QCD fixed points: Banks-Zaks scenario or dynamical gluon mass generation?
Gomez, J. D.; Natale, A. A.
2017-01-01
Fixed points in QCD can appear when the number of quark flavors (Nf) is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass (DGM) generation does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their β functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large Nf, we verify that between Nf = 8 and Nf = 12 both cases exhibit fixed points at similar coupling constant values (g∗). We argue that the states of minimum vacuum energy, as a function of the coupling constant up to g∗ and for several Nf values, are related to the dynamical gluon mass generation mechanism.
Quasi-fixed point scenarios and the Higgs mass in the E6 inspired SUSY models
Nevzorov, R
2013-01-01
We analyse the renormalization group (RG) flow of the gauge and Yukawa couplings within the E6 inspired supersymmetric (SUSY) models with extra U(1)_{N} gauge symmetry under which right-handed neutrinos have zero charge. In these models single discrete \\tilde{Z}^{H}_2 symmetry forbids the tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. We argue that the measured values of the SU(2)_W and U(1)_Y gauge couplings lie near the quasi-fixed points of the RG equations in these models. The solutions for the Yukawa couplings also approach the quasi-fixed points with increasing their values at the Grand Unification scale. We calculate the two-loop upper bounds on the lightest Higgs boson mass in the vicinity of these quasi-fixed points and compare the results of our analysis with the corresponding ones in the NMSSM. In all these cases the theoretical restrictions on the SM-like Higgs boson mass are rather close to 125 GeV.
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
Flat coalgebraic fixed point logics
Schröder, Lutz
2010-01-01
Fixed point logics have a wide range of applications in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the mu-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 mu-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 mu-calculus including, e.g., flat fragments of the graded mu-calculus and the alternating-time mu-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 mu-calculus but avo...
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 ...
Fixed Point and Aperiodic Tilings
Durand, Bruno; Shen, Alexander
2008-01-01
An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a ``robust'' aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.
Homotopies and the Universal Fixed Point Property
DEFF Research Database (Denmark)
Szymik, Markus
2015-01-01
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...
Fixed Point Actions for Lattice Fermions
Bietenholz, W
1994-01-01
The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be used to construct perfect lattice actions for asymptotically free fermionic theories like QCD or the Gross-Neveu model. The local fixed point actions for Wilson fermions break chiral symmetry, while in the staggered case the remnant $U(1)_e \\otimes U(1)_o$ symmetry is preserved. In addition, for Wilson fermions a nonlocal fixed point is found that corresponds to free chiral fermions. The vicinity of this fixed point is studied in the Gross-Neveu model using perturbation theory.
Fixed-point-like theorems on subspaces
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Bernard Cornet
2004-08-01
Full Text Available We prove a fixed-point-like theorem for multivalued mappings defined on the finite Cartesian product of Grassmannian manifolds and convex sets. Our result generalizes two different kinds of theorems: the fixed-point-like theorem by Hirsch et al. (1990 or Husseini et al. (1990 and the fixed-point theorem by Gale and Mas-Colell (1975 (which generalizes Kakutani's theorem (1941.
Fixed points of occasionally weakly biased mappings
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Y. Mahendra Singh, M. R. Singh
2012-09-01
Full Text Available Common fixed point results due to Pant et al. [Pant et al., Weak reciprocal continuity and fixed point theorems, Ann Univ Ferrara, 57(1, 181-190 (2011] are extended to a class of non commuting operators called occasionally weakly biased pair[ N. Hussain, M. A. Khamsi A. Latif, Commonfixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Analysis, 74, 2133-2140 (2011]. We also provideillustrative examples to justify the improvements. Abstract. Common fixed point results due to Pant et al. [Pant et al., Weakreciprocal continuity and fixed point theorems, Ann Univ Ferrara, 57(1, 181-190 (2011] are extended to a class of non commuting operators called occasionally weakly biased pair[ N. Hussain, M. A. Khamsi A. Latif, Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Analysis, 74, 2133-2140 (2011]. We also provide illustrative examples to justify the improvements.
Imaginary fixed points can be physical.
Zhong, Fan
2012-08-01
It has been proposed that a first-order phase transition driven to happen in the metastable region exhibits scaling and universality near an instability point controlled by an instability fixed point of a φ(3) theory. However, this fixed point has an imaginary value and the renormalization-group flow of the φ(3) coupling diverges at a finite scale. Here combining a momentum-space RG analysis and a nucleation theory near the spinodal point, we show that imaginary rather than real values are physical counterintuitively and thus the imaginary fixed point does control the scaling.
Fixed point theorems in spaces and -trees
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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.
Approximate Equilibrium Problems and Fixed Points
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H. Mazaheri
2013-01-01
Full Text Available We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.
On computing fixed points for generalized sandpiles
Formenti, Enrico; Masson, Benoît
2004-01-01
Presented at DMCS 2004 (Turku, FINLAND). Long version with proofs published in International Journal of Unconventional Computing, 2006; International audience; We prove fixed points results for sandpiles starting with arbitrary initial conditions. We give an effective algorithm for computing such fixed points, and we refine it in the particular case of SPM.
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...
Magnetic Fixed Points and Emergent Supersymmetry
Antipin, Oleg; Pica, Claudio; Sannino, Francesco
2011-01-01
We establish the existence of fixed points for certain gauge theories candidate to be magnetic duals of QCD with one adjoint Weyl fermion. In the perturbative regime of the magnetic theory the existence of a very large number of fixed points is unveiled. We classify them by analyzing their basin of attraction. The existence of several nonsupersymmetric fixed points for the magnetic gauge theory lends further support towards the existence of gauge-gauge duality beyond supersymmetry. We also discover that among these very many fixed points there are supersymmetric ones emerging from a generic nonsupersymmetric renormalization group flow. We therefore conclude that supersymmetry naturally emerges as a fixed point theory from a nonsupersymmetric Lagrangian without the need for fine-tuning of the bare couplings. Our results suggest that supersymmetry can be viewed as an emergent phenomenon in field theory. In particular there should be no need for fine-tuning the bare couplings when performing Lattice simulations ...
Fixed Point Curve for Weakly Inward Contractions and Approximate Fixed Point Property
Institute of Scientific and Technical Information of China (English)
P. Riyas; K. T. Ravindran
2013-01-01
In this paper, we discuss the concept of fixed point curve for linear interpo-lations of weakly inward contractions and establish necessary condition for a nonex-pansive mapping to have approximate fixed point property.
Fixed-point adiabatic quantum search
Dalzell, Alexander M.; Yoder, Theodore J.; Chuang, Isaac L.
2017-01-01
Fixed-point quantum search algorithms succeed at finding one of M target items among N total items even when the run time of the algorithm is longer than necessary. While the famous Grover's algorithm can search quadratically faster than a classical computer, it lacks the fixed-point property—the fraction of target items must be known precisely to know when to terminate the algorithm. Recently, Yoder, Low, and Chuang [Phys. Rev. Lett. 113, 210501 (2014), 10.1103/PhysRevLett.113.210501] gave an optimal gate-model search algorithm with the fixed-point property. Previously, it had been discovered by Roland and Cerf [Phys. Rev. A 65, 042308 (2002), 10.1103/PhysRevA.65.042308] that an adiabatic quantum algorithm, operating by continuously varying a Hamiltonian, can reproduce the quadratic speedup of gate-model Grover search. We ask, can an adiabatic algorithm also reproduce the fixed-point property? We show that the answer depends on what interpolation schedule is used, so as in the gate model, there are both fixed-point and non-fixed-point versions of adiabatic search, only some of which attain the quadratic quantum speedup. Guided by geometric intuition on the Bloch sphere, we rigorously justify our claims with an explicit upper bound on the error in the adiabatic approximation. We also show that the fixed-point adiabatic search algorithm can be simulated in the gate model with neither loss of the quadratic Grover speedup nor of the fixed-point property. Finally, we discuss natural uses of fixed-point algorithms such as preparation of a relatively prime state and oblivious amplitude amplification.
About Applications of the Fixed Point Theory
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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.
Approximate fixed point of Reich operator
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M. Saha
2013-01-01
Full Text Available In the present paper, we study the existence of approximate fixed pointfor Reich operator together with the property that the ε-fixed points are concentrated in a set with the diameter tends to zero if ε $to$ > 0.
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...
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.
Global Wilson-Fisher fixed points
Jüttner, Andreas; Litim, Daniel F.; Marchais, Edouard
2017-08-01
The Wilson-Fisher fixed point with O (N) universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed points to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantities such as scaling exponents and mass ratios are computed, for all N, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-N results do not converge pointwise towards the exact infinite-N limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.
Fixed-Point Configurable Hardware Components
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Rocher Romuald
2006-01-01
Full Text Available To reduce the gap between the VLSI technology capability and the designer productivity, design reuse based on IP (intellectual properties is commonly used. In terms of arithmetic accuracy, the generated architecture can generally only be configured through the input and output word lengths. In this paper, a new kind of method to optimize fixed-point arithmetic IP has been proposed. The architecture cost is minimized under accuracy constraints defined by the user. Our approach allows exploring the fixed-point search space and the algorithm-level search space to select the optimized structure and fixed-point specification. To significantly reduce the optimization and design times, analytical models are used for the fixed-point optimization process.
On hyperbolic fixed points in ultrametric dynamics
Lindahl, Karl-Olof; 10.1134/S2070046610030052
2011-01-01
Let K be a complete ultrametric field. We give lower and upper bounds for the size of linearization discs for power series over K near hyperbolic fixed points. These estimates are maximal in the sense that there exist examples where these estimates give the exact size of the corresponding linearization disc. In particular, at repelling fixed points, the linearization disc is equal to the maximal disc on which the power series is injective.
Random fixed points and random differential inclusions
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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.
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).
Fixed points of symplectic periodic flows
Pelayo, Alvaro
2010-01-01
The study of fixed points is a classical subject in geometry and dynamics. If the circle acts in a Hamiltonian fashion on a compact symplectic manifold M, then it is classically known that there are at least 1 + dim(M)/2 fixed points; this follows from Morse theory for the momentum map of the action. In this paper we use Atiyah-Bott-Berline-Vergne (ABBV) localization in equivariant cohomology to prove that this conclusion also holds for symplectic circle actions with non-empty fixed sets, as long as the Chern class map is somewhere injective -- the Chern class map assigns to a fixed point the sum of the action weights at the point. We complement this result with less sharp lower bounds on the number of fixed points, under no assumptions; from a dynamical systems viewpoint, our results imply that there is no symplectic periodic flow with exactly one or two equilibrium points on a compact manifold of dimension at least eight.
Au Fixed Point Development at NRC
Dedyulin, S. N.; Gotoh, M.; Todd, A. D. W.
2017-04-01
Two Au fixed points filled using metal of different nominal purities in carbon crucibles have been developed at the National Research Council Canada (NRC). The primary motivation behind this project was to provide the means for direct thermocouple calibrations at the Au freezing point (1064.18°C). Using a Au fixed point filled with the metal of maximum available purity [99.9997 % pure according to glow discharge mass spectroscopy (GDMS)], multiple freezing plateaus were measured in a commercial high-temperature furnace. Four Pt/Pd thermocouples constructed and calibrated in-house were used to measure the freezing plateaus. From the calibration at Sn, Zn, Al and Ag fixed points, the linear deviation function from the NIST-IMGC reference function (IEC 62460:2008 Standard) was determined and extrapolated to the freezing temperature of Au. For all the Pt/Pd thermocouples used in this study, the measured EMF values agree with the extrapolated values within expanded uncertainty, thus substantiating the use of 99.9997 % pure Au fixed point cell for thermocouple calibrations at NRC. Using the Au fixed point filled with metal of lower purity (99.99 % pure according to GDMS), the effect of impurities on the Au freezing temperature measured with Pt/Pd thermocouple was further investigated.
Fixed Point Theorems for Asymptotically Contractive Multimappings
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M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
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...
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 ...
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...
Duan's fixed point theorem: Proof and generalization
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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.
General Common Fixed Point Theorems and Applications
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Shyam Lal Singh
2012-01-01
Full Text Available The main result is a common fixed point theorem for a pair of multivalued maps on a complete metric space extending a recent result of Đorić and Lazović (2011 for a multivalued map on a metric space satisfying Ćirić-Suzuki-type-generalized contraction. Further, as a special case, we obtain a generalization of an important common fixed point theorem of Ćirić (1974. Existence of a common solution for a class of functional equations arising in dynamic programming is also discussed.
Simplicial fixed point algorithms and applications
Yang, Z.F.
1996-01-01
Fixed point theory is an important branch of modern mathematics and has always been a major theoretical tool in fields such as differential equations, topology, function analysis, optimal control, economics, and game theory. Its applicability has been increased enormously by the development of
Common Fixed Points for Weakly Compatible Maps
Indian Academy of Sciences (India)
Renu Chugh; Sanjay Kumar
2001-05-01
The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalized the results of Jungck [3], Fisher [1], Kang and Kim [8], Jachymski [2], and Rhoades [9].
A New Fixed Point Theorem and Applications
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Min Fang
2013-01-01
Full Text Available A new fixed point theorem is established under the setting of a generalized finitely continuous topological space (GFC-space without the convexity structure. As applications, a weak KKM theorem and a minimax inequalities of Ky Fan type are also obtained under suitable conditions. Our results are different from known results in the literature.
Some Generalizations of Jungck's Fixed Point Theorem
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J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
Generalized Common Fixed Point Results with Applications
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Marwan Amin Kutbi
2014-01-01
Full Text Available We obtained some generalized common fixed point results in the context of complex valued metric spaces. Moreover, we proved an existence theorem for the common solution for two Urysohn integral equations. Examples are presented to support our results.
Uniqueness of entire functions and fixed points
Chang, Jianming; Fang, Mingliang
2002-01-01
Let $f$ be a nonconstant entire function. %If $f(z)=z$ $\\Longleftrightarrow $ $f'(z)=z$, and %$f'(z)=z$ $\\Longrightarrow $ $f''(z)=z$, then $f\\equiv f'$. In particular, If $f$, $f'$ and $f''$ have the same fixed points, then $f\\equiv f'.$
Simplicial fixed point algorithms and applications
Yang, Z.F.
1996-01-01
Fixed point theory is an important branch of modern mathematics and has always been a major theoretical tool in fields such as differential equations, topology, function analysis, optimal control, economics, and game theory. Its applicability has been increased enormously by the development of simpl
Uniqueness of entire functions and fixed points
Chang, Jianming; Fang, Mingliang
2002-01-01
Let $f$ be a nonconstant entire function. %If $f(z)=z$ $\\Longleftrightarrow $ $f'(z)=z$, and %$f'(z)=z$ $\\Longrightarrow $ $f''(z)=z$, then $f\\equiv f'$. In particular, If $f$, $f'$ and $f''$ have the same fixed points, then $f\\equiv f'.$
Fixed points and self-reference
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Raymond M. Smullyan
1984-01-01
Full Text Available It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist.
Precise Point Positioning with Partial Ambiguity Fixing
Li, Pan; Zhang, Xiaohong
2015-01-01
Reliable and rapid ambiguity resolution (AR) is the key to fast precise point positioning (PPP). We propose a modified partial ambiguity resolution (PAR) method, in which an elevation and standard deviation criterion are first used to remove the low-precision ambiguity estimates for AR. Subsequently the success rate and ratio-test are simultaneously used in an iterative process to increase the possibility of finding a subset of decorrelated ambiguities which can be fixed with high confidence. One can apply the proposed PAR method to try to achieve an ambiguity-fixed solution when full ambiguity resolution (FAR) fails. We validate this method using data from 450 stations during DOY 021 to 027, 2012. Results demonstrate the proposed PAR method can significantly shorten the time to first fix (TTFF) and increase the fixing rate. Compared with FAR, the average TTFF for PAR is reduced by 14.9% for static PPP and 15.1% for kinematic PPP. Besides, using the PAR method, the average fixing rate can be increased from 83.5% to 98.2% for static PPP, from 80.1% to 95.2% for kinematic PPP respectively. Kinematic PPP accuracy with PAR can also be significantly improved, compared to that with FAR, due to a higher fixing rate. PMID:26067196
The universal cardinal ordering of fixed points
Energy Technology Data Exchange (ETDEWEB)
San Martin, Jesus [Departamento de Matematica Aplicada, E.U.I.T.I, Universidad Politecnica de Madrid, Ronda de Valencia 3, 28012 Madrid (Spain); Departamento de Fisica Matematica y Fluidos, U.N.E.D. Senda del Rey 9, 28040 Madrid (Spain); Moscoso, Ma Jose [Departamento de Matematica Aplicada, E.U.I.T.I, Universidad Politecnica de Madrid, Ronda de Valencia 3, 28012 Madrid (Spain); Gonzalez Gomez, A. [Departamento de Matematica Aplicada a los Recursos Naturales, E.T. Superior de Ingenieros de Montes, Universidad Politecnica de Madrid, 28040 Madrid (Spain)], E-mail: antonia.gonzalez@upm.es
2009-11-30
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)
Emergent physics: Fermi-point scenario.
Volovik, Grigory
2008-08-28
The Fermi-point scenario of emergent gravity has the following consequences: gravity emerges together with fermionic and bosonic matter; emergent fermionic matter consists of massless Weyl fermions; emergent bosonic matter consists of gauge fields; Lorentz symmetry persists well above the Planck energy; space-time is naturally four dimensional; the Universe is naturally flat; the cosmological constant is naturally small or zero; the underlying physics is based on discrete symmetries; 'quantum gravity' cannot be obtained by quantization of Einstein equations; and there is no contradiction between quantum mechanics and gravity, etc.
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.
An Extension of Gregus Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. O. Olaleru
2007-03-01
Full Text Available Let C be a closed convex subset of a complete metrizable topological vector space (X,d and T:CÃ¢Â†Â’C a mapping that satisfies d(Tx,TyÃ¢Â‰Â¤ad(x,y+bd(x,Tx+cd(y,Ty+ed(y,Tx+fd(x,Ty for all x,yÃ¢ÂˆÂˆC, where 0fixed point. The above theorem, which is a generalization and an extension of the results of several authors, is proved in this paper. In addition, we use the Mann iteration to approximate the fixed point of T.
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......-point approximation algorithm which maintains a single copy of intermediate results. We then prove the correctness of this algorithm....
Fixed point theory in distance spaces
Kirk, William
2014-01-01
This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain re...
Large mixing angles for neutrinos from infrared fixed points
Casas, J A; Navarro, I
2003-01-01
Radiative amplification of neutrino mixing angles may explain the large values required by solar and atmospheric neutrino oscillations. Implementation of such mechanism in the Standard Model and many of its extensions (including the Minimal Supersymmetric Standard Model) to amplify the solar angle, the atmospheric or both requires (at least two) quasi-degenerate neutrino masses, but is not always possible. When it is, it involves a fine-tuning between initial conditions and radiative corrections. In supersymmetric models with neutrino masses generated through the Kahler potential, neutrino mixing angles can easily be driven to large values at low energy as they approach infrared pseudo-fixed points at large mixing (in stark contrast with conventional scenarios, that have infrared pseudo-fixed points at zero mixing). In addition, quasi-degeneracy of neutrino masses is not always required.
On Fixed Points of Linguistic Dynamic Systems
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Linguistic dynamic systems (LDS) are dynamic systems whose state variables are generalized from numbers to words. Generally speaking, LDS can model all evolving processes in word domains by using linguistic evolving laws which are naturally the linguistic extension of evolving laws in numbers. There are two kinds of LDS; namely, type-I and type-II LDS. If the word domain is modeled by fuzzy sets, then the evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart. On the other hand, the evolving laws of a type-II LDS are modeled by fuzzy if/then rules. Note that the state spaces of both type-I and type-II LDSs are word continuum. However, in practice, the representation of the state space of a type-II LDS consists of finite number while its computation actually involves a word continuum. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. The properties of the fixed point of type-II LDS are also studied. In addition, linguistic controllers are designed to control type-II LDS to goal states specified in words.
Fixed points and controllability in delay systems
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Schaefer's fixed point theorem is used to study the controllability in an infinite delay system x ′ ( t = G ( t , x t + ( B u ( t . A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system x ′ ( t = λ [ G ( t , x t + ( B u ( t ] , 0 < λ < 1 , then there exists a solution for λ = 1 . The a priori bound is established by means of a Liapunov functional or applying an integral inequality. Applications to integral control systems are given to illustrate the approach.
Holographic non-Fermi-liquid fixed points.
Faulkner, Tom; Iqbal, Nabil; Liu, Hong; McGreevy, John; Vegh, David
2011-04-28
Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS(2)) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.
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.
Duality Fixed Point and Zero Point Theorems and Applications
Directory of Open Access Journals (Sweden)
Qingqing Cheng
2012-01-01
Full Text Available The following main results have been given. (1 Let E be a p-uniformly convex Banach space and let T:E→E* be a (p-1-L-Lipschitz mapping with condition 0<(pL/c21/(p-1<1. Then T has a unique generalized duality fixed point x*∈E and (2 let E be a p-uniformly convex Banach space and let T:E→E* be a q-α-inverse strongly monotone mapping with conditions 1/p+1/q=1, 0<(q/(q-1c2q-1<α. Then T has a unique generalized duality fixed point x*∈E. (3 Let E be a 2-uniformly smooth and uniformly convex Banach space with uniformly convex constant c and uniformly smooth constant b and let T:E→E* be a L-lipschitz mapping with condition 0<2b/c2<1. Then T has a unique zero point x*. These main results can be used for solving the relative variational inequalities and optimal problems and operator equations.
Equilibria, Fixed Points, and Complexity Classes
Yannakakis, Mihalis
2008-01-01
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games (stochastic and other games); stable configurations of neural networks; analysing basic stochastic models for evolution like branching processes and for language like stochastic context-free grammars; and models that incorporate the basic primitives of probability and recursion like recursive Markov chains. It is not known whether these problems can be solved in polynomial time. There are certain common computational principles underlying different types of equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP. Representative complete problems for these classes are respectively, pure Nash equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria in 2-player normal form games, and (mixed) Nash equilibria in normal form games with 3 (or ...
Fixed point theorems for generalized Lipschitzian semigroups
Directory of Open Access Journals (Sweden)
Jong Soo Jung
2001-01-01
semigroup of K into itself, that is, for s∈G, ‖Tsx−Tsy‖≤as‖x−y‖+bs(‖x−Tsx‖+‖y−Tsy‖+cs(‖x−Tsy‖+‖y−Tsx‖, for x,y∈K where as,bs,cs>0 such that there exists a t1∈G such that bs+cs<1 for all s≽t1. It is proved that if there exists a closed subset C of K such that ⋂sco¯{Ttx:t≽s}⊂C for all x∈K, then with [(α+βp(αp⋅2p−1−1/(cp−2p−1βp⋅Np]1/p<1 has a common fixed point, where α=lim sups(as+bs+cs/(1-bs-cs and β=lim sups(2bs+2cs/(1-bs-cs.
Lifting fixed points of completely positive semigroups
Prunaru, Bebe
2011-01-01
Let $\\{\\phi_s\\}_{s\\in S}$ be a commutative semigroup of completely positive and contractive linear maps acting on a von Neumann algebra $N$. Assume there exists a semigroup $\\{\\alpha_s\\}_{s\\in S}$ of *-endomorphisms of some larger von Neumann algebra $M\\supset N$ and a projection $p\\in M$ with $N=pMp$ such that $\\alpha_s(1-p)\\le 1-p$ for every $s\\in S$ and $\\phi_s(y)=p\\alpha_s(y)p$ for all $y\\in N$. If $\\inf_{s\\in S}\\alpha_s(1-p)=0$ then we show that the map $E:M\\to N$ defined by $E(x)=pxp$ for $x\\in M$ induces a complete isometry between the fixed point spaces of $\\{\\alpha_s\\}_{s\\in S}$ and $\\{\\phi_s\\}_{s\\in S}$.
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.
Fixed Points for Stochastic Open Chemical Systems
Malyshev, V A
2011-01-01
In the first part of this paper we give a short review of the hierarchy of stochastic models, related to physical chemistry. In the basement of this hierarchy there are two models --- stochastic chemical kinetics and the Kac model for Boltzman equation. Classical chemical kinetics and chemical thermodynamics are obtained as some scaling limits in the models, introduced below. In the second part of this paper we specify some simple class of open chemical reaction systems, where one can still prove the existence of attracting fixed points. For example, Michaelis\\tire Menten kinetics belongs to this class. At the end we present a simplest possible model of the biological network. It is a network of networks (of closed chemical reaction systems, called compartments), so that the only source of nonreversibility is the matter exchange (transport) with the environment and between the compartments. Keywords: chemical kinetics, chemical thermodynamics, Kac model, mathematical biology
MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS
Institute of Scientific and Technical Information of China (English)
Hassen Aydi; Erdal Karapinar; Calogero Vetro
2012-01-01
In 2011,Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces.In our paper,we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction.
