connected by smooth transitions. In particular, the small instanton transition for which a tensor multiplet is traded for 29 hypermultiplets is explicitly demonstrated. The particular limit in which these theories can be considered as six dimensional string theories without gravity are discussed. New fixed points (string theories) associated with $E_n$ global symmetries are discovered by taking the strong string coupling limit.
A Fixed Point, A Point of Interruption (Book Review
Directory of Open Access Journals (Sweden)
Mark Hewson
2006-01-01
Full Text Available A review of Alain Badiou, Infinite Thought: Truth and the Return to Philosophy, ed. and trans. Justin Clemens and Oliver Feltham, New Edition, London, Continuum, 2005. ISBN: 0826479294.
Kostov, Ivan
2012-06-29
We give an analytic expression for the correlation function of three large classical nonprotected operators in N=4 super-Yang-Mills theory at weak coupling. We restrict ourselves to operators belonging to an su(2) sector of the theory. In order to carry out the calculation, we derive, by unveiling a hidden factorization property, the thermodynamical limit of Slavnov's determinant.
Directory of Open Access Journals (Sweden)
You-Hui Su
2011-01-01
are obtained for the existence of at least one, triple, or arbitrary odd positive pseudosymmetric solutions by using pseudosymmetric technique and fixed-point theory in cone. As an application, two examples are given to illustrate the main results.
Riedl, Dennis; Heuer, Andreas; Strauss, Bernd
2015-06-01
Incentives guide human behavior by altering the level of external motivation. We apply the idea of loss aversion from prospect theory (Kahneman & Tversky, 1979) to the point reward systems in soccer and investigate the controversial impact of the three-point rule on reducing the fraction of draws in this sport. Making use of the Poisson nature of goal scoring, we compared empirical results with theoretically deduced draw ratios from 24 countries encompassing 20 seasons each (N = 118.148 matches). The rule change yielded a slight reduction in the ratio of draws, but despite adverse incentives, still 18% more matches ended drawn than expected, t(23) = 11.04, p theory assertions. Alternative point systems that manipulated incentives for losses yielded reductions at or below statistical expectation. This provides support for the deduced concept of how arbitrary aims, such as the reduction of draws in the world's soccer leagues, could be more effectively accomplished than currently attempted.
Analytic aspects of rational conformal field theories
International Nuclear Information System (INIS)
Kiritsis, E.B.; Lawrence Berkeley Lab., CA
1990-01-01
The problem of deriving linear differential equations for correlation functions of Rational Conformal Field Theories is considered. Techniques from the theory of fuchsian differential equations are used to show that knowledge of the central charge, dimensions of primary fields and fusion rules are enough to fix the differential equations for one- and two-point functions on the tours. Any other correlation function can be calculated along similar lines. The results settle the issue of 'exact solution' of rational conformal field theories. (orig.)
Young, Frederic; Siegel, Edward
Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!
International Nuclear Information System (INIS)
Choi, B.H.; Poe, R.T.; Tang, K.T.
1978-01-01
The body-fixed (BF) formulation for atom--diatom scatterings is developed to the extent that one can use it to perform accurate close-coupling calculation, without introducing further approximation except truncating a finite basis set of the target molecular wave function, on the same ground as one use the space-fixed (SF) formulation. In this formulation, the coupled differential equations are solved an the boundary conditions matched entirely in the BF coordinate system. A unitary transformation is used to obtain both the coupled differential equation and the boundary condition in BF system system from SF system. All properties of the solution with respect to parity are derived entirely from the transformation, without using the parity eignfunctions of the BF frame. Boundary conditions that yield the scattering (S) matrix and the reactance (R) matrix are presented for each parity in both the far asymptotic region (where the interaction and the centrifugal potentials are both negligible) and the near asymptotic region (where the interaction potential is negligible but the centrifugal potential is not). While our differential equations are the same as those derived by others with different methods, our asymptotic boundary conditions disagree with some existing ones. With a given form of the BF coupled differential equations, the acceptable boundary conditions are discussed
Semenov, Alexander; Dubernet, Marie-Lise; Babikov, Dmitri
2014-09-21
The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H2O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm(-1) the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm(-1) the errors are consistently in the range of 1%-2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n(2), where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n(3). Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.
van Lenthe, G Harry; Voide, Romain; Boyd, Steven K; Müller, Ralph
2008-10-01
Current practice to determine bone tissue modulus of murine cortical bone is to estimate it from three-point bending tests, using Euler-Bernoulli beam theory. However, murine femora are not perfect beams; hence, results can be inaccurate. Our aim was to assess the accuracy of beam theory, which we tested for two commonly used inbred strains of mice, C57BL/6 (B6) and C3H/He (C3H). We measured the three-dimensional structure of male and female B6 and C3H femora (N=20/group) by means of micro-computed tomography. For each femur five micro-finite element (micro-FE) models were created that simulated three-point bending tests with varying distances between the supports. Tissue modulus was calculated from beam theory using micro-FE results. The accuracy of beam theory was assessed by comparing the beam theory-derived moduli with the modulus as used in the micro-FE analyses. An additional set of fresh-frozen femora (10 B6 and 12 C3H) was biomechanically tested and subjected to the same micro-FE analyses. These combined experimental-computational analyses enabled an unbiased assessment of specimen-specific tissue modulus. We found that by using beam theory, tissue modulus was underestimated for all femora. Femoral geometry and size had strong effects on beam theory-derived tissue moduli. Owing to their relatively thin cortex, underestimation was markedly higher for B6 than for C3H. Underestimation was dependent on support width in a strain-specific manner. From our combined experimental-computational approach we calculated tissue moduli of 12.0+/-1.3 GPa and 13.4+/-2.1 GPa for B6 and C3H, respectively. We conclude that tissue moduli in murine femora are strongly underestimated when calculated from beam theory. Using image-based micro-FE analyses we could precisely quantify this underestimation. We showed that previously reported murine inbred strain-specific differences in tissue modulus are largely an effect of geometric differences, not accounted for by beam theory. We
The omega deformation, branes, integrability and Liouville theory
Nekrasov, Nikita; Witten, Edward
2010-09-01
We reformulate the Ω-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent results linking the Ω-deformation to integrable Hamiltonian systems in one direction and Liouville theory of two-dimensional conformal field theory in another direction.