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 for Pseudocontractive Mappings on Unbounded Domains
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García-Falset Jesús
2010-01-01
Full Text Available We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integral equations is given.
Fixed Points of -Endomorphisms of a Free Metabelian Lie Algebra
Indian Academy of Sciences (India)
Naime Ekici; Demet Parlak Sönmez
2011-11-01
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.
On Approximate Coincidence Point Properties and Their Applications to Fixed Point Theory
Wei-Shih Du
2012-01-01
We first establish some existence results concerning approximate coincidence point properties and approximate fixed point properties for various types of nonlinear contractive maps in the setting of cone metric spaces and general metric spaces. From these results, we present some new coincidence point and fixed point theorems which generalize Berinde-Berinde's fixed point theorem, Mizoguchi-Takahashi's fixed point theorem, and some well-known results in the literature.
Brouwer's ε-fixed point from Sperner's lemma
Dalen, D. van
2009-01-01
It is by now common knowledge that Brouwer gave mathematics in 1911 a miraculous tool, the fixed point theorem, and that later in life, he disavowed it. It usually came as a shock when he replied to the question “is the fixed point theorem correct ?” with a point blank “no”. This rhetoric exchange d
Characteristic Formulae for Relations with Nested Fixed Points
Directory of Open Access Journals (Sweden)
Luca Aceto
2012-02-01
Full Text Available A general framework for the connection between characteristic formulae and behavioral semantics is described in [2]. This approach does not suitably cover semantics defined by nested fixed points, such as the n-nested simulation semantics for n greater than 2. In this study we address this deficiency and give a description of nested fixed points that extends the approach for single fixed points in an intuitive and comprehensive way.
Existence of Multiple Fixed Points for Nonlinear Operators and Applications
Institute of Scientific and Technical Information of China (English)
Jing Xian SUN; Ke Mei ZHANG
2008-01-01
In this paper,by the fixed point index theory,the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied.Under suitable conditions,the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved.Finally,the theoretical results are applied to a nonlinear system of Hammerstein integral equations.
Replicon modes and fixed-point marginal stability for systems with extended impurities
de Cesare, Luigi; Mercaldo, Maria Teresa
1999-08-01
The fixed-point marginal stability, found for systems with extended quenched impurities within a one-step replica symmetry breaking (RSB) renormalization-group treatment, is further explored in terms of replicon eigenvalues, recently introduced as a simple way to investigate the fixed-point stability properties with respect to the continuous RSB modes. We find that the marginal stability occurs again when these modes are taken into account, in contrast with the short-range correlated impurity case where the continuous RSB fluctuations drastically change the one-step RSB fixed-point stability scenario.
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 POINT RESULTS ON METRIC-TYPE SPACES
Institute of Scientific and Technical Information of China (English)
Monica COSENTINO; Peyman SALIMI; Pasquale VETRO
2014-01-01
In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.
Caristi Fixed Point Theorem in Metric Spaces with a Graph
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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 fixed point results for dualistic rational contractions
Directory of Open Access Journals (Sweden)
Muhammad Nazam
2016-10-01
Full Text Available In this paper, we introduce a new contraction called dualistic contraction of rational type and obtain some fixed point results. These results generalize various comparable results appeared in the literature. We provide an example to show the superiority of our results over corresponding fixed point results proved in metric spaces.
FIXED POINTS THEOREMS IN MULTI-METRIC SPACES
Directory of Open Access Journals (Sweden)
Laurentiu I. Calmutchi
2011-07-01
Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.
Fixed points and infrared completion of quantum gravity
Christiansen, Nicolai; Pawlowski, Jan M; Rodigast, Andreas
2012-01-01
The phase diagram of four-dimensional Einstein-Hilbert gravity is studied using Wilson's renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed.
STABILITY OF A PARABOLIC FIXED POINT OF REVERSIBLE MAPPINGS
Institute of Scientific and Technical Information of China (English)
LIUBIN; YOUJIANGONG
1994-01-01
KAM theorem of reversible system is used to provide a sufficient condition which guarantees the stability of a parabolic fixed point of reversible mappings, The main idea is to discuss when the parabolic fixed point is surrounded by closed invariant carves and thus exhibits stable behaviour.
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...
Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Du Wei-Shih
2010-01-01
Full Text Available We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions.
ON COLLECTIVELY FIXED POINT THEOREMS ON FC-SPACES
Institute of Scientific and Technical Information of China (English)
Yongjie Piao
2010-01-01
Based on a KKM type theorem on FC-space,some new fixed point theorems for Fan-Browder type are established,and then some collectively fixed point theorems for a family of Φ-maps defined on product space of FC-spaees are given.These results generalize and improve many corresponding results.
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
Fixed points in a group of isometries
Voorneveld, M.
2001-01-01
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
Infra-red fixed points in supersymmetry
Indian Academy of Sciences (India)
B Ananthanarayan
2000-07-01
Model independent constraints on supersymmetric models emerge when certain couplings are drawn towards their infra-red (quasi) ﬁxed points in the course of their renormalization group evolution. The general principles are ﬁrst reviewed and the conclusions for some recent studies of theories with -parity and baryon and lepton number violations are summarized.
Fixed points and contraction factor functions
Voorneveld, M.
2001-01-01
In a complete metric space (X; d), we dene w-distance functions p : X X ! [0; 1), of which the metric d is a special case, and contraction factor functions r : X X ! [0; 1) such that if p(Tx;Ty) r(x; y)p(x; y) for all x; y 2 X, thenT : X ! X has a (unique) xed point.
Fixed points and contraction factor functions
Voorneveld, M.
2000-01-01
In a complete metric space (X; d), we dene w-distance functions p : X X ! [0; 1), of which the metric d is a special case, and contraction factor functions r : X X ! [0; 1) such that if p(Tx;Ty) r(x; y)p(x; y) for all x; y 2 X, thenT : X ! X has a (unique) xed point.
Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
Klebanov, Igor R; Pufu, Silviu S; Safdi, Benjamin R
2012-01-01
The renormalized entanglement entropy (REE) across a circle of radius R has been proposed as a c-function in Poincar\\'e invariant (2+1)-dimensional field theory. A proof has been presented of its monotonic behavior as a function of R, based on the strong subadditivity of entanglement entropy. However, this proof does not directly establish stationarity of REE at conformal fixed points of the renormalization group. In this note we study the REE for the free massive scalar field theory near the UV fixed point described by a massless scalar. Our numerical calculation indicates that the REE is not stationary at the UV fixed point.
Scheme Transformations in the Vicinity of an Infrared Fixed Point
DEFF Research Database (Denmark)
Ryttov, Thomas; Shrock, Robert
2012-01-01
We analyze the effect of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions. We show that there is far less freedom in carrying out such scheme transformations in this case than at an ultraviolet fixed point....... We construct a transformation from the $\\bar{MS}$ scheme to a scheme with a vanishing three-loop term in the $\\beta$ function and use this to assess the scheme dependence of an infrared fixed point in SU($N$) theories with fermions. Implications for the anomalous dimension of the fermion bilinear...
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Interconnection of private operational fixed point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS....137 Interconnection of private operational fixed point-to-point microwave stations....
Fixing the quantum three-point function
Energy Technology Data Exchange (ETDEWEB)
Jiang, Yunfeng; Kostov, Ivan [Institut de Physique Théorique, DSM, CEA, URA2306 CNRS,Saclay, F-91191 Gif-sur-Yvette (France); Loebbert, Florian [School of Natural Sciences, Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Niels Bohr International Academy & Discovery Center, Niels Bohr Institute,Blegdamsvej 17, 2100 Copenhagen (Denmark); Serban, Didina [Institut de Physique Théorique, DSM, CEA, URA2306 CNRS,Saclay, F-91191 Gif-sur-Yvette (France)
2014-04-03
We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and long-range spin chains. This transformation can be traced back to a combination of boost operators and an inhomogeneous version of Baxter’s corner transfer matrix. We reproduce the existing results for the one-loop structure constants in a simplified form and indicate how to use the method at higher loop orders. Then we evaluate the one-loop structure constants in the quasiclassical limit and compare them with the recent strong coupling computation.
Proceedings 8th Workshop on Fixed Points in Computer Science
Miller, Dale; 10.4204/EPTCS.77
2012-01-01
This volume contains the proceedings of the Eighth Workshop on Fixed Points in Computer Science which took place on 24 March 2012 in Tallinn, Estonia as an ETAPS-affiliated workshop. Past workshops have been held in Brno (1998, MFCS/CSL workshop), Paris (2000, LC workshop), Florence (2001, PLI workshop), Copenhagen (2002, LICS (FLoC) workshop), Warsaw (2003, ETAPS workshop), Coimbra (2009, CSL workshop), and Brno (2010, MFCS-CSL workshop). Fixed points play a fundamental role in several areas of computer science and logic by justifying induction and recursive definitions. The construction and properties of fixed points have been investigated in many different frameworks such as: design and implementation of programming languages, program logics, and databases. The aim of this workshop is to provide a forum for researchers to present their results to those members of the computer science and logic communities who study or apply the theory of fixed points.
On the δ-continuous fixed point property
Directory of Open Access Journals (Sweden)
F. Cammaroto
1990-01-01
Full Text Available In this paper, we define and investigate the δ-continuous retraction and the δ-continuous fixed point property. Theorem 1 of Connell [11] and Theorem 3.4 of Arya and Deb [2] are improved.
On some fixed point theorems in Banach spaces
Directory of Open Access Journals (Sweden)
D. V. Pai
1982-01-01
Full Text Available In this paper, some fixed point theorems are proved for multi-mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.
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].
Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces
Institute of Scientific and Technical Information of China (English)
H.M.Abu-Donia; A.A.Nasef
2008-01-01
The purpose of this paper is to introduce some types of compatibility of maps, and we prove some common fixed point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaces which defined by J.H.Park.
Combining Deduction Modulo and Logics of Fixed-Point Definitions
Baelde, David
2012-01-01
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of recursive specifications. These specifications are not directly complemented by fixed-point reasoning techniques and, correspondingly, do not have to satisfy strong monotonicity restrictions. We show how to incorporate a rewriting capability into logics of fixed-point definitions towards additionally supporting recursive specifications. In particular, we describe a natural deduction calculus that adds a form of "closed-world" equality - a key ingredient to supporting fixed-point definitions - to deduction modulo, a framework for extending a logic with a rewriting layer operating on formulas. We show that our calculus enjoys strong normalizability when the rewrite system satisfies general properties and we demonstrate its usefulness in specifying and reasoning about syntax-based ...
The Fixed Point Theory for Some Generalized Nonexpansive Mappings
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Enrique Llorens Fuster
2011-01-01
Full Text Available We study some aspects of the fixed point theory for a class of generalized nonexpansive mappings, which among others contain the class of generalized nonexpansive mappings recently defined by Suzuki in 2008.
On Approximate -Ternary -Homomorphisms: A Fixed Point Approach
Directory of Open Access Journals (Sweden)
Cho YJ
2011-01-01
Full Text Available Using fixed point methods, we prove the stability and superstability of -ternary additive, quadratic, cubic, and quartic homomorphisms in -ternary rings for the functional equation , for each .
Fixed Point Theorems for Times Reasonable Expansive Mapping
Directory of Open Access Journals (Sweden)
Chen Chunfang
2008-01-01
Full Text Available Abstract Based on previous notions of expansive mapping, times reasonable expansive mapping is defined. The existence of fixed point for times reasonable expansive mapping is discussed and some new results are obtained.
ORIGINAL Some Generalized Fixed Point Results on Compact ...
African Journals Online (AJOL)
Department of Mathematics College of Natural Science Jimma. University ... Fixed point theory in metric spaces perhaps originated from the well known .... METHODOLOGY. Study Site and Period ..... gs, J. Land, Mathsec. 37, 74-79. Fisher, B.
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.
Tracking unstable fixed points in parametrically dynamic systems
Mondragón, Raúl J.; Arrowsmith, David K.
1997-02-01
The method of Ott, Grebogi and Yorke is extended to control a two-parameter system when one of the parameters is time dependent and the other is used as the control-parameter. As one of the parameters changes, the unstable fixed point follows its branch of the bifurcation tree. We control a chaotic orbit such that it tracks this “moving” unstable fixed point using an adaptive control method.
Fixed Points of Multivalued Maps in Modular Function Spaces
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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.
Fixed Point Theorems for Generalized Mizoguchi-Takahashi Graphic Contractions
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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.
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....
Fixed Points of Two-Sided Fractional Matrix Transformations
Directory of Open Access Journals (Sweden)
Handelman David
2007-01-01
Full Text Available Let and be complex matrices, and consider the densely defined map on matrices. Its fixed points form a graph, which is generically (in terms of nonempty, and is generically the Johnson graph ; in the nongeneric case, either it is a retract of the Johnson graph, or there is a topological continuum of fixed points. Criteria for the presence of attractive or repulsive fixed points are obtained. If and are entrywise nonnegative and is irreducible, then there are at most two nonnegative fixed points; if there are two, one is attractive, the other has a limited version of repulsiveness; if there is only one, this fixed point has a flow-through property. This leads to a numerical invariant for nonnegative matrices. Commuting pairs of these maps are classified by representations of a naturally appearing (discrete group. Special cases (e.g., is in the radical of the algebra generated by and are discussed in detail. For invertible size two matrices, a fixed point exists for all choices of if and only if has distinct eigenvalues, but this fails for larger sizes. Many of the problems derived from the determination of harmonic functions on a class of Markov chains.
Image integrity authentication scheme based on fixed point theory.
Li, Xu; Sun, Xingming; Liu, Quansheng
2015-02-01
Based on the fixed point theory, this paper proposes a new scheme for image integrity authentication, which is very different from digital signature and fragile watermarking. By the new scheme, the sender transforms an original image into a fixed point image (very close to the original one) of a well-chosen transform and sends the fixed point image (instead of the original one) to the receiver; using the same transform, the receiver checks the integrity of the received image by testing whether it is a fixed point image and locates the tampered areas if the image has been modified during the transmission. A realization of the new scheme is based on Gaussian convolution and deconvolution (GCD) transform, for which an existence theorem of fixed points is proved. The semifragility is analyzed via commutativity of transforms, and three commutativity theorems are found for the GCD transform. Three iterative algorithms are presented for finding a fixed point image with a few numbers of iterations, and for the whole procedure of image integrity authentication; a fragile authentication system and a semifragile one are separately built. Experiments show that both the systems have good performance in transparence, fragility, security, and tampering localization. In particular, the semifragile system can perfectly resist the rotation by a multiple of 90° flipping and brightness attacks.
Design and Implementation of Fixed Point Arithmetic Unit
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S Ramanathan
2016-06-01
Full Text Available This paper aims at Implementation of Fixed Point Arithmetic Unit. The real number is represented in Qn.m format where n is the number of bits to the left of the binary point and m is the number of bits to the right of the binary point. The Fixed Point Arithmetic Unit was designed using Verilog HDL. The Fixed Point Arithmetic Unit incorporates adder, multiplier and subtractor. We carried out the simulations in ModelSim and Cadence IUS, used Cadence RTL Compiler for synthesis and used Cadence SoC Encounter for physical design and targeted 180 nm Technology for ASIC implementation. From the synthesis result it is found that our design consumes 1.524 mW of power and requires area 20823.26 μm2 .
Some Common Fixed Point Theorems in Generalized Vector Metric Spaces
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Rajesh Shrivastava
2013-11-01
Full Text Available In this paper we give some theorems on point of coincidence and common fixed point for two self mappings satisfying some general contractive conditions in generalized vector spaces. Our results generalize some well-known recent results in this direction.
On Common Fixed Point of Noncompatible Mapping Pairs
Institute of Scientific and Technical Information of China (English)
朱元泽; 吕中学
2002-01-01
In this paper, two common fixed point theorems for noncompatible maps in a metric space have been proved under the condition of without taking completeness of the space or continuity of the mapings into account. The related common point theorems were improved.
Design and DSP Implementation of Fixed-Point Systems
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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.
Retracts, fixed point property and existence of periodic points
Institute of Scientific and Technical Information of China (English)
MAI; Jiehua(
2001-01-01
［1］Sarkovskii, A. N. , Coexistence of cycles of a continuous map of a line into itself, Ukrain. Mat. Z. , 1964, 16(1): 61－71.［2］Li, T. Y., Misiurewicz, M., Pianigiani, G. et al., No division implies chaos, Trans. Amer. Math. Soc., 1982, 273(1):191－199.［3］Mai Jiehua, Multi-separation, centrifugality and centripetality imply chaos, Trans. Amer. Math. Soc., 1999, 351 (1):343－351.［4］Block, L., Coppel, W., Dynamics in One Dimension, Berlin, New York: Springer-Verlag, 1992.［5］Misiurewicz, M., Periodic points of maps of degree one of a circle, Ergod. Th. & Dynam. Sys. , 1982, 2(2): 221－227.［6］Alseda, L., Llibre, J., Misiurewicz, M., Periodic orbits of maps of Y, Trans. Amer. Math. Soc., 1989, 313(2): 475－538.［7］Baldwin, S. , An extension of Sarkovskii's theorem to the n-od, Ergod. Th. & Dynam. Sys. , 1991, 11(2): 249－271.［8］Alseda, L. , Ye, X. D. , No division and the set of periods for tree maps, Ergod. Th. & Dynam. Sys., 1995, 15(2): 221－237.［9］Leseduarte, M. C., Llibre, J., On the set of periods for σ maps, Trans. Amer. Math. Soc., 1995, 347(12): 4899－4942.［10］Armstrong, M. A., Basic Topology, New York: Springer-Verlag, 1983.［11］Dicks, W. , Llibre, J. , Orientation-preserving self-homeomorphisms of the surface of genus two have points of period at most two, Proc. Amer. Math. Soc., 1996, 124(5): 1583－1591.［12］Kolev, B., Peroueme, M. C., Recurrent surface homeonorphisms, Math. Proc. Camb. Phil. Soc., 1998, 124(1): 161－168.［13］Franks, J., Generalizations of the Poincare-Birkhoff theorem, Ann. Math., 1988, 128(1): 139－151.［14］Hall, G. R. , Some problems on dynamics of annulus maps, Contemporary Mathematics, 1988, 81(1): 135－152.［15］Barge, M., Matison, T., A Poincare-Birkhoff theorem on invariant plane continua, Ergod. Th. & Dynam. Sys., 1998, 18(1): 41－52.［16］Munkres, J. Pt., Topology, Englewood Cliffs: Prentice-Hall, 1975.
Fixed Points in Discrete Models for Regulatory Genetic Networks
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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.
IR fixed points in $SU(3)$ gauge Theories
Ishikawa, K -I; Nakayama, Yu; Yoshie, Y
2015-01-01
We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$ fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cut-off, which we cannot remove in the conformal field theories in sharp contrast with the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8 $ and $N_f=7$ and indeed identify the location of the IR fixed points in all cases.
Matrix product density operators: Renormalization fixed points and boundary theories
Energy Technology Data Exchange (ETDEWEB)
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)
2017-03-15
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Border collisions inside the stability domain of a fixed point
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2016-05-01
Recent studies on a power electronic DC/AC converter (inverter) have demonstrated that such systems may undergo a transition from regular dynamics (associated with a globally attracting fixed point of a suitable stroboscopic map) to chaos through an irregular sequence of border-collision events. Chaotic dynamics of an inverter is not suitable for practical purposes. However, the parameter domain in which the stroboscopic map has a globally attracting fixed point has generally been considered to be uniform and suitable for practical use. In the present paper we show that this domain actually has a complicated interior structure formed by boundaries defined by persistence border collisions. We describe a simple approach that is based on symbolic dynamics and makes it possible to detect such boundaries numerically. Using this approach we describe several regions in the parameter space leading to qualitatively different output signals of the inverter although all associated with globally attracting fixed points of the corresponding stroboscopic map.
Fixed Points of Two-Sided Fractional Matrix Transformations
Directory of Open Access Journals (Sweden)
David Handelman
2007-02-01
Full Text Available Let C and D be nÃƒÂ—n complex matrices, and consider the densely defined map ÃÂ†C,D:XÃ¢Â†Â¦(IÃ¢ÂˆÂ’CXDÃ¢ÂˆÂ’1 on nÃƒÂ—n matrices. Its fixed points form a graph, which is generically (in terms of (C,D nonempty, and is generically the Johnson graph J(n,2n; in the nongeneric case, either it is a retract of the Johnson graph, or there is a topological continuum of fixed points. Criteria for the presence of attractive or repulsive fixed points are obtained. If C and D are entrywise nonnegative and CD is irreducible, then there are at most two nonnegative fixed points; if there are two, one is attractive, the other has a limited version of repulsiveness; if there is only one, this fixed point has a flow-through property. This leads to a numerical invariant for nonnegative matrices. Commuting pairs of these maps are classified by representations of a naturally appearing (discrete group. Special cases (e.g., CDÃ¢ÂˆÂ’DC is in the radical of the algebra generated by C and D are discussed in detail. For invertible size two matrices, a fixed point exists for all choices of C if and only if D has distinct eigenvalues, but this fails for larger sizes. Many of the problems derived from the determination of harmonic functions on a class of Markov chains.
Disordered horizons: Holography of randomly disordered fixed points
Hartnoll, Sean A
2014-01-01
We deform conformal field theories with classical gravity duals by marginally relevant random disorder. We show that the disorder generates a flow to IR fixed points with a finite amount of disorder. The randomly disordered fixed points are characterized by a dynamical critical exponent $z>1$ that we obtain both analytically (via resummed perturbation theory) and numerically (via a full simulation of the disorder). The IR dynamical critical exponent increases with the magnitude of disorder, probably tending to $z \\to \\infty$ in the limit of infinite disorder.
Variational inequalities and fixed point problems : a survey
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Renu Chugh
2014-06-01
Full Text Available The variational inequality problem provides a broad unifying setting for the study of optimization, equilibrium and related problems and serves as a useful computational framework for the solution of a host of problems in very diverse applications. Variational inequalities have been a classical subject in mathematical physics, particularly in the calculus of variations associated with the minimization of infinite-dimensional functionals. This paper presents a survey of main results related to variational inequalities and fixed point problems defined on real Hilbert spaces and Banach spaces. Keywords: Fixed Point Problem, Inverse-Strongly-Monotone Mappings, Monotone Mappings, Projection Mappings, Variational Inequality Problem.
Convergence theorems for fixed points of demicontinuous pseudocontractive mappings
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Chidume CE
2005-01-01
Full Text Available Let be an open subset of a real uniformly smooth Banach space . Suppose is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where denotes the closure of . Then, it is proved that (i for every ; (ii for a given , there exists a unique path , , satisfying . Moreover, if or there exists such that the set is bounded, then it is proved that, as , the path converges strongly to a fixed point of . Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of .
Stability of common fixed points in uniform spaces
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Singh Shyam
2011-01-01
Full Text Available Abstract Stability results for a pair of sequences of mappings and their common fixed points in a Hausdorff uniform space using certain new notions of convergence are proved. The results obtained herein extend and unify several known results. AMS(MOS Subject classification 2010: 47H10; 54H25.
Wess Zumino Couplings for Generalized $\\Sigma$ Orbifold Fixed-points
Ospina-Giraldo, J F
2000-01-01
The Wess-Zumino couplings for generalized sigma-orbifold fixed-points are presented and the generalized GS 6-form that encoding the complete sigma-standard gauge-gravitational-non standard gauge anomaly and its opposite inflow is derived.
Fixed Points of Averages of Resolvents: Geometry and Algorithms
Bauschke, Heinz H; Wylie, Calvin J S
2011-01-01
To provide generalized solutions if a given problem admits no actual solution is an important task in mathematics and the natural sciences. It has a rich history dating back to the early 19th century when Carl Friedrich Gauss developed the method of least squares of a system of linear equations - its solutions can be viewed as fixed points of averaged projections onto hyperplanes. A powerful generalization of this problem is to find fixed points of averaged resolvents (i.e., firmly nonexpansive mappings). This paper concerns the relationship between the set of fixed points of averaged resolvents and certain fixed point sets of compositions of resolvents. It partially extends recent work for two mappings on a question of C. Byrne. The analysis suggests a reformulation in a product space. Furthermore, two new algorithms are presented. A complete convergence proof that is based on averaged mappings is provided for the first algorithm. The second algorithm, which currently has no convergence proof, iterates a map...
Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces
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Balwant Singh Thakur
1999-01-01
Full Text Available Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1
Fixed Point Theorems of the Iterated Function Systems
Institute of Scientific and Technical Information of China (English)
Ji You-qing; Liu Zhi; Ri Song-il
2016-01-01
In this paper, we present some fixed point theorems of iterated function systems consisting ofα-ψ-contractive type mappings in Fractal space constituted by the compact subset of metric space and iterated function systems consisting of Banach contractive mappings in Fractal space constituted by the compact subset of general-ized metric space, which is also extensively applied in topological dynamic system.
Fixed Points in Self-Similar Analysis of Time Series
Gluzman, S.; Yukalov, V. I.
1998-01-01
Two possible definitions of fixed points in the self-similar analysis of time series are considered. One definition is based on the minimal-difference condition and another, on a simple averaging. From studying stock market time series, one may conclude that these two definitions are practically equivalent. A forecast is made for the stock market indices for the end of March 1998.
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.
Solution of fractional differential equations via coupled fixed point
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Hojjat Afshari
2015-11-01
Full Text Available In this article, we investigate the existence and uniqueness of a solution for the fractional differential equation by introducing some new coupled fixed point theorems for the class of mixed monotone operators with perturbations in the context of partially ordered complete metric space.
Wess Zumino Couplings for Generalized Sigma Orbifold Fixed-points
Giraldo, Juan Fernando Ospina
2000-01-01
The Wess-Zumino couplings for generalized sigma-orbifold fixed-points are presented and the generalized GS 6-form that encoding the complete sigma-standard gauge-gravitational-non standard gauge anomaly and its opposite inflow is derived.
Some Fixed Point Results for TAC-Type Contractive Mappings
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Sumit Chandok
2016-01-01
Full Text Available We prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.
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.
Quantum fixed-point search algorithm with general phase shifts
Institute of Scientific and Technical Information of China (English)
2008-01-01
Grover presented the Phase-π/3 search by replacing the selective inversions by selective phase shifts of π/3.In this paper,we review and discuss the fixed-point search with general but equal phase shifts and the fixedpoint search with general but different phase shifts.
Fixed point theorems for d-complete topological spaces I
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Troy L. Hicks
1992-01-01
Full Text Available Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality.
Common fixed point result by using weak commutativity
Gupta, Vishal; Mani, Naveen; Devi, Seema
2017-07-01
The main objective of this paper is to establish a common fixed point result for ten mappings satisfying a weaker condition, has been obtained. Our main result generalizes various previously known results such as Kannan, Fisher, Hardy & Rogers and Pande & Dubey.
ISHIKAWA ITERATIVE PROCEDURE FORAPPROXIMATING FIXED POINTS OF STRICTLY PSEUDOCONTRACTIVE MAPPINGS
Institute of Scientific and Technical Information of China (English)
ZengLuchuan
2003-01-01
It is shown that any fixed point of a Lipschitzian,strictly pseudocontractive muping T on a closed convex subset K of a Banach space X may be approximated by Ishikawa iterative procedure. The results in this paper provide the new convergence criteria and novel convergence rate estimate for Ishikawa iterative sequence.
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...
Fixed Points on Abstract Structures without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita V.
2002-01-01
In this paper we present a study of definability properties of fixed points of effective operators on abstract structures without the equality test. In particular we prove that Gandy theorem holds for abstract structures. This provides a useful tool for dealing with recursive definitions using -f...
Common Fixed Points for Multimaps in Metric Spaces
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Rafa Espínola
2010-01-01
Full Text Available We discuss the existence of common fixed points in uniformly convex metric spaces for single-valued pointwise asymptotically nonexpansive or nonexpansive mappings and multivalued nonexpansive, ∗-nonexpansive, or ε-semicontinuous maps under different conditions of commutativity.
STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION VIA FIXED POINT
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a nonlinear neutral differential equation is considered.By a fixed point theory,we give some conditions to ensure that the zero solution to the equation is asymptotically stable.Some existing results are improved and generalized.
Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces
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Lu-Chuan Ceng
2014-01-01
Full Text Available We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.
Fixed point theorems for generalized contractions in ordered metric spaces
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
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.
Fixed-rate compressed floating-point arrays
Energy Technology Data Exchange (ETDEWEB)
2014-03-30
ZFP is a library for lossy compression of single- and double-precision floating-point data. One of the unique features of ZFP is its support for fixed-rate compression, which enables random read and write access at the granularity of small blocks of values. Using a C++ interface, this allows declaring compressed arrays (1D, 2D, and 3D arrays are supported) that through operator overloading can be treated just like conventional, uncompressed arrays, but which allow the user to specify the exact number of bits to allocate to the array. ZFP also has variable-rate fixed-precision and fixed-accuracy modes, which allow the user to specify a tolerance on the relative or absolute error.
Gravity Duals of Lifshitz-like Fixed Points
Kachru, Shamit; Mulligan, Michael
2008-01-01
We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent $z$, which governs the anisotropy between spatial and temporal scaling $t \\to \\lambda^z t$, $x \\to \\lambda x$; we focus on the case with $z=2$. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.
Common fixed point theorems for semigroups on metric spaces
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Young-Ye Huang
1999-01-01
if S is a left reversible semigroup of selfmaps on a complete metric space (M,d such that there is a gauge function φ for which d(f(x,f(y≤φ(δ(Of (x,y for f∈S and x,y in M, where δ(Of (x,y denotes the diameter of the orbit of x,y under f, then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M, the sequence of iterates {fn(x} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M,d.
Some common fixed point theorems in fuzzy metric spaces
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Deepak Singh
2012-04-01
Full Text Available The aim of this paper is to prove some common fixed point theorems in (GV-fuzzy metric spaces.While proving our results, we employed the idea of compatibility due to Jungck [14] together with subsequentially continuity due to Bouhadjera and Godet-Thobie [4] respectively (also alternately reciprocal continuity due to Pant [28] together with subcompatibility due to Bouhadjera and Godet-Thobie [4] as in Imdad et al. [12] wherein conditions on completeness of the underlying space (or subspaces together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due to Imdad et al.[10], Mihet [18], Mishra [19], Singh [28] and several others.
A new 6d fixed point from holography
Apruzzi, Fabio; Dibitetto, Giuseppe; Tizzano, Luigi
2016-11-01
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 AdS7 × M 3, where M 3 is topologically an S 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 overline{D6} 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.
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.
Fixed points of holomorphic mappings for domains in Banach spaces
Directory of Open Access Journals (Sweden)
Lawrence A. Harris
2003-01-01
Full Text Available We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.
Signatures of gravitational fixed points at the LHC
Litim, Daniel F
2008-01-01
We study quantum-gravitational signatures at the Large Hadron Collider (LHC) in the context of theories with extra spatial dimensions and a low fundamental Planck scale in the TeV range. Implications of a gravitational fixed point at high energies are worked out using Wilson's renormalisation group. We find that relevant cross-sections involving virtual gravitons become finite. We determine the $5\\sigma$ discovery reach for the fundamental Planck scale based on lepton pair production in hadronic collisions.
Transfinite methods in metric fixed-point theory
Directory of Open Access Journals (Sweden)
W. A. Kirk
2003-01-01
Full Text Available This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author's 1989 result on directionally nonexpansive mappings (which is somewhat sharpened, a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent extension of Caristi's theorem due to Saliga and the author. In each instance, transfinite methods seem necessary.
A common fixed point for operators in probabilistic normed spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [Faculty of Mathematics, Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of)], E-mail: mghaemi@iust.ac.ir; Lafuerza-Guillen, Bernardo [Department of Applied Mathematics, University of Almeria, Almeria (Spain)], E-mail: blafuerz@ual.es; Razani, A. [Department of Mathematics, Faculty of Science, I. Kh. International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of)], E-mail: razani@ikiu.ac.ir
2009-05-15
Probabilistic Metric spaces was introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger [Alsina C, Schweizer B, Sklar A. On the definition of a probabilistic normed spaces. Aequationes Math 1993;46:91-8]. Here, we consider the equicontinuity of a class of linear operators in probabilistic normed spaces and finally, a common fixed point theorem is proved. Application to quantum Mechanic is considered.0.
Computation of fixed point index and its applications
Xing, Hui; Sun, Jingxian
2015-01-01
In this paper, we make the nonlinear double integral equation of Hammerstein type the background of the research. Computation for the fixed point index of operators such as $A=K_{1}F_{1}K_ {2}F_{2}$ is given. As applications of the main results, we investigate the existence of positive solutions to the nonlinear double integral equation of Hammerstein type and the boundary value problem for the system of elliptic partial differential equations.
Existence and Uniqueness of Fixed Point in Partially Ordered Sets
Institute of Scientific and Technical Information of China (English)
Juan J. NIETO; Rosana RODR(I)GUEZ-L(O)PEZ
2007-01-01
We prove some fixed point theorems in partially ordered sets, providing an extension of theBanach contractive mapping theorem. Having studied previously the nondecreasing case, we considerin this paper nonincreasing mappings as well as non monotone mappings. We also present someapplications to first-order ordinary differential equations with periodic boundary conditions, provingthe existence of a unique solution admitting the existence of a lower solution.
Fixed point semantics and partial recursion in Coq
Bertot, Yves; Komendantsky, Vladimir
2008-01-01
International audience; We propose to use the Knaster-Tarski least fixed point theorem as a basis to define recursive functions in the Calculus of Inductive Constructions. This widens the class of functions that can be modelled in type-theory based theorem proving tools to potentially non-terminating functions. This is only possible if we extend the logical framework by adding some axioms of classical logic. We claim that the extended framework makes it possible to reason about terminating or...
Fixed-point B.G. Lee IDCT without multiplication
Zhu, P. P.; Liu, J. G.; Dai, S. K.
2007-12-01
An improved modified approach to compute the inverse discrete cosine transform (IDCT) is proposed based on B. G. Lee algorithm. We replace the multiplication operator in original B. G. Lee algorithm with addition and shift operators and looking-up table to implement the fix-point computation. Due to the absence of the multiplication operator, this modified algorithm will take less time to complete the same computation.
Approximate solutions of common fixed-point problems
Zaslavski, Alexander J
2016-01-01
This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal...
Pseudocontractions in the intermediate sense: Fixed and best proximity points
De la Sen, Manuel
2013-09-01
This paper studies a general contractive condition for a class of two-cyclic self-maps on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same subsets of its domain. If the space is uniformly convex and the subsets are non-empty, closed and convex then all the iterated sequences are proved to converge to a unique closed limiting finite sequence. Such a sequence contains the best proximity points of adjacent subsets which coincide with a unique fixed point if all such subsets intersect.
Fix-point Multiplier Distributions in Discrete Turbulent Cascade Models
Jouault, B; Lipa, P
1998-01-01
One-point time-series measurements limit the observation of three-dimensional fully developed turbulence to one dimension. For one-dimensional models, like multiplicative branching processes, this implies that the energy flux from large to small scales is not conserved locally. This then renders the random weights used in the cascade curdling to be different from the multipliers obtained from a backward averaging procedure. The resulting multiplier distributions become solutions of a fix-point problem. With a further restoration of homogeneity, all observed correlations between multipliers in the energy dissipation field can be understood in terms of simple scale-invariant multiplicative branching processes.
Fixed point theorems in complex valued metric spaces
Directory of Open Access Journals (Sweden)
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.
Fixed Points, Inner Product Spaces, and Functional Equations
Directory of Open Access Journals (Sweden)
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.
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
Combined GPS/GLONASS precise point positioning with fixed GPS ambiguities.
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-09-18
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.
An N/4 fixed-point duality quantum search algorithm
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here a fixed-point duality quantum search algorithm is proposed.This algorithm uses iteratively non-unitary operations and measurements to search an unsorted database.Once the marked item is found,the algorithm stops automatically.This algorithm uses a constant non-unitary operator,and requires N/4 steps on average(N is the number of data from the database) to locate the marked state.The implementation of this algorithm in a usual quantum computer is also demonstrated.
Improved fixed point iterative method for blade element momentum computations
DEFF Research Database (Denmark)
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
to the physical solution, especially for the locations near the blade tip and root where the failure rate of the iterative method is high. The stability and accuracy of aerodynamic calculations and optimizations are greatly reduced due to this problem. The intrinsic mechanisms leading to convergence problems......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...
Picard Approximation of Fixed Points of Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
黄家琳
2003-01-01
Let C be a bounded convex subset in a uniformly convex Banach space X, x0, un∈C, then xn+1=Snxn, where Sn=αn0I+αn1T+αn2T2+…+αnkTk+γnun, αni≥0, 0＜α≤αn0≤b＜1, ∑ki=0αni+γn=1, and n≥1. It is proved that xn converges to a fixed point on T if T is a nonexpansive mapping.
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
On a Fixed Point Theorem of Ky Fan
Institute of Scientific and Technical Information of China (English)
DE BLASI Francesco S.; GEORGIEV Pando Gr.
2002-01-01
We generalize a theorem of Ky Fan about the nearest distance between a closed convex setD in a Banach space E and its image by a function f: D → E, in several directions: (1) for noncompactsets D, when f(D) precompact; (2) for compact D and upper semicontinuous multifunction f; andmore generally, (3) for noncompact D and upper semicontinuous multifunction f with f(D) Hausdorffprecompact.In particular, we prove a version of the fixed point theorem of Kakutani-Ky Fan for multifunctions,whose values are convex closed bounded, thus not necessarily compact.
How to Find a Fixed Point in Shuffle Efficiently
Directory of Open Access Journals (Sweden)
Mikako Kageshima
2013-02-01
Full Text Available In electronic voting or whistle blowing, anonymity is necessary. Shuffling is a network security techniquethat makes the information sender anonymous. We use the concept of shuffling in internet-based lotteries,mental poker, E-commerce systems, and Mix-Net. However, if the shuffling is unjust, the anonymity,privacy, or fairness may be compromised. In this paper, we propose the method for confirming fairmixing by finding a fixed point in the mix system and we can keep the details on ‘how to shuffle’ secret.This method requires only two steps and is efficient.
Fixed-point blind source separation algorithm based on ICA
Institute of Scientific and Technical Information of China (English)
Hongyan LI; Jianfen MA; Deng'ao LI; Huakui WANG
2008-01-01
This paper introduces the fixed-point learning algorithm based on independent component analysis (ICA);the model and process of this algorithm and simulation results are presented.Kurtosis was adopted as the estimation rule of independence.The results of the experiment show that compared with the traditional ICA algorithm based on random grads,this algorithm has advantages such as fast convergence and no necessity for any dynamic parameter,etc.The algorithm is a highly efficient and reliable method in blind signal separation.
Generalized Mixed Equilibria, Variational Inclusions, and Fixed Point Problems
Directory of Open Access Journals (Sweden)
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.
Infrared Fixed Points in the minimal MOM Scheme
DEFF Research Database (Denmark)
Ryttov, Thomas
2014-01-01
We analyze the behavior of several renormalization group functions at infrared fixed points for $SU(N)$ gauge theories with fermions in the fundamental and two-indexed representations. This includes the beta function of the gauge coupling, the anomalous dimension of the gauge parameter...... and the anomalous dimension of the mass. The scheme in which the analysis is performed is the minimal momentum subtraction scheme through third loop order. Due to the fact that scheme dependence is inevitable once the perturbation theory is truncated we compare to previous identical studies done in the minimal...
Quasifixed point scenarios and the Higgs mass in the E6 inspired supersymmetric models
Nevzorov, R.
2014-03-01
We analyze the two-loop renormalization group (RG) flow of the gauge and Yukawa couplings within the E6 inspired supersymmetric models with extra U(1)N gauge symmetry under which right-handed neutrinos have zero charge. In these models, single discrete Z stretchy="false">˜2H symmetry forbids the tree-level flavor-changing transitions and the most dangerous baryon and lepton number violating operators. We consider two different scenarios A and B that involve extra matter beyond the minimal supersymmetric Standard Model contained in three and four 5+5¯ representations of SU(5), respectively, plus three SU(5) singlets which carry U(1)N charges. In scenario A, the measured values of the SU(2)W and U(1)Y gauge couplings lie near the fixed points of the RG equations. In scenario B, the contribution of two-loop corrections spoils the unification of gauge couplings, resulting in the appearance of the Landau pole below the grand unification scale MX. The solutions for the Yukawa couplings also approach the quasifixed points with increasing their values at the scale MX. We calculate the two-loop upper bounds on the lightest Higgs boson mass in the vicinity of these quasifixed points and compare the results of our analysis with the corresponding ones in the next-to-minimal supersymmetric Standard Model. In all these cases, the theoretical restrictions on the Standard-Model-like Higgs boson mass are rather close to 125 GeV.
Stable schedule matchings by a fixed point method
Komornik, Vilmos; Viauroux, Christelle K
2010-01-01
We generalize several schedule matching theorems of Baiou-Balinski (Math. Oper. Res., 27 (2002), 485) and Alkan-Gale (J. Econ. Th. 112 (2003), 289) by applying a fixed point method of Fleiner (Math. Oper. Res., 28 (2003), 103). Thanks to a more general construction of revealing choice maps we develop an algorithm to solve rather complex matching problems. The flexibility and efficiency of our approach is illustrated by various examples. We also revisit the mathematical structure of the matching theory by comparing various definitions of stable sets and various classes of choice maps. We demonstrate, by several examples, that the revealing property of the choice maps is the most suitable one to ensure the existence of stable matchings; both from the theoretical and the practical point of view.
Chiral-scale perturbation theory about an infrared fixed point
Directory of Open Access Journals (Sweden)
Crewther R.J.
2014-06-01
Full Text Available We review the failure of lowest order chiral SU(3L ×SU(3R perturbation theory χPT3 to account for amplitudes involving the f0(500 resonance and O(mK extrapolations in momenta. We summarize our proposal to replace χPT3 with a new effective theory χPTσ based on a low-energy expansion about an infrared fixed point in 3-flavour QCD. At the fixed point, the quark condensate ⟨q̅q⟩vac ≠ 0 induces nine Nambu-Goldstone bosons: π,K,η and a QCD dilaton σ which we identify with the f0(500 resonance. We discuss the construction of the χPTσ Lagrangian and its implications for meson phenomenology at low-energies. Our main results include a simple explanation for the ΔI = 1/2 rule in K-decays and an estimate for the Drell-Yan ratio in the infrared limit.
Fixed Point Transformations Based Iterative Control of a Polymerization Reaction
Tar, József K.; Rudas, Imre J.
As a paradigm of strongly coupled non-linear multi-variable dynamic systems the mathematical model of the free-radical polymerization of methyl-metachrylate with azobis (isobutyro-nitrile) as an initiator and toluene as a solvent taking place in a jacketed Continuous Stirred Tank Reactor (CSTR) is considered. In the adaptive control of this system only a single input variable is used as the control signal (the process input, i.e. dimensionless volumetric flow rate of the initiator), and a single output variable is observed (the process output, i.e. the number-average molecular weight of the polymer). Simulation examples illustrate that on the basis of a very rough and primitive model consisting of two scalar variables various fixed-point transformations based convergent iterations result in a novel, sophisticated adaptive control.
Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions
Charbonneau, Patrick; Yaida, Sho
2017-05-01
The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon—the Gardner transition—has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, du=6 . Here, we obtain evidence for the existence of these transitions in d
Scaled AAN for Fixed-Point Multiplier-Free IDCT
Directory of Open Access Journals (Sweden)
P. P. Zhu
2009-01-01
Full Text Available An efficient algorithm derived from AAN algorithm (proposed by Arai, Agui, and Nakajima in 1988 for computing the Inverse Discrete Cosine Transform (IDCT is presented. We replace the multiplications in conventional AAN algorithm with additions and shifts to realize the fixed-point and multiplier-free computation of IDCT and adopt coefficient and compensation matrices to improve the precision of the algorithm. Our 1D IDCT can be implemented by 46 additions and 20 shifts. Due to the absence of the multiplications, this modified algorithm takes less time than the conventional AAN algorithm. The algorithm has low drift in decoding due to the higher computational precision, which fully complies with IEEE 1180 and ISO/IEC 23002-1 specifications. The implementation of the novel fast algorithm for 32-bit hardware is discussed, and the implementations for 24-bit and 16-bit hardware are also introduced, which are more suitable for mobile communication devices.
A Fast Measurement based fixed-point Quantum Search Algorithm
Mani, Ashish
2011-01-01
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity represented by a basis state in the Hilbert space associated with the qubits. Thus, when qubits are measured, there is a high probability of finding the target entity. However, the number of times quantum rotation transform is to be applied for reaching near the vicinity of the target is a function of the number of target entities present in the unsorted database, which is generally unknown. A wrong estimate of the number of target entities can lead to overshooting or undershooting the targets, thus reducing the success probability. Some proposals have been made to overcome this limitation. These proposals either employ quantum counting to estimate the number of solutions or fixed point schemes. This paper proposes a new scheme for stopping the application of quantum rotation transformation on reaching near the ...
Quantum Algorithms with Fixed Points: The Case of Database Search
Grover, L K; Tulsi, T; Grover, Lov K.; Patel, Apoorva; Tulsi, Tathagat
2006-01-01
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which get around this limitation. The first replaces selective inversions in the algorithm by selective phase shifts of $\\frac{\\pi}{3}$. The second controls the selective inversion operations using two ancilla qubits, and irreversible measurement operations on the ancilla qubits drive the starting state towards the target state. Using $q$ oracle queries, these variations reduce the probability of finding a non-target state from $\\epsilon$ to $\\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead to robust quantum algorithms, and provide conceptually new schemes for error correction.
Average dimension of fixed point spaces with applications
Guralnick, Robert M
2010-01-01
Let $G$ be a finite group, $F$ a field, and $V$ a finite dimensional $FG$-module such that $G$ has no trivial composition factor on $V$. Then the arithmetic average dimension of the fixed point spaces of elements of $G$ on $V$ is at most $(1/p) \\dim V$ where $p$ is the smallest prime divisor of the order of $G$. This answers and generalizes a 1966 conjecture of Neumann which also appeared in a paper of Neumann and Vaughan-Lee and also as a problem in The Kourovka Notebook posted by Vaughan-Lee. Our result also generalizes a recent theorem of Isaacs, Keller, Meierfrankenfeld, and Moret\\'o. Various applications are given. For example, another conjecture of Neumann and Vaughan-Lee is proven and some results of Segal and Shalev are improved and/or generalized concerning BFC groups.
A Unified Fixed Point Theory in Generalized Convex Spaces
Institute of Scientific and Technical Information of China (English)
Sehie PARK
2007-01-01
Let β be the class of 'better' admissible multimaps due to the author.We introduce newconcepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convexuniform spaces and show that any compact closed multimap in β from a G-convex space into itselfwith the Klee approximable range has a fixed point.This new theorem contains a large number ofknown results on topological vector spaces or on various subclasses.of the class of admissible G-convexspaces.Such subclasses are those of C-spaces,sets of the Zima-Hadzic type,locally G-convex spaces,and LG-spaces.Mutual relations among those subclasses and some related results are added.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
DEFF Research Database (Denmark)
Ryttov, Thomas A.
2016-01-01
We suggest how to consistently calculate the anomalous dimension $\\gamma_*$ of the $\\bar{\\psi}\\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $\\gamma......_*$ 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...... order by order in $\\Delta_f$. We then compute $\\gamma_*$ through $O(\\Delta_f^2)$ for supersymmetric QCD in the $\\overline{\\text{DR}}$ scheme and find that it matches the exact known result. We find that $\\gamma_*$ is astonishingly well described in perturbation theory already at the few loops level...
Fixed point sets of maps homotopic to a given map
Directory of Open Access Journals (Sweden)
Christina L. Soderlund
2006-04-01
Full Text Available Let f:XÃ¢Â†Â’X be a self-map of a compact, connected polyhedron and ÃŽÂ¦Ã¢ÂŠÂ†X a closed subset. We examine necessary and sufficient conditions for realizing ÃŽÂ¦ as the fixed point set of a map homotopic to f. For the case where ÃŽÂ¦ is a subpolyhedron, two necessary conditions were presented by Schirmer in 1990 and were proven sufficient under appropriate additional hypotheses. We will show that the same conditions remain sufficient when ÃŽÂ¦ is only assumed to be a locally contractible subset of X. The relative form of the realization problem has also been solved for ÃŽÂ¦ a subpolyhedron of X. We also extend these results to the case where ÃŽÂ¦ is a locally contractible subset.
Scaled AAN for Fixed-Point Multiplier-Free IDCT
Zhu, P. P.; Liu, J. G.; Dai, S. K.; Wang, G. Y.