Lie point symmetries of differential-difference equations
Energy Technology Data Exchange (ETDEWEB)
Levi, D [Dipartimento di Ingegneria Elettronica, Universita degli Studi Roma Tre and Sezione INFN, Roma Tre, Via della Vasca Navale 84, 00146 Roma (Italy); Winternitz, P [Centre de recherches mathematiques et, Departement de mathematiques et statistique, Universite de Montreal, C.P. 6128, succ. Centre-ville, H3C 3J7, Montreal, Quebec (Canada); Yamilov, R I, E-mail: levi@roma3.infn.i, E-mail: wintern@crm.umontreal.c, E-mail: RvlYamilov@matem.anrb.r [Ufa Institute of Mathematics, Russian Academy of Sciences, 112 Chernyshevsky Street, Ufa 450008 (Russian Federation)
2010-07-23
We present an algorithm for determining the Lie point symmetries of differential equations on fixed non-transforming lattices, i.e. equations involving both continuous and discrete-independent variables. The symmetries of a specific integrable discretization of the Krichever-Novikov equation, the Toda lattice and Toda field theory are presented as examples of the general method. (fast track communication)
Schuler, Michael; Whitsitt, Seth; Henry, Louis-Paul; Sachdev, Subir; Läuchli, Andreas M
2016-11-18
The low-energy spectra of many body systems on a torus, of finite size L, are well understood in magnetically ordered and gapped topological phases. However, the spectra at quantum critical points separating such phases are largely unexplored for (2+1)D systems. Using a combination of analytical and numerical techniques, we accurately calculate and analyze the low-energy torus spectrum at an Ising critical point which provides a universal fingerprint of the underlying quantum field theory, with the energy levels given by universal numbers times 1/L. We highlight the implications of a neighboring topological phase on the spectrum by studying the Ising* transition (i.e. the transition between a Z_{2} topological phase and a trivial paramagnet), in the example of the toric code in a longitudinal field, and advocate a phenomenological picture that provides qualitative insight into the operator content of the critical field theory.
Perla, Rocco J.; Carifio, James
In sharp contrast to the early positivist view of the nature of science and scientific knowledge, Kuhn argues that the scientific enterprise involves states of continuous, gradual development punctuated by comparatively rare instances of turmoil and change, which ultimately brings about a new stability and a qualitatively changed knowledge base. Although this discontinuous or nonlinear view of scientific knowledge is shared by a number of philosophers of science and science educators currently, Kuhn's description of how progress in science occurs has never been formally modeled from a nonlinear mathematical perspective. In this article, we represent aspects of Kuhn's main thesis and ideas as stated in his classic work The Structure of Scientific Revolutions using catastrophe theory, which is a particular instantiation of chaos theory capable of describing discontinuous phenomenon. Through this catastrophe theory representation we attempt to depict and develop a formal nonlinear model of scientific change. The pedagogical implications of the model developed and presented are discussed.
Conformal Gauge-Yukawa Theories away From Four Dimensions
DEFF Research Database (Denmark)
Codello, Alessandro; Langaeble, Kasper; Litim, Daniel
2016-01-01
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD...
Classification of networks of automata by dynamical mean field theory
International Nuclear Information System (INIS)
Burda, Z.; Jurkiewicz, J.; Flyvbjerg, H.
1990-01-01
Dynamical mean field theory is used to classify the 2 24 =65,536 different networks of binary automata on a square lattice with nearest neighbour interactions. Application of mean field theory gives 700 different mean field classes, which fall in seven classes of different asymptotic dynamics characterized by fixed points and two-cycles. (orig.)
Zhang, Yufeng; Long, Man; Luo, Sida; Bao, Yu; Shen, Hanxia
2015-12-01
Transit route choice model is the key technology of public transit systems planning and management. Traditional route choice models are mostly based on expected utility theory which has an evident shortcoming that it cannot accurately portray travelers' subjective route choice behavior for their risk preferences are not taken into consideration. Cumulative prospect theory (CPT), a brand new theory, can be used to describe travelers' decision-making process under the condition of uncertainty of transit supply and risk preferences of multi-type travelers. The method to calibrate the reference point, a key parameter to CPT-based transit route choice model, determines the precision of the model to a great extent. In this paper, a new method is put forward to obtain the value of reference point which combines theoretical calculation and field investigation results. Comparing the proposed method with traditional method, it shows that the new method can promote the quality of CPT-based model by improving the accuracy in simulating travelers' route choice behaviors based on transit trip investigation from Nanjing City, China. The proposed method is of great significance to logical transit planning and management, and to some extent makes up the defect that obtaining the reference point is solely based on qualitative analysis.