2009-12-01
An efficient algorithm derived from AAN algorithm (proposed by Arai, Agui, and Nakajima in 1988) for computing the Inverse Discrete Cosine Transform (IDCT) is presented. We replace the multiplications in conventional AAN algorithm with additions and shifts to realize the fixed-point and multiplier-free computation of IDCT and adopt coefficient and compensation matrices to improve the precision of the algorithm. Our 1D IDCT can be implemented by 46 additions and 20 shifts. Due to the absence of the multiplications, this modified algorithm takes less time than the conventional AAN algorithm. The algorithm has low drift in decoding due to the higher computational precision, which fully complies with IEEE 1180 and ISO/IEC 23002-1 specifications. The implementation of the novel fast algorithm for 32-bit hardware is discussed, and the implementations for 24-bit and 16-bit hardware are also introduced, which are more suitable for mobile communication devices.
GUT precursors and fixed points in higher-dimensional theories
Indian Academy of Sciences (India)
Keith R Dienes; Emilian Dudas; Tony Gherghetta
2004-02-01
Within the context of traditional logarithmic grand unification at $M_{\\text{GUT}}≈ 10^{16}$ GeV, we show that it is nevertheless possible to observe certain GUT states such as $X$ and $Y$ gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as `GUT precursors'. Such states offer an interesting alternative possibility for new physics at the TeV scale, even when the scale of gauge coupling unification remains high, and suggest that it may be possible to probe GUT physics directly even within the 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.
Fixed-Point Optimization of Atoms and Density in DFT.
Marks, L D
2013-06-11
I describe an algorithm for simultaneous fixed-point optimization (mixing) of the density and atomic positions in Density Functional Theory calculations which is approximately twice as fast as conventional methods, is robust, and requires minimal to no user intervention or input. The underlying numerical algorithm differs from ones previously proposed in a number of aspects and is an autoadaptive hybrid of standard Broyden methods. To understand how the algorithm works in terms of the underlying quantum mechanics, the concept of algorithmic greed for different Broyden methods is introduced, leading to the conclusion that if a linear model holds that the first Broyden method is optimal, the second if a linear model is a poor approximation. How this relates to the algorithm is discussed in terms of electronic phase transitions during a self-consistent run which results in discontinuous changes in the Jacobian. This leads to the need for a nongreedy algorithm when the charge density crosses phase boundaries, as well as a greedy algorithm within a given phase. An ansatz for selecting the algorithm structure is introduced based upon requiring the extrapolated component of the curvature condition to have projected positive eigenvalues. The general convergence of the fixed-point methods is briefly discussed in terms of the dielectric response and elastic waves using known results for quasi-Newton methods. The analysis indicates that both should show sublinear dependence with system size, depending more upon the number of different chemical environments than upon the number of atoms, consistent with the performance of the algorithm and prior literature. This is followed by details of algorithm ranging from preconditioning to trust region control. A number of results are shown, finishing up with a discussion of some of the many open questions.
Fixed point theorems and stability of iterations in cone metric spaces
Directory of Open Access Journals (Sweden)
Yuan Qing
2012-04-01
Full Text Available In this paper, fixed point problems of weak contractions are investigated in cone metric spaces. Theorems of convergence and theorems of stability for fixed points of some weak contraction are established in cone metric spaces.
Miks, Antonin; Novak, Jiri
2014-06-30
This work performs an analysis of basic optical properties of zoom lenses with a fixed distance between object and image points and a fixed position of the image-space focal point. Formulas for the calculation of paraxial parameters of such optical systems are derived and the calculation is presented on examples.
Schrempp, Barbara
1994-01-01
The two-loop ``top-down'' renormalization group flow for the top, bottom and tau Yukawa couplings is explored in the framework of supersymmetric grand unification; reproduction of the physical bottom and tau masses is required. Instead of following the recent trend of implementing exact Yukawa coupling unification i) a search for infrared (IR) fixed lines and fixed points in the m(top)-tan(beta) plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. Two IR fixed lines, intersecting in an IR fixed point, are located. The more attractive fixed line has a branch of almost constant top mass, 168-180 GeV, close to the experimental value, for the large interval 2.5
Extraneous fixed points of Euler iteration and corresponding Sullivan's basin
Institute of Scientific and Technical Information of China (English)
WANG; Xinghua
2001-01-01
［1］Blanchard, P., Complex analytic dynamics on the Riemann sphere, Bull. (New Ser.) Amer. Math. Soc., 1984, 11: 85.［2］Lu Yinian, Complex Analytic Dynamics (in Chinese), Beijing: Science Press, 1997.［3］Ren Fuyao, Complex Analytic Dynamics (in Chinese), Shanghai: Press of Fudan University, 1997.［4］McMullen, C., Families of rational maps and iterative root finding algorithms, Annals of Math., 1987, 125: 467.［5］Curry, H., Garnett, L., Sullivan, D., On the iteration of a rational function: computer experiments with Newton's method, Commun. Math. Phys., 1983, 91: 267.［6］Fatou, P., Sur les equations fonctionnalles, Bull. Soc. Math. France, 1919, 47: 161; 1920, 48: 33—94; 208—314.［7］Si Zhongci, Yuan Yaxiang, Wonderful Computation, Changsha: Hunan Science and Technique Press, 1999.［8］Han Danfu, Wang Xinghua, On fixed points and Julia sets for iterations of two families, Chinese J. Numer. & Appl., 1997, 19(3): 94.［9］Sullivan, D., Quasiconformal homeomorphisms and dynamics I: Solution of the Fatou_Julia problem on wandering domains, Ann. Math., 1985, 122: 401.［10］Vrscay, E. R., Julia sets and Mandelbrot_like associated with higher order Schroder rational iteration functions, Math. Comput., 1986, 46: 151.［11］Vrscay, E. R., Gilbert, W. J., Extraneous fixed points, basin boundaries and chaotic dynamics for Schroder and Konig rational iteration functions, Numer. Math., 1988, 52: 1.［12］Smale, S., On the efficiency of algorithms of analysis, Bull. (New Ser.) Amer. Math. Soc., 1985, 13: 87.［13］Wilkinson, J. H., The Algebraic Eigenvalue Problem, Oxford: Oxford University Press, 1965.［14］Wang Heyu, Hu Qingbiao, Wang Xinghua, Continuity tracing of algebraic curves, Journal of Computer_Aided Design & Computer Graphics, 2000, 12: 789.［15］Bryuno, A. D., Convergence of transformations of differential equations to normal forms, Dokl Akad Nauk USSR, 1965, 165: 987.［16］Yoccoz, J. C., Linearisation des germes de
Some fixed point theorems for multivalued maps in ordered Banach spaces and applications
Directory of Open Access Journals (Sweden)
Zhai Chengbo
2005-01-01
Full Text Available The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.
Consistent Perturbative Fixed Point Calculations in QCD and SQCD
Ryttov, Thomas A
2016-01-01
We suggest how to consistently calculate the anomalous dimension $\\gamma_*$ of the $\\bar{\\psi}\\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $\\gamma_*$ 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 order by order in $\\Delta_f$. We then compute $\\gamma_*$ through $O(\\Delta_f^2)$ for supersymmetric QCD in the $\\overline{\\text{DR}}$ scheme and find that it matches the exact known result. We find that $\\gamma_*$ is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute $\\gamma_*$ through $O(\\Delta_f^3)$ for QCD and a variety of other n...
Fixed-point tile sets and their applications
Durand, Bruno; Shen, Alexander
2009-01-01
An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. This construction it rather flexible, so it can be used in many ways: we show how it can be used to implement substitution rules, to construct strongly aperiodic tile sets (any tiling is far from any periodic tiling), to give a new proof for the undecidability of the domino problem and related results, characterize effectively closed 1D subshift it terms of 2D shifts of finite type (improvement of a result by M. Hochman), to construct a tile set which has only complex ti...
Frobenius groups of automorphisms and their fixed points
Khukhro, Evgenii I; Shumyatsky, Pavel
2010-01-01
Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$. In this situation various properties of $G$ are shown to be close to the corresponding properties of $C_G(H)$. By using Clifford's theorem it is proved that the order $|G|$ is bounded in terms of $|H|$ and $|C_G(H)|$, the rank of $G$ is bounded in terms of $|H|$ and the rank of $C_G(H)$, and that $G$ is nilpotent if $C_G(H)$ is nilpotent. Lie ring methods are used for bounding the exponent and the nilpotency class of $G$ in the case of metacyclic $FH$. The exponent of $G$ is bounded in terms of $|FH|$ and the exponent of $C_G(H)$ by using Lazard's Lie algebra associated with the Jennings--Zassenhaus filtration and its connection with powerful subgroups. The nilpotency class of $G$ is bounded in terms of $|H|$ and the nilpotency class of $C_G(H)$ by considering Lie rings with a finite cyclic grading satisfying a certain `selective ni...
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors.
Fixed and periodic points in the probabilistic normed and metric spaces
Energy Technology Data Exchange (ETDEWEB)
Ghaemi, M.B. [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of) and Faculty of Mathematics, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)]. E-mail: M-Ghaemi@sbu.ac.ir; Razani, Abdolrahman [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of) and Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of)]. E-mail: razani@ikiu.ac.ir
2006-06-15
In this paper, a fixed point theorem is proved, i.e., if A is a C-contraction in the Menger space (S,F) and E-bar S be such that A(E)-bar is compact, then A has a fixed point. In addition, under the same condition, the existence of a periodic point of A is proved. Finally, a fixed point theorem in probabilistic normed spaces is proved.
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.
Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\\varepsilon$ Expansion arXiv
Osborn, Hugh
Fixed points for scalar theories in $4-\\varepsilon$, $6-\\varepsilon$ and $3-\\varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, $O(N)$, is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the $a$-theorem are used to help classify potential fixed points. At lowest order in the $\\varepsilon$-expansion it is shown that at fixed points there is a lower bound for $a$ which is saturated at bifurcation points.
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces
Directory of Open Access Journals (Sweden)
Gerald F. Jungck
2005-10-01
Full Text Available The concept of proper orbits of a map g is introduced and results of the following type are obtained. If a continuous self-map g of a Hausdorff topological space X has relatively compact proper orbits, then g has a fixed point. In fact, g has a common fixed point with every continuous self-map f of X which is nontrivially compatible with g. A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.
Common fixed point theorems for compatible self-maps of Hausdorff topological spaces
Directory of Open Access Journals (Sweden)
Jungck Gerald F
2005-01-01
Full Text Available The concept of proper orbits of a map is introduced and results of the following type are obtained. If a continuous self-map of a Hausdorff topological space has relatively compact proper orbits, then has a fixed point. In fact, has a common fixed point with every continuous self-map of which is nontrivially compatible with . A collection of metric and semimetric space fixed point theorems follows as a consequence. Specifically, a theorem by Kirk regarding diminishing orbital diameters is generalized, and a fixed point theorem for maps with no recurrent points is proved.
Parravicini, Paola; Cislaghi, Matteo; Condemi, Leonardo
2017-04-01
ARPA Lombardia is the Environmental Protection Agency of Lombardy, a wide region in the North of Italy. ARPA is in charge of river monitoring either for Civil Protection or water balance purposes. It cooperates with the Civil Protection Agency of Lombardy (RL-PC) in flood forecasting and early warning. The early warning system is based on rainfall and discharge thresholds: when a threshold exceeding is expected, RL-PC disseminates an alert from yellow to red. The conventional threshold evaluation is based on events at a fixed return period. Anyway, the impacts of events with the same return period may be different along the river course due to the specific characteristics of the affected areas. A new approach is introduced. It defines different scenarios, corresponding to different flood impacts. A discharge threshold is then associated to each scenario and the return period of the scenario is computed backwards. Flood scenarios are defined in accordance with National Civil Protection guidelines, which describe the expected flood impact and associate a colour to the scenario from green (no relevant effects) to red (major floods). A range of discharges is associated with each scenario since they cause the same flood impact; the threshold is set as the discharge corresponding to the transition between two scenarios. A wide range of event-based information is used to estimate the thresholds. As first guess, the thresholds are estimated starting from hydraulic model outputs and the people or infrastructures flooded according to the simulations. Eventually the model estimates are validated with real event knowledge: local Civil Protection Emergency Plans usually contain very detailed local impact description at known river levels or discharges, RL-PC collects flooding information notified by the population, newspapers often report flood events on web, data from the river monitoring network provide evaluation of actually happened levels and discharges. The methodology
Spectrum of the fixed point Dirac operator in the Schwinger model
Farchioni, F; Lang, C B; Wohlgenannt, M
1999-01-01
Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed point Dirac operator investigating also microscopic fluctuations and fermion condensation.
Fixed point results for generalized alpha-psi-contractions in metric-like spaces and applications
Directory of Open Access Journals (Sweden)
Hassen Aydi
2015-05-01
Full Text Available In this article, we introduce the concept of generalized $\\alpha\\text{-}\\psi$-contraction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered.
Analysis and confirmation of fixed points in logistic mapping digital-flow chaos
Institute of Scientific and Technical Information of China (English)
Guobao Xu; Deling Zheng; Geng Zhao
2003-01-01
The fixed points in logistic mapping digital-flow chaos strange attractor are studied in detail. When k=n in logistic equa-tion, there exist no more than 2n fixed points, which are deduced and proved theoretically. Three corollaries about the fixed points oflogistic mapping are proposed and proved respectively. These theoretn and corollaries provide a theoretical basis for choosingparameter of chaotic sequences in chaotic secure communication and chaotic digital watermarking. And they are testified by simulation.
Generalized contraction resulting tripled fixed point theorems in complex valued metric spaces
Directory of Open Access Journals (Sweden)
Madhu Singh
2016-10-01
Full Text Available Owning the concept of complex valued metric spaces introduced by Azam et al.[1] many authors prove several fixed point results for mappings satisfying certain contraction conditions. Coupled and tripled fixed point problems have attracted much attention in recent times. In this note, common tripled fixed point theorems for a pairs of mappings satisfying certain rational contraction in complex valued metric spaces are proved. Some illustrative examples are also given which demonstrate the validity of the hypotheses of our results.
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.
On the invariant motions of rigid body rotation over the fixed point, via Euler angles
Ershkov, Sergey V
2016-01-01
The generalized Euler case (rigid body rotation over the fixed point) is discussed here: - the center of masses of non-symmetric rigid body is assumed to be located at the equatorial plane on axis Oy which is perpendicular to the main principal axis Ox of inertia at the fixed point. Such a case was presented in the rotating coordinate system, in a frame of reference fixed in the rotating body for the case of rotation over the fixed point (at given initial conditions). In our derivation, we have represented the generalized Euler case in the fixed Cartesian coordinate system; so, the motivation of our ansatz is to elegantly transform the proper components of the previously presented solution from one (rotating) coordinate system to another (fixed) Cartesian coordinates. Besides, we have obtained an elegantly analytical case of general type of rotations; also, we have presented it in the fixed Cartesian coordinate system via Euler angles.
An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
Ryttov, Thomas A
2012-01-01
We give a detailed analysis of the effects of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions. We list necessary conditions that such transformations must obey and show that, although these can easily be satisfied in the vicinity of an ultraviolet fixed point, they constitute significant restrictions on scheme transformations at an infrared fixed point. We construct acceptable scheme transformations and use these to study the scheme-dependence of an infrared fixed point, making comparison with our previous three-loop and four-loop calculations of the location of this point in the $\\bar{MS}$ scheme. We also use an illustrative hypothetical exact $\\beta$ function to investigate how accurately analyses of finite-order series expansions probe an infrared fixed point and the effect of a scheme transformation on these. Some implications of our work are discussed.
An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
DEFF Research Database (Denmark)
Ryttov, Thomas; Shrock, Robert
2012-01-01
We give a detailed analysis of the effects of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions. We list necessary conditions that such transformations must obey and show that, although these can easily...... be satisfied in the vicinity of an ultraviolet fixed point, they constitute significant restrictions on scheme transformations at an infrared fixed point. We construct acceptable scheme transformations and use these to study the scheme-dependence of an infrared fixed point, making comparison with our previous...... three-loop and four-loop calculations of the location of this point in the $\\bar{MS}$ scheme. We also use an illustrative hypothetical exact $\\beta$ function to investigate how accurately analyses of finite-order series expansions probe an infrared fixed point and the effect of a scheme transformation...
Infrared behaviour and fixed points in Landau gauge QCD
Pawlowski, J M; Nedelko, S N; Von Smekal, L; Pawlowski, Jan M.; Litim, Daniel F.; Nedelko, Sergei; Smekal, Lorenz von
2004-01-01
We investigate the infrared behaviour of gluon and ghost propagators in Landau gauge QCD by means of an exact renormalisation group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimisation procedure is devised to remove residual regulator dependences. In Landau gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.
Infrared Behavior and Fixed Points in Landau-Gauge QCD
Pawlowski, Jan M.; Litim, Daniel F.; Nedelko, Sergei; von Smekal, Lorenz
2004-10-01
We investigate the infrared behavior of gluon and ghost propagators in Landau-gauge QCD by means of an exact renormalization group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimization procedure is devised to remove residual regulator dependences. In Landau-gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.
Common fixed points for generalized contractive mappings in cone metric spaces
Directory of Open Access Journals (Sweden)
Hassen Aydi
2012-06-01
Full Text Available The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.
Generalization of common fixed point theorems for weakly commuting maps by altering distances
Directory of Open Access Journals (Sweden)
K. P. R. Sastry
2000-09-01
Full Text Available The main purpose of this paper is to obtain conditions for the existence of a unique common fixed point for four selfmaps on a complete metric space by altering distances between the points.
Tripled common fixed point theorems for w-compatible mappings in ordered cone metric spaces
Directory of Open Access Journals (Sweden)
P. P. Murthy
2012-07-01
Full Text Available The purpose of this note is to establish a triplet coincidence point theorem in ordered cone metric spaces over solid cone. Our result extends coupled common fixed point theorems due to Nashine, Kadelburg and Radenovic [1].
Asymptotic behavior of two algorithms for solving common fixed point problems
Zaslavski, Alexander J.
2017-04-01
The common fixed point problem is to find a common fixed point of a finite family of mappings. In the present paper our goal is to obtain its approximate solution using two perturbed algorithms. The first algorithm is an iterative method for problems in a metric space while the second one is a dynamic string-averaging algorithms for problems in a Hilbert space.
Common Fixed Point Theorems for Weakly Compatible Maps Satisfying a General Contractive Condition
Directory of Open Access Journals (Sweden)
Cristina Di Bari
2008-01-01
Full Text Available We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.
ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in Lp spaces, in Hardy spaces Hp , and in Sobolev spaces Hr,p, for 1 ＜ p ＜ + ∞ and r ≥ 0.
On the fixed points of nonexpansive mappings in direct sums of Banach spaces
Wiśnicki, Andrzej
2011-01-01
We show that if a Banach space X has the weak fixed point property for nonexpansive mappings and Y has the generalized Gossez-Lami Dozo property or is uniformly convex in every direction, then the direct sum of X and Y with a strictly monotone norm has the weak fixed point property. The result is new even if Y is finite-dimensional.
Some fixed point results for rational type and subrational type contractive mappings
Directory of Open Access Journals (Sweden)
Huang Huaping
2017-08-01
Full Text Available In this paper, we introduce the concepts of rational type and subrational type contractive mappings. We expand and improve some fixed point theorems obtained by Alsulami et al. (Fixed Point Theory Appl., 2015, 2015: 97. Moreover, we give an example to support our results.
Common Fixed Points of Weakly Contractive and Strongly Expansive Mappings in Topological Spaces
Directory of Open Access Journals (Sweden)
Hussain N
2010-01-01
Full Text Available Using the notion of weakly -contractive mappings, we prove several new common fixed point theorems for commuting as well as noncommuting mappings on a topological space X. By analogy, we obtain a common fixed point theorem of mappings which are strongly -expansive on X.
ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS
Institute of Scientific and Technical Information of China (English)
SUN Jingxian; ZHANG Kemei
2003-01-01
In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.
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.
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.
Area law for fixed points of rapidly mixing dissipative quantum systems
Energy Technology Data Exchange (ETDEWEB)
Brandão, Fernando G. S. L. [Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052 (United States); Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom); Cubitt, Toby S. [Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom); DAMTP, University of Cambridge, Cambridge (United Kingdom); Lucia, Angelo, E-mail: anlucia@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Madrid (Spain); Michalakis, Spyridon [Institute for Quantum Information and Matter, Caltech, California 91125 (United States); Perez-Garcia, David [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Madrid (Spain); IMI, Universidad Complutense de Madrid, Madrid (Spain); ICMAT, C/Nicolás Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain)
2015-10-15
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.
Construction of a non-trivial planar field theory with ultraviolet stable fixed point
Energy Technology Data Exchange (ETDEWEB)
Felder, G.
1985-11-01
We study a phi/sub 4//sup 4/ planar euclidean quantum field theory with propagator 1/psup(2-epsilon/2), epsilon > 0. With the help of the tree expansion of Gallavotti and Nicolo, this non-renormalizable theory is shown to have a non-trivial ultraviolet-stable fixed point at negative coupling constant. The vicinity of the fixed point is discussed.
Coupled Fixed Point Theorems with New Implicit Relations and an Application
Directory of Open Access Journals (Sweden)
G. V. R. Babu
2014-01-01
Full Text Available We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010. We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010 to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006. As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.
Design and construction of a gallium fixed-point blackbody at CENAM
Energy Technology Data Exchange (ETDEWEB)
Cardenas G, D., E-mail: dcardena@cenam.mx [Centro Nacional de Metrologia, Km 4.5 Carretera a los Cues, El Marques, 76246 Santiago de Queretaro, Queretaro (Mexico)
2015-07-01
For temperatures below silver fixed-point defined by the International Temperature Scale of 1990, a transfer radiation thermometer can be calibrated using either of two calibration schemes: a variable temperature blackbody with a standard platinum resistance thermometer as a reference, or with a set of fixed-point blackbodies. CENAM is presently working with the first scheme, and it is developing fixed-point blackbodies to have the capability to work with the second scheme too. For this purpose a gallium fixed-point blackbody to calibrate CENAM transfer radiation thermometer was designed and constructed. The blackbody cavity has a cylinder-cone shape with effective emissivity equal to 0.9992±0.0004 in the 8 μm to 14 μm wavelength range. The radiance temperature of the gallium fixed-point blackbody was estimated to have and expanded uncertainty of 54 m K, with a coverage factor k = 2. (Author)
Patil, Dinesh; Das, Niva; Routray, Aurobinda
2011-01-01
The main focus of the paper is to bring out the differences in performance related issues of Fast-ICA algorithm associated with floating point and fixed point digital signal processing (DSP) platforms. The DSP platforms consisting of TMS320C6713 floating point processor and TMS320C6416 fixed point processor from Texas Instruments have been chosen for this purpose. To study the consistency of performance, the algorithm has been subjected to three different test cases comprising of a mixture of synthetic signals, a mixture of speech signals and a mixture of synthetic signals in presence of noise, respectively. The performance of the Fast-ICA algorithm on floating point and fixed point platform are compared on the basis of accuracy of separation and execution time. Experimental results show insignificant differences in the accuracy of separation and execution time obtained from fixed point processor when compared with those obtained from floating point processor. This clearly strengthens the feasibility issue concerning hardware realization of Fast-ICA on fixed point platform for specific applications.
New fixed and periodic point results on cone metric spaces
Directory of Open Access Journals (Sweden)
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.
Gauge-fixing parameter dependence of two-point gauge variant correlation functions
Zhai, C
1996-01-01
The gauge-fixing parameter \\xi 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 ...
Eigenvectors and fixed point of non-linear operators
Directory of Open Access Journals (Sweden)
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].
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.
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
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Gene Frantz
2007-01-01
Full Text Available 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.
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
Comparison of Sigma-Point and Extended Kalman Filters on a Realistic Orbit Determination Scenario
Gaebler, John; Hur-Diaz. Sun; Carpenter, Russell
2010-01-01
Sigma-point filters have received a lot of attention in recent years as a better alternative to extended Kalman filters for highly nonlinear problems. In this paper, we compare the performance of the additive divided difference sigma-point filter to the extended Kalman filter when applied to orbit determination of a realistic operational scenario based on the Interstellar Boundary Explorer mission. For the scenario studied, both filters provided equivalent results. The performance of each is discussed in detail.
On Fixed Points of Generalized α-φ Contractive Type Mappings in Partial Metric Spaces
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Priya Shahi
2016-08-01
Full Text Available Recently, Samet et al. (B. Samet, C. Vetro and P. Vetro, Fixed point theorem for $\\alpha$-$\\psi$ contractive type mappings, Nonlinear Anal. 75 (2012, 2154--2165 introduced a very interesting new category of contractive type mappings known as $\\alpha$-$\\psi$ contractive type mappings. The results obtained by Samet et al. generalize the existing fixed point results in the literature, in particular the Banach contraction principle. Further, Karapinar and Samet (E. Karapinar and B. Samet, Generalized $\\alpha$-$\\psi$-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis 2012 Article ID 793486, 17 pages doi:10.1155/2012/793486 generalized the $\\alpha$-$\\psi$ contractive type mappings and established some fixed point theorems for this generalized class of contractive mappings. In (G. S. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994, 183--197, the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we establish the fixed point theorems for generalized $\\alpha$-$\\psi$ contractive mappings in the context of partial metric spaces. As consequences of our main results, we obtain fixed point theorems on partial metric spaces endowed with a partial order and that for cyclic contractive mappings. Our results extend and strengthen various known results. Some examples are also given to show that our generalization from metric spaces to partial metric spaces is real.
Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions
Hussain, N.
2008-02-01
The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.
An extension of the compression-expansion fixed point theorem of functional type
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Richard I. Avery
2016-09-01
Full Text Available In this article we use an interval of functional type as the underlying set in our compression-expansion fixed point theorem argument which can be used to exploit properties of the operator to improve conditions that will guarantee the existence of a fixed point in applications. An example is provided to demonstrate how intervals of functional type can improve conditions in applications to boundary value problems. We also show how one can use suitable $k$-contractive conditions to prove that a fixed point in a functional-type interval is unique.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
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Sunny Chauhan
2013-01-01
Full Text Available We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
Results on n-tupled fixed points in complete asymptotically regular metric spaces
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Anupam Sharma
2014-10-01
Full Text Available The notion of n-tupled fixed point is introduced by Imdad, Soliman, Choudhury and Das, Jour. of Operators, Vol. 2013, Article ID 532867. In this manuscript, we prove some n-tupled fixed point theorems (for even n for mappings having mixed monotone property in partially ordered complete asymptotically regular metric spaces. Our main theorem improves the corresponding results of Imdad, Sharma and Rao (M. Imdad, A. Sharma, K.P.R. Rao, Generalized n-tupled fixed point theorems for nonlinear contractions, preprint.
Coupled Fixed Point Theorems for Weak Contraction Mappings under F-Invariant Set
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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.
Fixed point theorems in locally convex spaces—the Schauder mapping method
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2006-01-01
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.
A fixed-point principle for a pair of non-commutative operators
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Penumarthy Parvateesam Murthy
2014-09-01
Full Text Available In this paper, a fixed point principle for a pair of operators (fi,X,d, i = 1,2, where (X,d is a metric space and f1, f2: X → X, is established under the generalized uniform equivalence condition of different orbits generated by the maps f1 and f2 separately, which gives another generalization of the fixed point principle of Leader [1] and estimates approximations to the fixed points of both the operators simultaneously.
Approximating fixed points for nonself mappings in CAT(0) spaces
Razani Abdolrahman; Shabani Saeed
2011-01-01
Abstract Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K → X be a nonself mapping, satisfying Condition (E) with F(T): = {x ∈ K : Tx = x} ≠ ∅. Suppose {xn} is generated iteratively by x1 ∈ K, xn+1 = P ((1 - αn)xn ⊕ αnTP [(1 - βn)xn ⊕ βnTxn]),n ≥ 1, where {αn} and {βn} are real sequences in [ε, 1 - ε] for some ε W...
Approximating fixed points for nonself mappings in CAT(0) spaces
Razani Abdolrahman; Shabani Saeed
2011-01-01
Abstract Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K → X be a nonself mapping, satisfying Condition (E) with F(T): = {x ∈ K : Tx = x} ≠ ∅. Suppose {xn} is generated iteratively by x1 ∈ K, xn+1 = P ((1 - αn)xn ⊕ αnTP [(1 - βn)xn ⊕ βnTxn]),n ≥ 1, where {αn} and {βn} are real sequences in [ε, 1 - ε] for some ε W...
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.
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Tuyen Truong
2011-01-01
Full Text Available Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and uniformly smooth Banach space. 2010 Mathematics Subject Classification: 47H09; 47J25; 47J30.
Rathee, Savita; Dhingra, Kusum; Kumar, Anil
2016-01-01
Here, we extend the notion of (E.A.) property in a convex metric space defined by Kumar and Rathee (Fixed Point Theory Appl 1-14, 2014) by introducing a new class of self-maps which satisfies the common property (E.A.) in the context of convex metric space and ensure the existence of common fixed point for this newly introduced class of self-maps. Also, we guarantee the existence of common best proximity points for this class of maps satisfying generalized non-expansive type condition. We furnish an example in support of the proved results.
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K. Ravi
2014-03-01
Full Text Available In this paper, using fixed point method we prove the generalized Hyers Ulam Rassias stability of the additive cubic functional equationf(x-ky=k2[f(x+y+ f(x-y]+2(1- k2f(x for fixed integers k, with k≠0,±1 in paranormed spaces.
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B. C. Dhage
2004-09-01
Full Text Available In this paper a random version of a fixed-point theorem of Schaefer is obtained and it is further applied to a certain nonlinear functional random integral equation for proving the existence result under Caratheodory conditions.
Some common fixed point theorems in polish space using new type of contractive conditions
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Ramakant Bhardwaj
2012-09-01
Full Text Available In this paper, we established some common fixed point theorems for random operators in polish spaces, by using some new types of contractive condition. Our result is a generalization of various known results.
Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations
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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.
Common Fixed Point Theorem in Cone Metric Space for Rational Contractions
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R. Uthayakumar
2013-09-01
Full Text Available In this paper we prove the common fixed point theorem in cone metric space for rational expression in normal cone setting. Our results generalize the main result of Jaggi [10] and Dass, Gupta [11].
Random fixed points of non-self maps and random approximations
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Ismat Beg
1997-01-01
Full Text Available In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.
Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals
Indian Academy of Sciences (India)
K R Parthasarathy
2007-11-01
By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.
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K. P. R. Sastry
2015-01-01
Full Text Available In this paper, we prove the existence of fixed points of contractive and Geraghty contraction maps in complete metric spaces under the influence of altering distances. Our results extend and generalize some of the known results.
QCD fixed points: Banks-Zaks or dynamical gluon mass generation?
Gomez, J D
2016-01-01
Fixed points in QCD can appear when the number of quark flavors ($N_f$) is increased above a certain critical value as proposed by Banks and Zaks (BZ). There is also the possibility that QCD possess an effective charge indicating an infrared frozen coupling constant. In particular, an infrared frozen coupling associated to dynamical gluon mass generation (DGM) does lead to a fixed point even for a small number of quarks. We compare the BZ and DGM mechanisms, their $\\beta$ functions and fixed points, and within the approximations of this work, which rely basically on extrapolations of the dynamical gluon masses at large $N_f$, we verify that near the so called QCD conformal window both cases exhibit fixed points at similar coupling constant values ($g^*$). We argue that the states of minimum vacuum energy, as a function of the coupling constant up to $g^*$ and for several $N_f$ values, are related to the dynamical gluon mass generation mechanism.
TF type contractive conditions for Kannan and Chatterjea fixed point theorems
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Mehmet Kir
2013-12-01
Full Text Available In this paper, the notation of TF-contractive conditions are investigated for Kannan and Chatterjea type mappings. It is shown that these mappings have a unique fixed point in complete metric spaces.
Fixed Point Theorem of Half-Continuous Mappings on Topological Vector Spaces
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Imchit Termwuttipong
2010-01-01
Full Text Available Some fixed point theorems of half-continuous mappings which are possibly discontinuous defined on topological vector spaces are presented. The results generalize the work of Philippe Bich (2006 and several well-known results.
Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes
DEFF Research Database (Denmark)
Birkedal, Lars; Mogelberg, R.E.
2013-01-01
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...... 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...
Fixed point theorems for compatible mappings of type (P and applications to dynamic programming
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H. K. Pathak
1995-11-01
Full Text Available In this paper, we prove some common fixed point theorems for compatible mappings of type (P. As applications, the existence and uniqueness of common solutions for a class of the functional equations in dynamic programming are discussed.
New Fixed Point Results for Fractal Generation in Jungck Noor Orbit with s-Convexity
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Shin Min Kang
2015-01-01
Full Text Available We establish new fixed point results in the generation of fractals (Julia sets, Mandelbrot sets, and Tricorns and Multicorns for linear or nonlinear dynamics by using Jungck Noor iteration with s-convexity.
Fixed point sensitivity analysis of interacting structured populations.
Barabás, György; Meszéna, Géza; Ostling, Annette
2014-03-01
Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation.
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?
Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces
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Erdal Karapınar
2010-01-01
Full Text Available Some results of (Ćirić, 1974 on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.
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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.
Study of Fixed Point Theorem for Common Limit Range Property and Application to Functional Equations
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Nashine Hemant Kumar
2014-06-01
Full Text Available The aim of our paper is to use common limit range property for two pairs of mappings deriving common fixed point results under a generalized altering distance function. Some examples are given to exhibit different type of situation which shows the requirements of conditions of our results. At the end the existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming with the help of a common fixed point theorem is presented.
On a new fixed point of the renormalization group operator for area-preserving maps
Energy Technology Data Exchange (ETDEWEB)
Fuchss, K. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States); Wurm, A. [Department of Physical and Biological Sciences, Western New England College, Springfield, MA 01119 (United States); Morrison, P.J. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, TX 78712 (United States)]. E-mail: morrison@physics.utexas.edu
2007-07-02
The breakup of the shearless invariant torus with winding number {omega}=2-1 is studied numerically using Greene's residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed.
A-properness and fixed point theorems for dissipative type maps
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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.
Common fixed point theorems for sub-sequential continuous mapping in fuzzy metric space
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Arihant Jain
2013-03-01
Full Text Available The present paper deals with common fixed point theorems in fuzzy metric spaces employing the notion of sub-sequentially continuity. Moreover we have to show that in the context of sequentially continuity, the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.
New fixed points of the renormalisation group for two-body scattering
Energy Technology Data Exchange (ETDEWEB)
Birse, M.C. [The University of Manchester, Theoretical Physics Division, School of Physics and Astronomy, Manchester (United Kingdom); Epelbaum, E. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Fakultaet fuer Physik und Astronomie, Bochum (Germany); Gegelia, J. [Juelich Center for Hadron Physics, Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia)
2016-02-15
We outline a separable matrix ansatz for the potentials in effective field theories of non-relativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation for these potentials. New fixed points indicate a much richer structure than previously recognized in the RG flows of simple short-range potentials. (orig.)
Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces
2008-01-01
We prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space, also we showed that if the G-metric space (X,G) is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space (X,dG), where (X,dG) is the usual metric space which defined from the G-metric space (X,G).
Some New Weakly Contractive Type Multimaps and Fixed Point Results in Metric Spaces
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Abdou AfrahAN
2009-01-01
Full Text Available Some new weakly contractive type multimaps in the setting of metric spaces are introduced, and we prove some results on the existence of fixed points for such maps under certain conditions. Our results extend and improve several known results including the corresponding recent fixed point results of Pathak and Shahzad (2009, Latif and Abdou (2009, Latif and Albar (2008, Cirić (2008, Feng and Liu (2006, and Klim and Wardowski (2007.
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)
Pérez-Soba, Marta; Maas, Rob
2015-01-01
We cannot predict the future with certainty, but we know that it is influenced by our current actions, and that these in turn are influenced by our expectations. This is why future scenarios have existed from the dawn of civilization and have been used for developing military, political and economic
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1996-01-01
The main purpose of this paper is to give a synthetic presentation of hte well-known scenario method. Different schools and traditions will be shortly presented. In addition guidelines for hte use of this method will be discussed. Finally, applications will also be outlined as well as some critic...
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...
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Joao M. Goncalves
2015-12-01
Full Text Available Personal information is increasingly gathered and used for providing services tailored to user preferences, but the datasets used to provide such functionality can represent serious privacy threats if not appropriately protected. Work in privacy-preserving data publishing targeted privacy guarantees that protect against record re-identification, by making records indistinguishable, or sensitive attribute value disclosure, by introducing diversity or noise in the sensitive values. However, most approaches fail in the high-dimensional case, and the ones that don't introduce a utility cost incompatible with tailored recommendation scenarios. This paper aims at a sensible trade-off between privacy and the benefits of tailored recommendations, in the context of privacy-preserving data publishing. We empirically demonstrate that significant privacy improvements can be achieved at a utility cost compatible with tailored recommendation scenarios, using a simple partition-based sanitization method.
A Continuation Method for Solving Fixed Point Problems in Unbounded Convex Sets
Institute of Scientific and Technical Information of China (English)
SU MENG-LONG; LU XIAN-RUI; MA YONG
2009-01-01
In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper.
Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Ordered b-Metric Spaces
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Farzaneh Zabihi
2014-01-01
Full Text Available We introduce the new notion of a hybrid rational Geraghty contractive mapping and investigate the existence of fixed point and coincidence point for such mappings in ordered b-metric spaces. We also provide an example to illustrate the results presented herein. Finally, we establish an existence theorem for a solution of an integral equation.
AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs Equations
Rinaldi, Massimiliano
2015-01-01
We study the Einstein Yang-Mills Higgs equations in the $SO(3)$ representation on a isotropic and homogeneous flat Universe, in the presence of radiation and matter fluids. We map the equations of motion into a closed dynamical system of first-order differential equations and we find the equilibrium points. We show that there is only one stable fixed point that corresponds to an accelerated expanding Universe in the future. In the past, instead, there is an unstable fixed point that implies a stiff-matter domination. In between, we find three other unstable fixed points, corresponding, in chronological order, to radiation domination, to matter domination, and, finally, to a transition from decelerated expansion to accelerated expansion. We solve the system numerically and we confirm that there are smooth trajectories that correctly describe the evolution of the Universe, from a remote past dominated by radiation to a remote future dominated by dark energy, passing through a matter-dominated phase.
Directory of Open Access Journals (Sweden)
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
Directory of Open Access Journals (Sweden)
Yeol Je Cho
2008-03-01
Full Text Available Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative schemes are demonstrated.
Directory of Open Access Journals (Sweden)
Cho YeolJe
2007-01-01
Full Text Available Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative schemes are demonstrated.
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.
Total Stability Properties Based on Fixed Point Theory for a Class of Hybrid Dynamic Systems
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M. De la Sen
2009-01-01
Full Text Available Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems by using the powerful tool of fixed point theory. The class of hybrid systems dealt consists, in general, of coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed parts are linear and, in general, time-varying. The obtained sufficient conditions on robust stability under a wide class of harmless perturbations are dependent on the values of the parameters defining the over-bounding functions of those perturbations. The weakness of the coupling dynamics in terms of norm among the analog and digital substates of the whole dynamic system guarantees the total stability provided that the corresponding uncoupled nominal subsystems are both exponentially stable. Fixed point stability theory is used for the proofs of stability. A generalization of that result is given for the case that sampling is not uniform. The boundedness of the state-trajectory solution at sampling instants guarantees the global boundedness of the solutions for all time. The existence of a fixed point for the sampled state-trajectory solution at sampling instants guarantees the existence of a fixed point of an extended auxiliary discrete system and the existence of a global asymptotic attractor of the solutions which is either a fixed point or a limit n globally stable asymptotic oscillation.
Large- and Small-Aperture Fixed-Point Cells of Cu, Pt C, and Re C
Anhalt, Klaus; Wang, Yunfen; Yamada, Yoshiro; Hartmann, Jürgen
2008-06-01
Extending the application of metal (carbide) carbon eutectic fixed-point cells to radiometry, e.g., for measurements in irradiance mode, requires fixed-point cells with large apertures. In order to make large-aperture cells more readily usable in furnace systems with smaller furnace tubes commonly used for small-aperture fixed-point cells, a novel cell design was developed. For each of Cu, Pt C, and Re C fixed points, two types of fixed-point cells were manufactured, the small- and large-aperture cell. For Pt C and Re C, the large-aperture cells were filled with a hyper-eutectic metal carbon mixture; for the small cells, a hypo-eutectic mixture was used for filling. For each material, the small and large cells were compared with respect to radiometric differences. Whereas plateau shape and melting temperature are in good agreement for the small- and large-aperture Cu cells, a larger difference was observed between small- and large-aperture cells of Pt C and Re C, respectively. The origin of these observations, attributed to the temperature distribution inside the furnace, ingot contamination during manufacture, and non-uniform ingot formation for the larger cells, is discussed. The comparison of measurements by a radiation thermometer and filter radiometer of the Re C and Pt C large-aperture cells showed large differences that could be explained only by a strong radiance distribution across the cavity bottom. Further investigations are envisaged to clarify the cause.
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.
Institute of Scientific and Technical Information of China (English)
Yekini SHEHU
2014-01-01
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gˆateaux differentiable norm. Assume that every nonempty closed con-vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map-pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con-vex optimization problems, and split feasibility problems. Our result extends many recent important results.
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 Krasnoselski-Mann iterations which converge to fixed points of f under certain compactness conditions. But, as we show, already for uniformly convex spaces in general no bound on the rate of convergence can be computed uniformly in f. However, the iterations yield even without any compactness assumption...... and for arbitrary normed spaces approximate fixed points of arbitrary quality for bounded C (asymptotic regularity, Ishikawa 1976). We apply proof theoretic techniques (developed in previous papers) to non-effective proofs of this regularity and extract effective uniform bounds (with elementary proofs) on the rate...
Discovering and quantifying nontrivial fixed points in multi-field models
Energy Technology Data Exchange (ETDEWEB)
Eichhorn, A. [Imperial College, Blackett Laboratory, London (United Kingdom); Helfer, T. [Imperial College, Blackett Laboratory, London (United Kingdom); King' s College, London (United Kingdom); Mesterhazy, D. [Institute for Theoretical Physics, University of Bern, Albert Einstein Center for Fundamental Physics, Bern (Switzerland); Scherer, M.M. [Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany)
2016-02-15
We use the functional renormalization group and the -expansion concertedly to explore multicritical universality classes for coupled +{sub i} O(N{sub i}) vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed-point solutions for the regime of small N{sub i}. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points. (orig.)
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}.
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...
Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
Fodor, Zoltan; Kuti, Julius; Mondal, Santanu; Nogradi, Daniel; Wong, Chik Him
2016-01-01
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the $\\beta$-function was recently reported in the theory (Cheng:2014jba) with uncertainty in the location of the critical gauge coupling inside the narrow $[ 6.0
NEW FIXED POINT THEOREMS FOR P1-COMPACT MAPPINGS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
F.E. Browder and W. V. Petryshyn[1] defined the topological degree for Aproper mappings and then W. V. Petryshyn[2] studied a class of A-proper mappings, namely,P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn[2], we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem,Petryshyn's theorem, etc.
Fixed-point theorems for families of weakly non-expansive maps
Mai, Jie-Hua; Liu, Xin-He
2007-10-01
In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.
Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems
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Mohammad Imdad
2013-01-01
Full Text Available The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008. We also furnish some illustrative examples to support our main results.
Parallel fixed point implementation of a radial basis function network in an FPGA.
de Souza, Alisson C D; Fernandes, Marcelo A C
2014-09-29
This paper proposes a parallel fixed point radial basis function (RBF) artificial neural network (ANN), implemented in a field programmable gate array (FPGA) trained online with a least mean square (LMS) algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx), with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA.
Stability of the fixed points of the complex Swift-Hohenberg equation
Khairudin, N. I.; Abdullah, F. A.; Hassan, Y. A.
2016-02-01
We performed an investigation of the stability of fixed points in the complex Swift- Hohenberg equation using a variational formulation. The analysis is based on fixed points Euler-Lagrange equations and analytically showed that the Jacobian eigenvalues touched the imaginary axis and in general, Hopf bifurcation arises. The eigenvalues undergo a stability criterion in order to have Hopf's stability. Trial functions and linear loss dispersion parameter ε are responsible for the existence of stable pulse solutions in this system. We study behavior of the stable soliton-like solutions as we vary a bifurcation ε.
Chiral symmetry breaking in three-dimensional quantum electrodynamics as fixed point annihilation
Herbut, Igor F
2016-01-01
Spontaneous chiral symmetry breaking in three dimensional ($d=3$) quantum electrodynamics is understood as annihilation of an infrared-stable fixed point that describes the large-N conformal phase by another unstable fixed point at a critical number of fermions $N=N_c$. We discuss the root of universality of $N_c$ in this picture, together with some features of the phase boundary in the $(d,N)$ plane. In particular, it is shown that as $d\\rightarrow 4$, $N_c\\rightarrow 0$ with a constant slope, our best estimate of which suggests that $N_c = 2.89$ in $d=3$.
Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings
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Shahzad Naseer
2005-01-01
Full Text Available Let be a nonempty closed convex subset of a reflexive real Banach space which has a uniformly Gâteaux differentiable norm. Assume that is a sunny nonexpansive retract of with as the sunny nonexpansive retraction. Let , , be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that , , satisfy some mild conditions.
ON THE EXISTENCE OF FIXED POINTS FOR MAPPINGS OF ASYMPTOTICALLY NONEXPANSIVE TYPE
Institute of Scientific and Technical Information of China (English)
ZENG Luchuan
2004-01-01
Let C be a nonempty weakly compact convex subset of a Banach space X, and T: C → C a mapping of asymptotically nonexpansive type. Then there hold the following conclusions: (I) if X has uniform normal structure and limsup |||TjN||| ＜√N(X), where j→∞ |||TjN||| is the exact Lipschitz constant of TjN , N is some positive integer, and N(X) is the normal structure coefficient of X, then T has a fixed point; (ii) if X is uniformly convex in every direction and has weak uniform normal structure, then T has a fixed point.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
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Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
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A. Abkar
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly L(τ spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA
Directory of Open Access Journals (Sweden)
Alisson C. D. de Souza
2014-09-01
Full Text Available This paper proposes a parallel fixed point radial basis function (RBF artificial neural network (ANN, implemented in a field programmable gate array (FPGA trained online with a least mean square (LMS algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx, with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA.
Directory of Open Access Journals (Sweden)
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.
Non-perturbative fixed points and renormalization group improved effective potential
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A.G. Dias
2014-12-01
Full Text Available The stability conditions of a renormalization group improved effective potential have been discussed in the case of scalar QED and QCD with a colorless scalar. We calculate the same potential in these models assuming the existence of non-perturbative fixed points associated with a conformal phase. In the case of scalar QED the barrier of instability found previously is barely displaced as we approach the fixed point, and in the case of QCD with a colorless scalar not only the barrier is changed but the local minimum of the potential is also changed.
Infinite disorder and correlation fixed point in the Ising model with correlated disorder
Chatelain, Christophe
2017-03-01
Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations of the Ising model (q = 2), directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percolation fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations.
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.
Convexity of the Set of Fixed Points Generated by Some Control Systems
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Vadim Azhmyakov
2009-01-01
Full Text Available We deal with an application of the fixed point theorem for nonexpansive mappings to a class of control systems. We study closed-loop and open-loop controllable dynamical systems governed by ordinary differential equations (ODEs and establish convexity of the set of trajectories. Solutions to the above ODEs are considered as fixed points of the associated system-operator. If convexity of the set of trajectories is established, this can be used to estimate and approximate the reachable set of dynamical systems under consideration. The estimations/approximations of the above type are important in various engineering applications as, for example, the verification of safety properties.
Alternative co-digestion scenarios for efficient fixed-dome reactor biomethanation processes
DEFF Research Database (Denmark)
Fotidis, Ioannis; Laranjeiro, Tiago; Angelidaki, Irini
2016-01-01
Many of the existing low-tech biogas reactors in the remote rural areas of developing countries have been abandoned due to the lack of substrates. This study investigated if unutilized biomasses are able to support an efficient biomethanation process with low carbon footprint, in these rural areas......-digestion scenario with 45% and 13% higher energy recovery from biomasses' utilization and 69% and 25% less greenhouse gas (GHG) emissions, compared to R30 and R45, respectively. These results indicate that it is possible to operate efficiently low-tech biogas reactors with utilized biomasses as anaerobic digestion...
α-Coupled Fixed Points and Their Application in Dynamic Programming
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J. Harjani
2014-01-01
Full Text Available We introduce the definition of α-coupled fixed point in the space of the bounded functions on a set S and we present a result about the existence and uniqueness of such points. Moreover, as an application of our result, we study the problem of existence and uniqueness of solutions for a class of systems of functional equations arising in dynamic programming.
Fixed Points of α-Admissible Mappings on Partial Metric Spaces
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İncı M. Erhan
2014-01-01
Full Text Available In this paper, a general class of α-admissible contractions on partial metric spaces is introduced. Fixed point theorems for these contractions on partial metric spaces and their consequences are stated and proved. Illustrative example is presented.
A Fixed Point Approach to the Fuzzy Stability of a Mixed Typ e Functional Equation
Institute of Scientific and Technical Information of China (English)
Cheng Li-hua; Zhang Jun-min
2016-01-01
Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.
Fixed Point of Generalized Eventual Cyclic Gross in Fuzzy Norm Spaces for Contractive Mappings
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S. A. M. Mohsenialhosseini
2015-01-01
Full Text Available We define generalized eventual cyclic gross contractive mapping in fuzzy norm spaces, which is a generalization of the eventual cyclic gross contractions. Also we prove the existence of a fixed point for this type of contractive mapping on fuzzy norm spaces.
Weakly repelling fixed points and multiply-connected wandering domains of meromorphic functions
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if f has only finitely many weakly repelling fixed points,then there is no multiply-connected wandering domain in its Fatou set.
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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.
Fixed Point Theory for Cyclic Weak $phi-$contraction in Fuzzy Metric Spaces
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M. Hasan
2012-02-01
Full Text Available In this paper, we introduce cyclic weak $phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.
Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings
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Marin Borcut
2014-01-01
Full Text Available We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.
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Bhavana Deshpande
2014-01-01
Full Text Available We establish a common coupled fixed point theorem for weakly compatible mappings on modified intuitionistic fuzzy metric spaces. As an application of our result, we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to demonstrate our result.
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.
A Fixed Point Theorem for Set-Valued Mapping in Abstract Convex Space with Application
Institute of Scientific and Technical Information of China (English)
FAN Xiao Dong; XIANG Shu Wen
2009-01-01
A new fixed point theorem and the selection property for upper semi-continuous setvalued mappings in abstract convexity space are established. As their applications the existence of Nash equilibrium for n-person non-cooperative generalized games is proved.
Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
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Zhaohui Gu
2008-02-01
Full Text Available Let X be a uniformly convex Banach space, and let S,Ã‚Â T be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T.
Institute of Scientific and Technical Information of China (English)
Xing-hui GAO; Hai-yun ZHOU
2012-01-01
In this paper,we consider hybrid algorithms for finding common elements of the set of common fixed points of two families quasi-φ-non-expansive mappings and the set of solutions of an equilibrium problem.We establish strong convergence theorems of common elements in uniformly smooth and strictly convex Banach spaces with the property (K).
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces
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Sahar M. Ali
2007-01-01
Full Text Available We proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.
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R.A. Rashwan
2014-07-01
Full Text Available The aim of this paper is to study weak and strong convergence of an implicit random iterative process with errors to a common random fixed point of two finite families of asymptotically nonexpansive random mappings in a uniformly convex separable Banach space.
Browder's Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces
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Cancan M
2010-01-01
Full Text Available We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.
Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces
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Li Yongjin
2008-01-01
Full Text Available Let be a uniformly convex Banach space, and let be a pair of mean nonexpansive mappings. In this paper, it is proved that the sequence of Ishikawa iterations associated with and converges to the common fixed point of and .
A Fixed Point Theorem and Some Generalized Ky Fan's Minimax Inequalities
Institute of Scientific and Technical Information of China (English)
LUo XIAN-QIANG
2011-01-01
In this paper,we establish a fixed point theorem for set-valued mapping on a topological vector space without “local convexity”.And we also establish some generalized Ky Fan's minimax inequalities for set-value vector mappings,which are the generalization of some previous results.
An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions
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Vaezpour SM
2009-01-01
Full Text Available In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.
A Quantitative Version of Kirk's Fixed Point Theorem for Asymptotic Contractions
DEFF Research Database (Denmark)
Gerhardy, Philipp
2006-01-01
In [J.Math.Anal.App.277(2003) 645-650], W.A.Kirk introduced the notion of asymptotic contractions and proved a fixed point theorem for such mappings. Using techniques from proof mining, we develop a variant of the notion of asymptotic contractions and prove a quantitative version of the correspon...
A Coupled Fixed Point Theorem for Geraghty Contractions in Partially Ordered Metric Spaces
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K.P.R. Sastry
2014-07-01
Full Text Available In this paper we establish results on the existence and uniqueness of coupled fixed points of Geraghty contraction on a partially ordered set with a metric, with the continuity of the altering distance function dropped. Our results are improvements over the results of GVR Babu and P.Subhashini [3].
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...
Stallinga, S.; Rieger, B.
2012-01-01
We introduce a method for determining the position and orientation of fixed dipole emitters based on a combination of polarimetry and spot shape detection. A key element is an effective Point Spread Function model based on Hermite functions. The model offers a good description of the shape variation
Gradient flow and IR fixed point in SU(2) with Nf=8 flavors
Leino, Viljami; Rantaharju, Jarno; Rantalaiho, Teemu; Rummukainen, Kari; Suorsa, Joni M; Tuominen, Kimmo
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. The results show a clear indication of infrared fixed point consistent with perturbation theory.
Three-element zoom lens with fixed distance between focal points.
Mikš, Antonin; Novák, Jiří; Novák, Pavel
2012-06-15
This work deals with a theoretical analysis of zoom lenses with a fixed distance between focal points. Equations are derived for the primary (paraxial) design of the basic parameters of a three-element zoom lens. It is shown that the number of optical elements for such a lens must be larger than two.
Establishment of the Co-C Eutectic Fixed-Point Cell for Thermocouple Calibrations at NIMT
Ongrai, O.; Elliott, C. J.
2017-08-01
In 2015, NIMT first established a Co-C eutectic temperature reference (fixed-point) cell measurement capability for thermocouple calibration to support the requirements of Thailand's heavy industries and secondary laboratories. The Co-C eutectic fixed-point cell is a facility transferred from NPL, where the design was developed through European and UK national measurement system projects. In this paper, we describe the establishment of a Co-C eutectic fixed-point cell for thermocouple calibration at NIMT. This paper demonstrates achievement of the required furnace uniformity, the Co-C plateau realization and the comparison data between NIMT and NPL Co-C cells by using the same standard Pt/Pd thermocouple, demonstrating traceability. The NIMT measurement capability for noble metal type thermocouples at the new Co-C eutectic fixed point (1324.06°C) is estimated to be within ± 0.60 K (k=2). This meets the needs of Thailand's high-temperature thermocouple users—for which previously there has been no traceable calibration facility.
The fixed point theorems of 1-set-contractive operators in Banach space
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Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
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.
Conformal fixed point of SU(3) gauge theory with 12 fundamental fermions
Aoyama, Tatsumi; Itou, Etsuko; Kurachi, Masafumi; Lin, C -J David; Matsufuru, Hideo; Ogawa, Kenji; Ohki, Hiroshi; Onogi, Tetsuya; Shintani, Eigo; Yamazaki, Takeshi
2011-01-01
We study the infrared properties of SU(3) gauge theory coupled to 12 massless Dirac fermions in the fundamental representation. The renormalized running coupling constant is calculated in the Twisted Polyakov loop scheme on the lattice. From the step-scaling analysis, we find that the infrared behavior of the theory is governed by a non-trivial fixed point.
Analyzing fixed points of intracellular regulation networks with interrelated feedback topology
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Radde Nicole
2012-06-01
Full Text Available Abstract Background Modeling the dynamics of intracellular regulation networks by systems of ordinary differential equations has become a standard method in systems biology, and it has been shown that the behavior of these networks is often tightly connected to the network topology. We have recently introduced the circuit-breaking algorithm, a method that uses the network topology to construct a one-dimensional circuit-characteristic of the system. It was shown that this characteristic can be used for an efficient calculation of the system’s fixed points. Results Here we extend previous work and show several connections between the circuit-characteristic and the stability of fixed points. In particular, we derive a sufficient condition on the characteristic for a fixed point to be unstable for certain graph structures and demonstrate that the characteristic does not contain the information to decide whether a fixed point is asymptotically stable. All statements are illustrated on biological network models. Conclusions Single feedback circuits and their role for complex dynamic behavior of biological networks have extensively been investigated, but a transfer of most of these concepts to more complex topologies is difficult. In this context, our algorithm is a powerful new approach for the analysis of regulation networks that goes beyond single isolated feedback circuits.
Property P and some fixed point results on a new ϕ-weakly contractive mapping
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Mahmoud Bousselsal
2014-03-01
Full Text Available In this paper, we prove some fixed point results for new weakly contractive maps in G− metric spaces. It is proved that these maps satisfy property P. The results obtained in this paper generalize several well known comparable results in the literature.
Approximating fixed points of generalized nonexpansive mappings via faster iteration schemes
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Anupam Sharma
2014-09-01
Full Text Available In this paper, we approximate fixed points of generalized nonexpansive mappings in Banach spaces under relatively faster iteration schemes and also prove some weak and strong convergence theorems. Our results generalize and improve several previously known results of the existing literature.
Fixed Point Theorems of Set-Valued Mappings in Partially Ordered Hausdorff Topological Spaces
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Shujun Jiang
2014-01-01
Full Text Available In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.
Institute of Scientific and Technical Information of China (English)
Xie Ping DING
2006-01-01
Some new continuous selection theorems are first proved in noncompact topological spaces.As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.
Long-Term Stability of WC-C Peritectic Fixed Point
Khlevnoy, B. B.; Grigoryeva, I. A.
2015-03-01
The tungsten carbide-carbon peritectic (WC-C) melting transition is an attractive high-temperature fixed point with a temperature of . Earlier investigations showed high repeatability, small melting range, low sensitivity to impurities, and robustness of WC-C that makes it a prospective candidate for the highest fixed point of the temperature scale. This paper presents further study of the fixed point, namely the investigation of the long-term stability of the WC-C melting temperature. For this purpose, a new WC-C cell of the blackbody type was built using tungsten powder of 99.999 % purity. The stability of the cell was investigated during the cell aging for 50 h at the cell working temperature that tooks 140 melting/freezing cycles. The method of investigation was based on the comparison of the WC-C tested cell with a reference Re-C fixed-point cell that reduces an influence of the probable instability of a radiation thermometer. It was shown that after the aging period, the deviation of the WC-C cell melting temperature was with an uncertainty of.
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.
Fixed partitioning and salient points with MPEG-7 cluster correlograms for image categorization
Abdullah, Azizi; Veltkamp, Remco C.; Wiering, Marco A.
2010-01-01
This paper compares fixed partitioning and salient points schemes for dividing an image into patches, in combination with low-level MPEG-7 visual descriptors to represent the patches with particular patterns. A clustering technique is applied to construct a compact representation by grouping similar
Supergravity Solutions in the Low-$\\tan\\beta$ $ \\lambda_t$ Fixed Point Region
Barger, V; Ohmann, P
1994-01-01
There has been much discussion in the literature about applying the radiative electroweak symmetry breaking (EWSB) requirement to GUT models with supergravity. We motivate and discuss the application of the EWSB requirement to the low $\\tan\\beta$ fixed-point region and describe the solutions we find.
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
Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
Fodor, Zoltan; Holland, Kieran; Kuti, Julius; Mondal, Santanu; Nogradi, Daniel; Wong, Chik Him
2016-11-01
We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point (IRFP) of the β -function was recently reported in the theory [A. Cheng, A. Hasenfratz, Y. Liu, G. Petropoulos, and D. Schaich, J. High Energy Phys. 05 (2014) 137] with uncertainty in the location of the critical gauge coupling inside the narrow [6.0 fixed point and scale invariance in the theory with model-building implications. Using the exact same renormalization scheme as the previous study, we show that no fixed point of the β -function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the Nf=12 model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD β -function for arbitrary flavor number are discussed with respect to our work.
Traces of a fixed point : Unravelling the phase diagram at large Nf
Deuzeman, Albert; Lombardo, Maria Paola; Pallante, Elisabetta
2009-01-01
With a sufficiently high number of fundamental fermionic flavours present, Yang-Mills theory develops an infrared fixed point and becomes (quasi-)conformal in nature. The range of flavour numbers for which this occurs defines the conformal window, the lower limit of which has yet to be determined. W
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.
Radiative symmetry breaking from interacting UV fixed points arXiv
Abel, Steven
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.
Pearce, Jonathan V.; Gisby, John A.; Steur, Peter P. M.
2016-08-01
A knowledge of the effect of impurities at the level of parts per million on the freezing temperature of very pure metals is essential for realisation of ITS-90 fixed points. New information has become available for use with the thermodynamic modelling software MTDATA, permitting calculation of liquidus slopes, in the low concentration limit, of a wider range of binary alloy systems than was previously possible. In total, calculated values for 536 binary systems are given. In addition, new experimental determinations of phase diagrams, in the low impurity concentration limit, have recently appeared. All available data have been combined to provide a comprehensive set of liquidus slopes for impurities in ITS-90 metal fixed points. In total, liquidus slopes for 838 systems are tabulated for the fixed points Hg, Ga, In, Sn, Zn, Al, Ag, Au, and Cu. It is shown that the value of the liquidus slope as a function of impurity element atomic number can be approximated using a simple formula, and good qualitative agreement with the existing data is observed for the fixed points Al, Ag, Au and Cu, but curiously the formula is not applicable to the fixed points Hg, Ga, In, Sn, and Zn. Some discussion is made concerning the influence of oxygen on the liquidus slopes, and some calculations using MTDATA are discussed. The BIPM’s consultative committee for thermometry has long recognised that the sum of individual estimates method is the ideal approach for assessing uncertainties due to impurities, but the community has been largely powerless to use the model due to lack of data. Here, not only is data provided, but a simple model is given to enable known thermophysical data to be used directly to estimate impurity effects for a large fraction of the ITS-90 fixed points.
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.
Brown, G E; Lee, Chang-Hwan; Park, Hong-Jo; Rho, Mannque
2006-02-17
Building on, and extending, the result of a higher-order in-medium chiral perturbation theory combined with renormalization group arguments and a variety of observations of the vector manifestation of Harada-Yamawaki hidden local symmetry theory, we obtain a surprisingly simple description of kaon condensation by fluctuating around the "vector manifestation" fixed point identified to be the chiral restoration point. Our development establishes that strangeness condensation takes place at approximately 3n0 where n0 is nuclear matter density. This result depends only on the renormalization-group (RG) behavior of the vector interactions, other effects involved in fluctuating about the bare vacuum in so many previous calculations being irrelevant in the RG about the fixed point. Our results have major effects on the collapse of neutron stars into black holes.
Hybrid Fixed Point Theorems in Symmetric Spaces via Common Limit Range Property
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Imdad Mohammad
2014-12-01
Full Text Available In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012, 611-620 are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.
Many-body localization in one dimension as a dynamical renormalization group fixed point.
Vosk, Ronen; Altman, Ehud
2013-02-08
We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as loglogt found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.
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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.
Tian, Zhen; Jia, Xun; Jiang, Steve B
2013-01-01
In the treatment plan optimization for intensity modulated radiation therapy (IMRT), dose-deposition coefficient (DDC) matrix is often pre-computed to parameterize the dose contribution to each voxel in the volume of interest from each beamlet of unit intensity. However, due to the limitation of computer memory and the requirement on computational efficiency, in practice matrix elements of small values are usually truncated, which inevitably compromises the quality of the resulting plan. A fixed-point iteration scheme has been applied in IMRT optimization to solve this problem, which has been reported to be effective and efficient based on the observations of the numerical experiments. In this paper, we aim to point out the mathematics behind this scheme and to answer the following three questions: 1) whether the fixed-point iteration algorithm converges or not? 2) when it converges, whether the fixed point solution is same as the original solution obtained with the complete DDC matrix? 3) if not the same, wh...
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Lu-Chuan Ceng
2012-01-01
Full Text Available We investigate the problem of finding a common solution of a general system of variational inequalities, a variational inclusion, and a fixed-point problem of a strictly pseudocontractive mapping in a real Hilbert space. Motivated by Nadezhkina and Takahashi's hybrid-extragradient method, we propose and analyze new hybrid-extragradient iterative algorithm for finding a common solution. It is proven that three sequences generated by this algorithm converge strongly to the same common solution under very mild conditions. Based on this result, we also construct an iterative algorithm for finding a common fixed point of three mappings, such that one of these mappings is nonexpansive, and the other two mappings are strictly pseudocontractive mappings.
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.
Fixed point variational solutions for uniformly continuous pseudocontractions in banach spaces
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2006-01-01
Full Text Available Let E be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let K be a nonempty closed convex subset of E , and let T:K→K be a uniformly continuous pseudocontraction. If f:K→K is any contraction map on K and if every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers { α n } , { μ n } , that the iteration process z 1 ∈K , z n+1 = μ n ( α n T z n +( 1− α n z n +( 1− μ n f( z n , n∈ℕ , strongly converges to the fixed point of T , which is the unique solution of some variational inequality, provided that K is bounded.
A nontrivial critical fixed point for replica-symmetry-breaking transitions
Charbonneau, Patrick
2016-01-01
The transformation of the free-energy landscape from smooth to fractal is the richest feature of mean-field disordered systems. A well-studied example is the de Almeida-Thouless transition for spin glasses in a magnetic field, and a similar phenomenon--the Gardner transition--has recently been predicted for structural glasses. However, the existence of these phase transitions has been called into question below the upper critical dimension d_u=6. Here, we obtain evidence for these transitions in dimensions d
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.
General Iterative Algorithms for Hierarchical Fixed Points Approach to Variational Inequalities
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Nopparat Wairojjana
2012-01-01
Full Text Available This paper deals with new methods for approximating a solution to the fixed point problem; find x̃∈F(T, where H is a Hilbert space, C is a closed convex subset of H, f is a ρ-contraction from C into H, 00, 0<γ<γ̅/ρ, T is a nonexpansive mapping on C, and PF(T denotes the metric projection on the set of fixed point of T. Under a suitable different parameter, we obtain strong convergence theorems by using the projection method which solves the variational inequality 〈(A-γfx̃+τ(I-Sx̃,x-x̃〉≥0 for x∈F(T, where τ∈[0,∞. Our results generalize and improve the corresponding results of Yao et al. (2010 and some authors. Furthermore, we give an example which supports our main theorem in the last part.
Anomaly Mediation and Fixed Point in Partially N = 2 Supersymmetric Standard Models
Yin, Wen
2016-01-01
To explain the tension between the observed Higgs boson mass and the experimental deviations from the Standard Model (SM) prediction in flavor physics, especially the experimental anomaly of the muon anomalous dipole moment (muon $g-2$), we study partially $N=2$ supersymmetric (SUSY) extensions of the SM (partially $N=2$ SSMs). In this kind of model, an $N=2$ SUSY sector is sequestered from the SUSY breaking due to $SO(2)_R$ symmetry at the tree-level. We show that the low energy physics in the $N=2$ sector is controlled by a fixed point and hence approximately UV insensitive. Moreover at this fixed point, the tachyonic slepton problem of anomaly mediation is always solved. In a concrete partially $N=2$ SSM, the muon $g-2$ anomaly is explained within the $1\\sigma$ level error with $mathcal{O}(100)$TEV cosmologically favored gravitino. We also propose some new dark matter candidates as a natural consequence of partially $N=2$ SSMs.
Institute of Scientific and Technical Information of China (English)
ALI M.; SAHA L.M.
2005-01-01
A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1＞0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an altemative method to calculate λ1has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.
Fixed point structure of the conformal factor field in quantum gravity
Dietz, Juergen A.; Morris, Tim R.; Slade, Zoë H.
2016-12-01
The O (∂2) background-independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong-sign kinetic term. This sign change is shown to have a profound effect on the renormalization group properties, broadly resulting in a continuum of fixed points supporting both a discrete and a continuous eigenoperator spectrum, the latter always including relevant directions. The properties at the Gaussian fixed point are understood in particular depth, but also detailed studies of the local potential approximation, and the full O (∂2) approximation are given. These results are related to evidence for asymptotic safety found by other authors.
Alignment Solution for CT Image Reconstruction by Fixed Point and Virtual Rotation Axis
Jun, Kyungtaek; Kwon, Kyu
2016-01-01
Since X-ray tomography is now widely adopted in many different areas, it becomes more crucial to find a robust routine of handling tomographic data to get quality reconstructed images. Though there are several existing techniques, it seems helpful to have a more automated method to remove the possible errors that hinder clearer image reconstruction. Here, we proposed an alternative method and new algorithm using the sinogram and the fixed point. A new physical concept of Center of Attenuation (CA) was also introduced to figure out how this fixed point is applied to the image reconstruction with errors we further categorized. Our technique showed a promising performance in restoring images with translation and vertical tilt errors.
NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES
Institute of Scientific and Technical Information of China (English)
DING Xie-ping(丁协平); Park Jong-yeoul
2002-01-01
By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem, some new collectively fixed point theorems for a family of set-valued mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G-convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence theorems of abstract economies are also obtained in G-convex spaces. Our theorems improve, unify and generalized many important known results in recent literature.
Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
Farchioni, F.; Hip, I.; Lang, C. B.
1998-12-01
We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.
Common Fixed Point of Multivalued Generalized φ-Weak Contractive Mappings
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Behzad Djafari Rouhani
2010-01-01
Full Text Available Fixed point and coincidence results are presented for multivalued generalized φ-weak contractive mappings on complete metric spaces, where φ:[0,+∞→[0,+∞ is a lower semicontinuous function with φ(0=0 and φ(t>0 for all t>0. Our results extend previous results by Zhang and Song (2009, as well as by Rhoades (2001, Nadler (1969, and Daffer and Kaneko (1995.
The analysis of the number of fixed points in the key extending algorithm of RC4
Institute of Scientific and Technical Information of China (English)
2008-01-01
The probabilities of the state transitions of the initial value So in the S table of RC4 are described by a kind of bistochastic matrices, and then a computational formula for such bistochastic matrices is given, by which the mathematical expectation of the number of fixed points in the key extending algorithm of RC4 is obtained. As a result, a statistical weakness of the key extending algorithm of RC4 is presented.
THE FAST FIXED-POINT ALGORITHM FOR SPECKLE REDUCTION OF POLARIMETRIC SAR IMAGE
Institute of Scientific and Technical Information of China (English)
Fu Yusheng; Chen Xiaoning; Pi Yiming; Hou Yinming
2005-01-01
In this letter, a simple and efficient method of image speckle reduction for polarimetric SAR is put forward. It is based on the fast fixed-point ICA (Independent Component Analysis) algorithm of orthogonal and symmetric matrix. Simulation experiment is carried out to separate speckle noise from the polarimetric SAR images, and it indicates that this algorithm has high convergency speed and stability, the image speckle noise is reduced effectively and the speckle index is low, and the image quality is improved obviously.
Existence and Approximation of Fixed Points for Set-Valued Mappings
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Reich Simeon
2010-01-01
Full Text Available Taking into account possibly inexact data, we study both existence and approximation of fixed points for certain set-valued mappings of contractive type. More precisely, we study the existence of convergent iterations in the presence of computational errors for two classes of set-valued mappings. The first class comprises certain mappings of contractive type, while the second one contains mappings satisfying a Caristi-type condition.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
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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.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
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Erzakova Nina A
2004-01-01
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.
Modified van der Pauw method based on formulas solvable by the Banach fixed point method
2012-01-01
We propose a modification of the standard van der Pauw method for determining the resistivity and Hall coefficient of flat thin samples of arbitrary shape. Considering a different choice of resistance measurements we derive a new formula which can be numerically solved (with respect to sheet resistance) by the Banach fixed point method for any values of experimental data. The convergence is especially fast in the case of almost symmetric van der Pauw configurations (e.g., clover shaped samples).
The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings
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S. S. Chang
2012-01-01
Full Text Available The purpose of this paper is to propose an algorithm for solving the split common fixed point problems for total asymptotically strictly pseudocontractive mappings in infinite-dimensional Hilbert spaces. The results presented in the paper improve and extend some recent results of Moudafi (2011 and 2010, Xu (2010 and 2006, Censor and Segal (2009, Censor et al. (2005, Masad and Reich (2007, Censor et al. (2007, Yang (2004, and others.
Paraxial analysis of four-component zoom lens with fixed distance between focal points.
Miks, Antonin; Novak, Jiri
2012-07-20
Zoom lenses with a fixed distance between focal points are analyzed. Formulas are derived for the primary design of basic parameters of a four-component zoom lens. It is also demonstrated that a three-component zoom lens can be analyzed using derived formulas. Zoom lenses with such a design can be used in a 4-f system with variable magnification or as a part of a double side telecentric lenses with variable magnification.
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.
Krasnoselskii-type fixed point theorems under weak topology settings and applications
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Tian Xiang
2010-03-01
Full Text Available In this article, we establish some fixed point results of Krasnoselskii type for the sum T+S, where S is weakly continuous and T may not be continuous. Some of the main results complement and encompass the previous ones. As an application, we study the existence of solution to one parameter operator equations. Finally, our results are used to prove the existence of solution for integral equations in reflexive Banach spaces.
Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces
Institute of Scientific and Technical Information of China (English)
Shi Sheng ZHANG; H. W. JOSEPH LEE; Chi Kin CHAN
2007-01-01
The purpose of this paper is to study the convergence problem of the iteration schemexn+1=λn+1y + (1-λn+1)Tn+1Xn for a family of infinitely many nonexpansive mappings T1, T2,…ina Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly tothe nearest common fixed point of this family of nonexpansive mappings. The results presented in thispaper extend and improve some recent results.
Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas
Karl, Markus
2016-01-01
Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross-Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent $\\eta \\simeq -3$ and, related to this, a large dynamical exponent $z \\simeq 5$ are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phase-ordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a clo...
Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas
Karl, Markus; Gasenzer, Thomas
2017-09-01
Universal scaling behavior in the relaxation dynamics of an isolated two-dimensional Bose gas is studied by means of semi-classical stochastic simulations of the Gross–Pitaevskii model. The system is quenched far out of equilibrium by imprinting vortex defects into an otherwise phase-coherent condensate. A strongly anomalous non-thermal fixed point is identified, associated with a slowed decay of the defects in the case that the dissipative coupling to the thermal background noise is suppressed. At this fixed point, a large anomalous exponent η ≃ -3 and, related to this, a large dynamical exponent z≃ 5 are identified. The corresponding power-law decay is found to be consistent with three-vortex-collision induced loss. The article discusses these aspects of non-thermal fixed points in the context of phase-ordering kinetics and coarsening dynamics, thus relating phenomenological and analytical approaches to classifying far-from-equilibrium scaling dynamics with each other. In particular, a close connection between the anomalous scaling exponent η, introduced in a quantum-field theoretic approach, and conservation-law induced scaling in classical phase-ordering kinetics is revealed. Moreover, the relation to superfluid turbulence as well as to driven stationary systems is discussed.
Small Multiple Fixed-Point Cell as Calibration Reference for a Dry Block Calibrator
Marin, S.; Hohmann, M.; Fröhlich, T.
2017-02-01
A small multiple fixed-point cell (SMFPC) was designed to be used as in situ calibration reference of the internal temperature sensor of a dry block calibrator, which would allow its traceable calibration to the International Temperature Scale of 1990 (ITS-90) in the operating range of the block calibrator from 70°C to 430°C. The ITS-90 knows in this temperature range, three fixed-point materials (FPM) indium, tin and zinc, with their respective fixed-point temperatures (θ_FP), In (θ_FP = 156.5985°C), Sn (θ_FP = 231.928°C) and Zn (θ_FP = 419.527°C). All of these FPM are contained in the SMFPC in a separate chamber, respectively. This paper shows the result of temperature measurements carried out in the cell within a period of 16 months. The test setup used here has thermal properties similar to the dry block calibrator. The aim was to verify the metrological properties and functionality of the SMFPC for the proposed application.
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun-Jung [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Institut fuer Physik, Universitaet Augsburg, D-86135 Augsburg (Germany); Vojta, Matthias [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, D-76128 Karlsruhe (Germany)
2005-11-02
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
Lee, Hyun-Jung; Bulla, Ralf; Vojta, Matthias
2005-11-01
The numerical renormalization group method is used to investigate zero-temperature phase transitions in quantum impurity systems, in particular in the particle-hole symmetric soft-gap Anderson model. The model displays two stable phases whose fixed points can be built up of non-interacting single-particle states. In contrast, the quantum phase transitions turn out to be described by interacting fixed points, and their excitations cannot be described in terms of free particles. We show that the structure of the many-body spectrum of these critical fixed points can be understood using renormalized perturbation theory close to certain values of the bath exponents which play the role of critical dimensions. Contact is made with perturbative renormalization group calculations for the soft-gap Anderson and Kondo models. A complete description of the quantum critical many-particle spectra is achieved using suitable marginal operators; technically this can be understood as epsilon-expansion for full many-body spectra.
Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces
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Yongfu Su
2006-01-01
Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K→E be an asymptotically nonexpansive mapping with {kn}⊂[1,∞ such that ∑n=1∞(kn−1<∞ and F(T is nonempty, where F(T denotes the fixed points set of T. Let {αn}, {αn'}, and {αn''} be real sequences in (0,1 and ε≤αn,αn',αn''≤1−ε for all n∈ℕ and some ε>0. Starting from arbitrary x1∈K, define the sequence {xn} by x1∈K, zn=P(αn''T(PTn−1xn+(1−αn''xn, yn=P(αn'T(PTn−1zn+(1−αn'xn, xn+1=P(αnT(PTn−1yn+(1−αnxn. (i If the dual E* of E has the Kadec-Klee property, then { xn} converges weakly to a fixed point p∈F(T; (ii if T satisfies condition (A, then {xn} converges strongly to a fixed point p∈F(T.
The Fixed Point Property in c0 with an Equivalent Norm
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Berta Gamboa de Buen
2011-01-01
Full Text Available We study the fixed point property (FPP in the Banach space c0 with the equivalent norm ‖⋅‖D. The space c0 with this norm has the weak fixed point property. We prove that every infinite-dimensional subspace of (c0,‖⋅‖D contains a complemented asymptotically isometric copy of c0, and thus does not have the FPP, but there exist nonempty closed convex and bounded subsets of (c0,‖⋅‖D which are not ω-compact and do not contain asymptotically isometric c0—summing basis sequences. Then we define a family of sequences which are asymptotically isometric to different bases equivalent to the summing basis in the space (c0,‖⋅‖D, and we give some of its properties. We also prove that the dual space of (c0,‖⋅‖D over the reals is the Bynum space l1∞ and that every infinite-dimensional subspace of l1∞ does not have the fixed point property.
Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
Bae, Jin-Beom
2014-01-01
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving for the crossing symmetry condition, we propose a new approach based on specification for the low-lying spectrum distribution. We find the traditional one-gap bootstrapping is not suited since the nontrivial fixed point expected from large-N expansion sits at deep interior (not at boundary or kink) of allowed solution region. We propose two-gap bootstrapping that specifies scaling dimension of two lowest scalar operators. The approach carves out vast region of lower scaling dimensions and universally features two tips. We find that the sought-for nontrivial fixed point now sits at one of the tips, while the Gaussian fixed point sits at the other tip. The scaling dimensions of scalar operators fit well with expectation based on large-N expansion. We also find indication that t...
Scaling in the vicinity of the four-state Potts fixed point
Blöte, H. W. J.; Guo, Wenan; Nightingale, M. P.
2017-08-01
We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.
The infrared fixed point of the top quark mass and its implications within the MSSM
Carena, M S
1994-01-01
We analyse the general features 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 consider the constraints on the mass parameters, which are derived from the condition of a proper radiative electroweak symmetry breaking in the low and moderate \\tan\\beta regime. In the case of universal soft supersymmetry breaking parameters at the high energy scale, the radiative SU(2)_L \\times U(1)_Y breaking, together with the top quark Yukawa fixed point structure imply that, for any given value of the top quark mass, the Higgs and supersymmetric particle spectrum is fully determined as a function of only two supersymmetry breaking parameters. We show that, for the interesting range of top quark mass values M_t\\simeq 175\\pm 10 GeV, both a light chargino and a light stop may be present in the spectrum. In addition, for a given top quark mass, the infrared fixed point solution of the top quark Yukawa coupl...
Fixed points of the SRG evolution and the on-shell limit of the nuclear force
Arriola, E Ruiz; Timoteo, V S
2016-01-01
We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff $\\lambda \\rightarrow 0$ may be obtained from the eigenvalues of the hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit $\\lambda \\to 0$ on a finite momentum grid. Another issue we investigate is the location on the diagonal of the hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the ce...
Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings
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M. De la Sen
2012-01-01
Full Text Available p(≥2-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.
Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction
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Poom Kumam
2013-01-01
Full Text Available Ran and Reurings (2004 established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.
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.
Pireddu, Marina
2009-01-01
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the Paths" method, since we deal with maps that expand the arcs along one direction. Our technique is also significant from a dynamical point of view, as it allows to detect complex dynamics. In particular, we are able to prove semi-conjugacy to the Bernoulli shift and thus positivity of the topological entropy, the presence of topological transitivity and sensitivity with respect to initial conditions, density of periodic points. Moreover, our approach, although mathematically rigorous, avoids the use of sophisticated topological theories and it is relatively easy to apply to specific models arising in the applications. For example we have here employed the Stretching along the paths method to study discrete and continuous-time models arising from economics and biology.
Fixed Point Theorems on Generalized Metric Spaces for Mappings in a Class Of Almost φ-Contractions
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Kikina Luljeta
2015-09-01
Full Text Available In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.
Fixed Points for E-Asymptotic Contractions and Boyd-Wong Type E-Contractions in Uniform Spaces
Aghanians, A.; Fallahi, K.; Nourouzi, K.
2013-01-01
In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version of Kirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.
On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos
Bauer, Andrej
2009-01-01
In the effective topos there exists a chain-complete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the Bourbaki-Witt theorem and Tarski's fixed-point theorem for chain-complete lattices do not have constructive (topos-valid) proofs.
Institute of Scientific and Technical Information of China (English)
WANG Jun; YI Hongxun; CAI Huiping
2004-01-01
In this paper, we study the problem on the fixed points of the lth power of linear differential polynomials generated by second order linear differential equations.Because of the control of differential equation, we can obtain some precise estimate of their fixed points.
Institute of Scientific and Technical Information of China (English)
Yongjie Piao
2008-01-01
In this paper, we prove that a family of self-maps {TI,j}I,j ∈N in 2-metric space has a unique common fixed point if (I) {TI,j}I,j∈N satisfies the same type contractive con-main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.
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Songnian He
2012-01-01
Full Text Available Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {Tk}k=1∞:C→C an infinite family of nonexpansive mappings with the nonempty set of common fixed points ⋂k=1∞Fix(Tk, and f:C→C a contraction. We introduce an explicit iterative algorithm xn+1=αnf(xn+(1-αnLnxn, where Ln=∑k=1n(ωk/snTk,Sn=∑k=1nωk, and wk>0 with ∑k=1∞ωk=1. Under certain appropriate conditions on {αn}, we prove that {xn} converges strongly to a common fixed point x* of {Tk}k=1∞, which solves the following variational inequality: 〈x*-f(x*,J(x*-p〉≤0, p∈⋂k=1∞Fix(Tk, where J is the (normalized duality mapping of X. This algorithm is brief and needs less computational work, since it does not involve W-mapping.
Yamada, Y.; Wang, Y.; Sasajima, N.
2006-10-01
WC-C, Cr3C2-C and Mn7C3-C peritectic systems were investigated for their potential of serving as high-temperature reference points in thermometry. Mixtures of high-purity graphite powder with W, Cr and Mn powder of 99.99%, 99.9% and 99.95% purity by mass, respectively, were placed in graphite blackbody crucibles and melting/freezing plateaus were observed by means of a radiation thermometer. The observed melting temperatures were 2749 °C (WC-C), 1826 °C (Cr3C2-C) and 1331 °C (Mn7C3-C), with a repeatability—in each case—of 0.02 K. The melting range for WC-C and Cr3C2-C peritectics was roughly 0.1 K. WC-C showed a flat freezing plateau that agreed with the melting plateau within the repeatability. The three fixed points are possible candidates, like the metal (carbide)-carbon eutectic fixed points, in the realization of an improved high-temperature scale above the copper point.
Edler, F.; Huang, K.
2016-12-01
Fifteen miniature fixed-point cells made of three different ceramic crucible materials (Al2O3, ZrO2, and Al2O3 (86 %)+ZrO2 (14 %)) were filled with pure palladium and used for the calibration of type B thermocouples (Pt30%Rh/Pt6%Rh). The melting behavior of the palladium was investigated by using different high-temperature furnaces usable in horizontal and vertical positions. It was found that the electromotive forces measured at the melting temperature of palladium are consistent with a temperature equivalent of ±0.25 K when using a furnace with an adequate temperature homogeneity (±1 K over a length of 12 cm), independent of the ceramic crucible materials. The emfs measured in the one-zone furnaces with larger temperature gradients along the crucibles are sensitive related to the position of the crucibles in the temperature gradient of these furnaces. This is caused by higher parasitic heat flux effects which can cause measurement errors up to about {-}(1 {-}2) K, depending on the thermal conductivity of the ceramic material. It was found that the emfs measured by using crucibles with lower thermal conductivity (ZrO2) were less dependent on parasitic heat flux effects than crucibles made of material of higher thermal conductivity (Al2O3). The investigated miniature fixed points are suitable for the repeatable realization of the melting point of palladium to calibrate noble metal thermocouples without the disadvantages of the wire-bridge method or the wire-coil method.
Estimating the Contribution of Impurities to the Uncertainty of Metal Fixed-Point Temperatures
Hill, K. D.
2014-04-01
The estimation of the uncertainty component attributable to impurities remains a central and important topic of fixed-point research. Various methods are available for this estimation, depending on the extent of the available information. The sum of individual estimates method has considerable appeal where there is adequate knowledge of the sensitivity coefficients for each of the impurity elements and sufficiently low uncertainty regarding their concentrations. The overall maximum estimate (OME) forsakes the behavior of the individual elements by assuming that the cryoscopic constant adequately represents (or is an upper bound for) the sensitivity coefficients of the individual impurities. Validation of these methods using melting and/or freezing curves is recommended to provide confidence. Recent investigations of indium, tin, and zinc fixed points are reported. Glow discharge mass spectrometry was used to determine the impurity concentrations of the metals used to fill the cells. Melting curves were analyzed to derive an experimental overall impurity concentration (assuming that all impurities have a sensitivity coefficient equivalent to that of the cryoscopic constant). The two values (chemical and experimental) for the overall impurity concentrations were then compared. Based on the data obtained, the pragmatic approach of choosing the larger of the chemical and experimentally derived quantities as the best estimate of the influence of impurities on the temperature of the freezing point is suggested rather than relying solely on the chemical analysis and the OME method to derive the uncertainty component attributable to impurities.
Infrared behavior and fixed-point structure in the compactified Ginzburg--Landau model
Linhares, C A; Souza, M L
2011-01-01
We consider the Euclidean $N$-component Ginzburg--Landau model in $D$ dimensions, of which $d$ ($d\\leq D$) of them are compactified. As usual, temperature is introduced through the mass term in the Hamiltonian. This model can be interpreted as describing a system in a region of the $D$-dimensional space, limited by $d$ pairs of parallel planes, orthogonal to the coordinates axis $x_1,\\,x_2,\\,...,\\,x_d$. The planes in each pair are separated by distances $L_1,\\;L_2,\\; ...,\\,L_d$. For $D=3$, from a physical point of view, the system can be supposed to describe, in the cases of $d=1$, $d=2$, and $d=3$, respectively, a superconducting material in the form of a film, of an infinitely long wire having a retangular cross-section and of a brick-shaped grain. We investigate in the large-$N$ limit the fixed-point structure of the model, in the absence or presence of an external magnetic field. An infrared-stable fixed point is found, whether of not an external magnetic field is applied, but for different ranges of valu...
Ultraviolet fixed point and massive composite particles in TeV scales
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She-Sheng Xue
2014-10-01
Full Text Available We present a further study of the dynamics of high-dimension fermion operators attributed to the theoretical inconsistency of the fundamental cutoff (quantum gravity and the parity-violating gauge symmetry of the standard model. Studying the phase transition from a symmetry-breaking phase to a strong-coupling symmetric phase and the β-function behavior in terms of four-fermion coupling strength, we discuss the critical transition point as a ultraviolet-stable fixed point where a quantum field theory preserving the standard model gauge symmetry with composite particles can be realized. The form-factors and masses of composite particles at TeV scales are estimated by extrapolating the solution of renormalization-group equations from the infrared-stable fixed point where the quantum field theory of standard model is realized and its phenomenology including Higgs mass has been experimentally determined. We discuss the probability of composite-particle formation and decay that could be experimentally verified in the LHC by measuring the invariant mass of relevant final states and their peculiar kinetic distributions.
Dry Block Calibrator with Improved Temperature Field and Integrated Fixed-Point Cells
Hohmann, Michael; Marin, Sebastian; Schalles, Marc; Fröhlich, Thomas
2017-02-01
To reduce uncertainty of calibrations of contact thermometers using dry block calibrators, a concept was developed at Institute for Process Measurement and Sensor Technology of Technische Universität Ilmenau. This concept uses a multi-zone heating, heat flux sensors and a multiple fixed-point cell. The paper shows the concept and its validation on the basis of a dry block calibrator with a working temperature range of 70°C to 430°C. The experimental results show a stability of ± 4 mK for the reference temperature and axial temperature differences in the normalization block less than ± 55 mK.
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
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Thabet Abdeljawad
2012-01-01
Full Text Available In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F:X×X→X and g:X→X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012 have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012.
An algorithm for variational inequalities with equilibrium and fixed point constraints
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Bui Van Dinh
2015-12-01
Full Text Available In this paper, we propose a new hybrid extragradient-viscosity algorithm for solving variational inequality problems, where the constraint set is the common elements of the set of solutions of a pseudomonotone equilibrium problem and the set of fixed points of a demicontractive mapping. Using the hybrid extragradient-viscosity method and combining with hybrid plane cutting techniques, we obtain the algorithm for this problem. Under certain conditions on parameters, the convergence of the iteration sequences generated by the algorithms is obtained.
Institute of Scientific and Technical Information of China (English)
刘颖范; 陈晓红
2004-01-01
Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model, input-output equation were introduced, as well as three corresponding questions, namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained, which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprise's consuming operator.
Multiplicities of fixed points of holomorphic maps in several complex variables
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Let Δv be the unit ball in Cv with center 0 (the origin of Cv)and let F:Δv→Cv be a holomorphic map with F(0)=0. This paper is to study the fixed point multiplicities at the origin 0 of the iterates Fi=F。…。F (i times), i=1,2,… . This problem is easy when v=1, but it is very complicated when v>1. We will study this problem generally.
Hints of 5d Fixed Point Theories from Non-Abelian T-duality
Lozano, Yolanda; Rodriguez-Gomez, Diego
2013-01-01
In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS(6) solution constructed in Lozano et al. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS(6) solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.
Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
Hogervorst, Matthijs; van Rees, Balt C
2016-01-01
We consider the continuation of free and interacting scalar field theory to non-integer spacetime dimension d. We find that the correlation functions in these theories are necessarily incompatible with unitarity (or with reflection positivity in Euclidean signature). In particular, the theories contain negative norm states unless d is a positive integer. These negative norm states can be obtained via the OPE from simple positive norm operators, and are therefore an integral part of the theory. At the Wilson-Fisher fixed point the non-unitarity leads to the existence of complex anomalous dimensions. We demonstrate that they appear already at leading order in the epsilon expansion.
Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups
Institute of Scientific and Technical Information of China (English)
Lu Chuan ZENG
2004-01-01
Let X be a Banach space with a weak uniform normal structure and C a non-empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t): t ∈ S} of selfmappings on C satisfyinglim inf |‖T(t)‖| ＜ WCS(X)S(∈)t→∞has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and |‖T(t) ‖ | is the exact Lipschitz constant of T(t).
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.
Subcategories of fixed points of mutations in root categories with type n-1
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
For any n 3, let R(n) denote the root category of finite-dimensional nilpotent representations of cyclic quiver with n vertices. In the present paper, we prove that R(n-1) is triangle-equivalent to the subcategory of fixed points of certain left (or right) mutation in R(n). As an application, it is shown that the affine Kac-Moody algebra of type n-2 is isomorphic to a Lie subalgebra of the Kac-Moody algebra of type n-1.
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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.
Common fixed point theorems for occasionally weakly compatible self mappings in Menger spaces
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Sumitra Dalal
2013-07-01
Full Text Available The aim of this paper is to establish common fixed point theorems for two pairs of maps satisfying a new contractive condition of integral type using the concept of occasionally weakly compatible single and multi-valued maps in probabilistic metric spaces. Our results neither require completeness of space nor the continuity of the maps involved there in .Our results extend, generalize and improve the results of existing in literature . Related examples have also been quoted.
Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings
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Kanokwan Sitthithakerngkiet
2013-01-01
Full Text Available Let K be a nonempty compact convex subset of a topological vector space. In this paper-sufficient conditions are given for the existence of x∈K such that F(T∩VEP(F≠∅, where F(T is the set of all fixed points of the multivalued mapping T and VEP(F is the set of all solutions for vector equilibrium problem of the vector-valued mapping F. This leads us to generalize and improve some existence results in the recent references.
Institute of Scientific and Technical Information of China (English)
WANG XIONG-RUI; Ji You-qing
2011-01-01
In this paper,the iteration xn+1 =any + (1 - αn)Tk(n)i(n)xn for a family of asymptotically nonexpansive mappings T1,T2,...,TN is originally introduced in an uniformly convex Banach space.Motivated by recent papers,we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings.The results presented in this paper expand and improve correponding ones from Hilbert spaces to uniformly convex Banach spaces,or from nonexpansive mappings to asymptotically nonexpansive mappings.
Energy Technology Data Exchange (ETDEWEB)
Berges, J. [Technische Hochschule Darmstadt (Germany). Inst. fuer Kernphysik]|[California Univ., Santa Barbara, CA (United States). Inst. for Theoretical Physics; Rothkopf, A. [Tokyo Univ. (Japan). Dept. of Physics; Schmidt, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2008-02-15
Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The non-thermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early universe after inflation and the question of fast thermalization in heavy-ion collision experiments. (orig.)
On the Computational Content of the Krasnoselski and Ishikawa Fixed Point Theorems
DEFF Research Database (Denmark)
Kohlenbach, Ulrich
2001-01-01
of the asymptotic regularity. We first consider the classical case of uniformly convex spaces which goes back to Krasnoselski (1955) and show how a logically motivated modification allows to obtain an improved bound. Moreover, we get a completely elementary proof for a result which was obtained in 1990 by Kirk...... and Martinez-Yanez only with the use of the deep Browder-Göhde-Kirk fixed point theorem. In section 4 we report on new results ([29]) we established for the general case of arbitrary normed spaces including new quantitative versions of Ishikawa's theorem (for bounded C) and its extension due to Borwein, Reich...
Infinite-randomness fixed points for chains of non-Abelian quasiparticles.
Bonesteel, N E; Yang, Kun
2007-10-05
One-dimensional chains of non-Abelian quasiparticles described by SU(2)k Chern-Simons-Witten theory can enter random singlet phases analogous to that of a random chain of ordinary spin-1/2 particles (corresponding to k-->infinity). For k=2 this phase provides a random singlet description of the infinite-randomness fixed point of the critical transverse field Ising model. The entanglement entropy of a region of size L in these phases scales as S(L) approximately lnd/3 log(2)L for large L, where d is the quantum dimension of the particles.
Fermi surfaces in general codimension and a new controlled nontrivial fixed point.
Senthil, T; Shankar, R
2009-01-30
The energy of a d-dimensional Fermi system typically varies only along d(c)=1 ("radial") dimensions. We consider d(c)=1+epsilon and study a transition to superconductivity in an epsilon expansion. The nontrivial fixed point describes a scale invariant theory with an effective space-time dimension D=d(c)+1. Remarkably, the results can be reproduced by the Hertz-Millis action for the superconducting order parameter in higher effective space-time dimensions. We consider possible realizations of the transition at epsilon=1, which corresponds to a linear Fermi surface in d=3.
Infinite randomness fixed point of the superconductor-metal quantum phase transition.
Del Maestro, Adrian; Rosenow, Bernd; Müller, Markus; Sachdev, Subir
2008-07-18
We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one-dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. [Phys. Rev. Lett. 99, 230601 (2007)10.1103/PhysRevLett.99.230601] that the transition is characterized by the same strong-disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field.
Rare event simulation for stochastic fixed point equations related to the smoothing transform
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.; Xu, Jie
2013-01-01
In several applications arising in computer science, cascade theory, and other applied areas, it is of interest to evaluate the tail probabilities of non-homogeneous stochastic fixed point equations. Recently, techniques have been developed for the related linear recursions, yielding tail estimates...... and importance sampling methods for these recursions. However, such methods do not routinely generalize to non-homogeneous recursions. Drawing on techniques from the weighted branching process literature, we present a consistent, strongly efficient importance sampling algorithm for estimating the tail...... probabilities for the case of non-homogeneous recursions....
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Lu-Chuan Ceng
2014-01-01
Full Text Available We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.
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.
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.
Development of a new radiometer for the thermodynamic measurement of high temperature fixed points
Energy Technology Data Exchange (ETDEWEB)
Dury, M. R.; Goodman, T. M.; Lowe, D. H.; Machin, G.; Woolliams, E. R. [National Physical Laboratory, Teddington (United Kingdom)
2013-09-11
The National Physical Laboratory (NPL) has developed a new radiometer to measure the thermodynamic melting point temperatures of high temperature fixed points with ultra-low uncertainties. In comparison with the NPL's Absolute Radiation Thermometer (ART), the 'THermodynamic Optical Radiometer' (THOR) is more portable and compact, with a much lower size-of-source effect and improved performance in other parameters such as temperature sensitivity. It has been designed for calibration as a whole instrument via the radiance method, removing the need to calibrate the individual subcomponents, as required by ART, and thereby reducing uncertainties. In addition, the calibration approach has been improved through a new integrating sphere that has been designed to have greater uniformity.
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M. De la Sen
2009-01-01
Full Text Available A generalization of Halpern's iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern's iteration, a contractive mapping, and a nonexpansive one. The sum of the real coefficient sequences of four of the above terms is not required to be unity at each sample but it is assumed to converge asymptotically to unity. Halpern's iteration solution is proven to converge strongly to a unique fixed point of the asymptotically nonexpansive mapping.
The Brouwer fixed point theorem and tetragon with all vertexes in a surface
Institute of Scientific and Technical Information of China (English)
麦结华
1999-01-01
Let D be a disc with radius r in the Euclidean plane R2, and let F be a Lipschitz continuous real valued function on D. Suppose A1A2A3A4 is an isosceles trapezoid with lengths of edges not greater than r, and ∠A1A2A3=α≤π/2. By means of the Brouwer fixed point theorem, it is proved that if F has a Lipschitz constant λ≤min{1, tgα}, then there exist four coplanar points in the surface M = {（x, y, F（x, y））∈R3: （x, y）∈D}which span a tetragon congruent to A1A2A3A4. In addition, some further problems are discussed.
Quasi-gaussian fixed points and factorial cumulants in nuclear multifragmentation
Lacroix, D
1996-01-01
We re-analyze the conditions for the phenomenon of intermittency (self-similar fluctuations) to occur in models of multifragmentation. Analyzing two different mechanisms, the bond-percolation and the ERW (Elattari, Richert and Wagner) statistical fragmentation models, we point out a common quasi-gaussian shape of the total multiplicity distribution in the critical range. The fixed-point property is also observed for the multiplicity of the second bin. Fluctuations are studied using scaled factorial cumulants instead of scaled factorial moments. The second-order cumulant displays the intermittency signal while higher order cumulants are equal to zero, revealing a large information redundancy in scaled factorial moments. A practical criterion is proposed to identify the gaussian feature of light-fragment production, distinguishing between a self-similarity mechanism (ERW) and the superposition of independent sources (percolation).
Off-Axis Orbits in Realistic Helical Wigglers Fixed Points and Time Averaged Dynamical Variables
ThomasDonohue, John
2004-01-01
Many years ago Fajans, Kirkpatrick and Bekefi studied off-axis orbits in a realistic helical wiggler, both experimentally and theoretically. They found that as the distance from the axis of symmetry to the guiding center increased, both the mean axial velocity and the precession frequency of the guiding center varied. . They proposed a clever semi-empirical model which yielded an excellent description of both these variations. We point out that a approximate model proposed by us several years ago can be made to predict these delicate effects correctly, provided we extend our truncated quadratic Hamiltonian to include appropriate cubic terms. We develop an argument similar to the virial theorem to compare time averaged and fixed-point values of dynamical variables. Illustrative comparisons of our model with numerical calculation are presented.
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
We investigate the infrared dynamics of a nonsupersymmetric SU(X) gauge theory featuring an adjoint fermion, Nf Dirac flavors and an Higgs-like complex Nf x Nf scalar which is a gauge singlet. We first establish the existence of an infrared stable perturbative fixed point and then investigate...... the spectrum near this point. We demonstrate that this theory naturally features a light scalar degree of freedom to be identified with the dilaton and elucidate its physical properties. We compute the spectrum and demonstrate that at low energy the nonperturbative part of the spectrum of the theory is the one...... 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...
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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.
Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
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P. Pasom
2012-01-01
Full Text Available Let C be a nonempty bounded closed convex subset of a complete CAT(0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmkxk⊕tmkTmnky(m-1k, y(m-1k=(1-t(m-1kxk⊕t(m-1kTm-1nky(m-2k,y(m-2k=(1-t(m-2kxk⊕t(m-2kTm-2nky(m-3k,…,y2k=(1-t2kxk⊕t2kT2nky1k,y1k=(1-t1kxk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.
Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces
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Aniefiok Udomene
2006-03-01
Full Text Available Let E be a reflexive Banach space with a uniformly GÃƒÂ¢teaux differentiable norm, let K be a nonempty closed convex subset of E, and let T:KÃ¢Â†Â’K be a uniformly continuous pseudocontraction. If f:KÃ¢Â†Â’K is any contraction map on K and if every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers {ÃŽÂ±n}, {ÃŽÂ¼n}, that the iteration process z1Ã¢ÂˆÂˆK, zn+1=ÃŽÂ¼n(ÃŽÂ±nTzn+(1Ã¢ÂˆÂ’ÃŽÂ±nzn+(1Ã¢ÂˆÂ’ÃŽÂ¼nf(zn, nÃ¢ÂˆÂˆÃ¢Â„Â•, strongly converges to the fixed point of T, which is the unique solution of some variational inequality, provided that K is bounded.
Goldberg, Daniel N.; Krishna Narayanan, Sri Hari; Hascoet, Laurent; Utke, Jean
2016-05-01
We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.
Nonthermal Fixed Points in Quantum Field Theory Beyond the Weak-Coupling Limit
Berges, Jürgen
2016-01-01
Quantum systems in extreme conditions can exhibit universal behavior far from equilibrium associated to nonthermal fixed points, with a wide range of topical applications from early-universe inflaton dynamics and heavy-ion collisions to strong quenches in ultracold quantum gases. So far, most studies rely on a mapping of the quantum dynamics onto a classical-statistical theory that can be simulated on a computer. However, the mapping is based on a weak-coupling limit while phenomenological applications often require moderate values of couplings. We report on the observation of nonthermal fixed points directly in quantum field theory beyond the weak-coupling limit. For the example of a relativistic scalar \\mathrm{O}(N) symmetric quantum field theory, we numerically solve the nonequilibrium dynamics employing a 1/N expansion to next-to-leading order, which does not rely on a small coupling parameter. Starting from two different sets of (a) over-occupied and (b) strong-field initial conditions, we find that nont...
Investigation of Furnace Uniformity and its Effect on High-Temperature Fixed-Point Performance
Khlevnoy, B.; Sakharov, M.; Ogarev, S.; Sapritsky, V.; Yamada, Y.; Anhalt, K.
2008-02-01
A large-area furnace BB3500YY was designed and built at the VNIIOFI as a furnace for high-temperature metal (carbide)-carbon (M(C)-C) eutectic fixed points and was then investigated at the NMIJ. The dependence of the temperature uniformity of the furnace on various heater and cell holder arrangements was investigated. After making some improvements, the temperature of the central part of the furnace was uniform to within 2K over a length of 40 mm—the length of the fixed-point cell—at a temperature of 2,500°C. With this furnace, the melting plateaux of Re-C and TiC-C were shown to be better than those observed in other furnaces. For instance, a Re-C cell showed melting plateaux with a 0.1K melting range and a duration of about 40 min. Furthermore, to verify the capability of the furnace to fill cells, one Re-C and one TiC-C cell were made using the BB3500YY. The cells were then compared to a Re-C cell made in a Nagano furnace and a TiC-C cell filled in a BB3200pg furnace. The agreement in plateau shapes demonstrates the capability of the BB3500YY furnace to also function as a filling furnace.
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.
Dipeptide Aggregation in Aqueous Solution from Fixed Point-Charge Force Fields.
Götz, Andreas W; Bucher, Denis; Lindert, Steffen; McCammon, J Andrew
2014-04-08
The description of aggregation processes with molecular dynamics simulations is a playground for testing biomolecular force fields, including a new generation of force fields that explicitly describe electronic polarization. In this work, we study a system consisting of 50 glycyl-l-alanine (Gly-Ala) dipeptides in solution with 1001 water molecules. Neutron diffraction experiments have shown that at this concentration, Gly-Ala aggregates into large clusters. However, general-purpose force fields in combination with established water models can fail to correctly describe this aggregation process, highlighting important deficiencies in how solute-solute and solute-solvent interactions are parametrized in these force fields. We found that even for the fully polarizable AMOEBA force field, the degree of association is considerably underestimated. Instead, a fixed point-charge approach based on the newly developed IPolQ scheme [Cerutti et al. J. Phys. Chem.2013, 117, 2328] allows for the correct modeling of the dipeptide aggregation in aqueous solution. This result should stimulate interest in novel fitting schemes that aim to improve the description of the solvent polarization effect within both explicitly polarizable and fixed point-charge frameworks.
Institute of Scientific and Technical Information of China (English)
朴勇杰
2009-01-01
The definitions of S-KKM property and F-invariable property for multi-valued mapping are established, and by which, a new almost fixed point theorem and several fixed point theorems on Haudorff locally G-convex uniform space are obtained, and a quasi-variational in-equality theorem for acyclic map on Hausdorff φ-space is proved. Our results improve and generalize the corresponding results in recent literatures.
Holden, Joshua
2011-01-01
Brizolis asked for which primes p greater than 3 does there exist a pair (g, h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fixed point of the discrete logarithm with base g. Zhang (1995) and Cobeli and Zaharescu (1999) answered with a "yes" for sufficiently large primes and gave estimates for the number of such pairs when g and h are primitive roots modulo p. In 2000, Campbell showed that the answer to Brizolis was "yes" for all primes. The first author has extended this question to questions about counting fixed points, two-cycles, and collisions of the discrete exponential map. In this paper, we use p-adic methods, primarily Hensel's lemma and p-adic interpolation, to count fixed points, two cycles, collisions, and solutions to related equations modulo powers of a prime p.
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M. Eshaghi Gordji
2012-01-01
Full Text Available We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.
M. Eshaghi Gordji; H. Baghani; G. H. Kim
2012-01-01
We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.
Rodé's theorem on common fixed points of semigroup of nonexpansive mappings in CAT(0 spaces
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Anakkamatee Watcharapong
2011-01-01
Full Text Available Abstract We extend Rodé's theorem on common fixed points of semigroups of nonexpansive mappings in Hilbert spaces to the CAT(0 space setting. 2000 Mathematics Subject Classification: 47H09; 47H10.
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Hallowed Olaoluwa
2015-01-01
Full Text Available In this research work, some results on the existence and approximation of common coupled fixed points of contractive maps in cone metric spaces are unified and generalized based on a new method.
Possible large-N fixed-points and naturalness for O(N) scalar fields
Krishnaswami, Govind S
2009-01-01
We try to use scale-invariance and the large-N limit to find a non-trivial 4d O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action for space-time dependent background fields to be finite and scale-invariant when regulators are removed. We find a line of non-trivial UV fixed-points in the large-N limit, parameterized by a dimensionless coupling. They reduce to classical lambda phi^4 theory when hbar vanishes. For hbar non-zero, neither action nor measure is scale invariant, but the effective action is. Scale invariance makes it natural to set a mass deformation to zero. The model has phases where O(N) invariance is unbroken or spontaneously broken. Masses of the lightest excitations above the unbroken vacuum are found. We derive a non-linear equation for oscillations about the broken vacuum. The interaction potential is shown to have a locality property at large-N. In 3d, our construction reduces to th...
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.
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
}, D_n\\} +B_n$, where $\\{ (A_n,B_n,D_n): n \\in \\pintegers \\}$ is an i.i.d.\\ sequence of random variables. Next, we consider recursions where the driving sequence of vectors, $\\{(A_n, B_n, D_n): n \\in \\pintegers \\}$, is modulated by a Markov chain in general state space. We demonstrate an asymmetry......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 ${\\bf E} [\\log \\: A......] 0)$, we establish a central limit theorem for the forward recursion generated by the SFPE, namely the process $V_n= A_n \\max\\{V_{n-1...
Finite Size Scaling of the Higgs-Yukawa Model near the Gaussian Fixed Point
Chu, David Y -J; Knippschild, Bastian; Lin, C -J David; Nagy, Attila
2016-01-01
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.
Nonequilibrium dynamical mean-field study of the nonthermal fixed point in the Hubbard model
Tsuji, Naoto; Eckstein, Martin; Werner, Philipp
2014-03-01
A fundamental question of whether and how an isolated quantum many-body system thermalizes has been posed and attracted broad interest since its ideal realization using cold atomic gases. In particular, it has been indicated by various theoretical studies that the system does not immediately thermalize but often shows ``prethermalization'' as a quasi-stationary state, where local observables quickly arrive at the thermal values while the full momentum distribution stays nonthermal for long time. Here we study the thermalization process for the fermionic Hubbard model in the presence of the antiferromagnetic long-range order. Time evolution is obtained by the nonequilibrium dynamical mean-field theory. Due to classical fluctuations, prethermalization is prevented, and the transient dynamics is governed by a nonthermal fixed point, which we discuss belongs to a universality class distinct from the conventional Ginzburg-Landau theory.
Bhole, Gaurav; Anjusha, V. S.; Mahesh, T. S.
2016-04-01
A robust control over quantum dynamics is of paramount importance for quantum technologies. Many of the existing control techniques are based on smooth Hamiltonian modulations involving repeated calculations of basic unitaries resulting in time complexities scaling rapidly with the length of the control sequence. Here we show that bang-bang controls need one-time calculation of basic unitaries and hence scale much more efficiently. By employing a global optimization routine such as the genetic algorithm, it is possible to synthesize not only highly intricate unitaries, but also certain nonunitary operations. We demonstrate the unitary control through the implementation of the optimal fixed-point quantum search algorithm in a three-qubit nuclear magnetic resonance (NMR) system. Moreover, by combining the bang-bang pulses with the crusher gradients, we also demonstrate nonunitary transformations of thermal equilibrium states into effective pure states in three- as well as five-qubit NMR systems.
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.
Type-Based Termination, Inflationary Fixed-Points, and Mixed Inductive-Coinductive Types
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Andreas Abel
2012-02-01
Full Text Available Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away. Termination and productivity are non-trivial yet desired program properties, and several type systems have been put forward that guarantee termination, compositionally. These type systems are intimately connected to the definition of least and greatest fixed-points by ordinal iteration. While most type systems use conventional iteration, we consider inflationary iteration in this article. We demonstrate how this leads to a more principled type system, with recursion based on well-founded induction. The type system has a prototypical implementation, MiniAgda, and we show in particular how it certifies productivity of corecursive and mixed recursive-corecursive functions.
Hints of 5d fixed point theories from non-Abelian T-duality
Energy Technology Data Exchange (ETDEWEB)
Lozano, Yolanda; Colgáin, Eoin Ó; Rodríguez-Gómez, Diego [Department of Physics, University of Oviedo,Avda. Calvo Sotelo 18, 33007 Oviedo (Spain)
2014-05-05
In this paper we investigate the properties of the putative 5d fixed point theory that should be dual, through the holographic correspondence, to the new supersymmetric AdS{sub 6} solution constructed in http://dx.doi.org/10.1103/PhysRevLett.110.231601. This solution is the result of a non-Abelian T-duality transformation on the known supersymmetric AdS{sub 6} solution of massive Type IIA. The analysis of the charge quantization conditions seems to put constraints on the global properties of the background, which, combined with the information extracted from considering probe branes, suggests a 2-node quiver candidate for the dual CFT.
ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T ={T(t):t∈S}be a Lipschitzian semigroup on C with lim inf|||T(t)||| ＜ Np, where Np isn→∞t∈s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x ∈ E implies ωw(x) E; (P2)T is asymptotically regular on E. The authors prove that there exists a z ∈ E such that T(s)z = z for all s ∈ S. Further, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.
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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.
Stallinga, Sjoerd; Rieger, Bernd
2012-03-12
We introduce a method for determining the position and orientation of fixed dipole emitters based on a combination of polarimetry and spot shape detection. A key element is an effective Point Spread Function model based on Hermite functions. The model offers a good description of the shape variations with dipole orientation and polarization detection channel, and provides computational advantages over the exact vectorial description of dipole image formation. The realized localization uncertainty is comparable to the free dipole case in which spots are rotationally symmetric and can be well modeled with a Gaussian. This result holds for all dipole orientations, for all practical signal levels, and for defocus values within the depth of focus, implying that the massive localization bias for defocused emitters with tilted dipole axis found with Gaussian spot fitting is eliminated.
A Maximum Entropy Fixed-Point Route Choice Model for Route Correlation
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Louis de Grange
2014-06-01
Full Text Available In this paper we present a stochastic route choice model for transit networks that explicitly addresses route correlation due to overlapping alternatives. The model is based on a multi-objective mathematical programming problem, the optimality conditions of which generate an extension to the Multinomial Logit models. The proposed model considers a fixed point problem for treating correlations between routes, which can be solved iteratively. We estimated the new model on the Santiago (Chile Metro network and compared the results with other route choice models that can be found in the literature. The new model has better explanatory and predictive power that many other alternative models, correctly capturing the correlation factor. Our methodology can be extended to private transport networks.
A topological version of the Poincar\\'e-Birkhoff theorem with two fixed points
Bonino, Marc
2010-01-01
The main result of this paper gives a topological property satisfied by any homeomorphism of the annulus $\\mathbb{A}=\\mathbb{S}^1 \\times [-1,1]$ isotopic to identity and with at most one fixed point. This generalizes the classical Poincar\\'e-Birkhoff theorem because this property certainly does not hold for an area preserving homeomorphism of $\\mathbb{A}$ with the usual boundary twist condition. We also have two corollaries of this result. The first one shows in particular that the boundary twist assumption may be replaced with the weaker property that there is a forward orbit in $\\mathbb{A}$ making an arbitrarily large number of turns in the clockwise direction and likewise in the counterclockwise direction. The second one is a version of the Conley-Zehnder theorem in $\\mathbb{A}$.
Gilchrist, S A; Barnes, G
2016-01-01
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin (Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.
Spin glass in a field: a new zero-temperature fixed point in finite dimensions.
Angelini, Maria Chiara; Biroli, Giulio
2015-03-06
By using real-space renormalization group (RG) methods, we show that spin glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two nonperturbative zero-temperature fixed points of the RG flow. We compute the critical exponents and discuss the RG flow and its relevance for three-dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry-breaking theories. These results provide a new perspective on the long-standing debate about the behavior of spin glasses in a field.
Gilchrist, S. A.; Braun, D. C.; Barnes, G.
2016-12-01
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a numerical method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration scheme that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.
Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
Devakul, Trithep; Majumdar, Satya N.; Huse, David A.
2017-03-01
We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.
Investigation of Fixed Points Exceeding 2500 °C Using Metal Carbide-Carbon Eutectics
Sasajima, N.; Yamada, Y.; Sakuma, F.
2003-09-01
The melting and freezing plateaus of four metal carbide-carbon (MC-C) eutectics, B4C-C, δ(Mo carbide)-C, TiC-C and ZrC-C eutectics were investigated by radiation thermometry for the first time. The observed melting temperatures were 2386 °C, 2583 °C, 2761 °C and 2883 °C, respectively. The plateau shapes of δ(Mo carbide)-C, TiC-C and ZrC-C eutectics are relatively flat compared to the quite rounded plateau shape of the B4C-C eutectic. The results indicate that MC-C eutectics can establish a new series of high-temperature fixed points above 2500 °C.
An Analysis of 2D Bi-Orthogonal Wavelet Transform Based On Fixed Point Approximation
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P. Vijayalakshmi
2014-04-01
Full Text Available As the world advances with technology and research, images are being widely used in many fields such as biometrics, remote sensing, reconstruction etc. This tremendous growth in image processing applications, demands majorly for low power consumption, low cost and small chip area. In this paper we analyzed 2D bi-orthogonal wavelet transform based on Fixed point approximation. Filter coefficients of the bi-orthogonal wavelet filters are quantized before implementation. The efficiency of the results is measured for some standard gray scale images by comparing the original input images and the reconstructed images. SNR and PSNR value shows that this implementation is performed effectively without any loss in image quality.
Algorithms of common solutions to quasi variational inclusion and fixed point problems
Institute of Scientific and Technical Information of China (English)
ZHANG Shi-sheng; LEE Joseph H. W.; CHAN Chi Kin
2008-01-01
The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich (Ekonomika i Matematicheskie Metody, 1976, 12(4):747-756), but also extend and replenish the corresponding results obtained by Iiduka and Takahashi (Nonlinear Anal TMA, 2005, 61(3):341-350), Takahashi and Toyoda (J Optim Theory Appl, 2003,118(2):417-428), Nadezhkina and Takahashi (J Optim Theory Appl, 2006, 128(1):191-201), and Zeng and Yao (Taiwanese Journal of Mathematics, 2006, 10(5):1293-1303).
Free-time and fixed end-point multi-target optimal control theory: Application to quantum computing
Mishima, K.; Yamashita, K.
2011-01-01
An extension of free-time and fixed end-point optimal control theory (FRFP-OCT) to monotonically convergent free-time and fixed end-point multi-target optimal control theory (FRFP-MTOCT) is presented. The features of our theory include optimization of the external time-dependent perturbations with high transition probabilities, that of the temporal duration, the monotonic convergence, and the ability to optimize multiple-laser pulses simultaneously. The advantage of the theory and a comparison with conventional fixed-time and fixed end-point multi-target optimal control theory (FIFP-MTOCT) are presented by comparing data calculated using the present theory with those published previously [K. Mishima, K. Yamashita, Chem. Phys. 361, (2009), 106]. The qubit system of our interest consists of two polar NaCl molecules coupled by dipole-dipole interaction. The calculation examples show that our theory is useful for minor adjustment of the external fields.
Mishima, K; Yamashita, K
2009-01-21
We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on.
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.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Robust Fixed Point Transformations in Adaptive Control Using Local Basin of Attraction
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József K. Tar
2009-03-01
Full Text Available A further step towards a novel approach to adaptive nonlinear control developedat Budapest Tech in the past few years is reported. This approach obviates the use of thecomplicated Lyapunov function technique that normally provides global stability ofconvergence at the costs of both formal and essential restrictions, by applying Cauchysequences of local, bounded basin of attraction in an iterative control that is free of suchrestrictions. Its main point is the creation of a robust iterative sequence that only slightlydepends on the features of the controlled system and mainly is determined be the controlparameters applied. It is shown that as far as its operation is considered the proposedmethod can be located between the robust Variable Structure / Sliding Mode and theadaptive Slotine-Li control in the case of robots or other Classical Mechanical Systems.The operation of these method is comparatively analyzed for a wheel + connected masssystem in which this latter component is “stabilized” along one of the spokes of the wheelin the radial direction by an elastic spring. The robustness of these methods is alsoinvestigated againts unknown external disturbances of quite significant amplitudes. Thenumerical simulations substantiate the superiority of the robust fixed point transformationsin the terms of accuracy, simplicity, and smoothness of the control signals applied.
Institute of Scientific and Technical Information of China (English)
Xia ZHOU; Shou Ming ZHONG
2011-01-01
In this paper the asymptotical stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan's results.
van Maanen, Leendert; de Jong, Ritske; van Rijn, Hedderik
2014-01-01
When multiple strategies can be used to solve a type of problem, the observed response time distributions are often mixtures of multiple underlying base distributions each representing one of these strategies. For the case of two possible strategies, the observed response time distributions obey the fixed-point property. That is, there exists one reaction time that has the same probability of being observed irrespective of the actual mixture proportion of each strategy. In this paper we discuss how to compute this fixed-point, and how to statistically assess the probability that indeed the observed response times are generated by two competing strategies. Accompanying this paper is a free R package that can be used to compute and test the presence or absence of the fixed-point property in response time data, allowing for easy to use tests of strategic behavior. PMID:25170893
Luo, Zhu-Xi; Lake, Ethan; Wu, Yong-Shi
2017-07-01
The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, and conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixed-point states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global on-site unitary symmetry is imposed on the tensor network states.
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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
China's Economy in 2005: At a New Turning Point and Need to Fix Its Development Problems
Institute of Scientific and Technical Information of China (English)
John Wong
2006-01-01
China's economy in 2005 chalked up another year of 9.9 percent surging growth. In 2005 the government's attention was focused on the many negative consequences of China's past unbridled economic growth, from rural poverty to environmental degradation and wide income disparities, calling for more "sustainable growth" or "balanced development".The new development paradigm fit nicely into President Hu Jintao 's concept of "scientific development", and was embraced by the 11th Five-Year Program (2006- 2010).The year 2006 might go down in China's economic history as an important turning point, as the Hu-Wen leadership will start new development strategies to fix problems previously associated with strong economic growth. Strictly speaking, many of China's "growth problems ", from regional disparities to environmental degradation, are actually quite inevitable - as a part of the development process. But their gravity has often been aggravated by poor governance, blatantly pro-growth policies, and local corruption.Overall, the Chinese leadership has come to realize that its past development patterns are physically unsustainable, and politically and socially unacceptable. It has embraced the need to change. But all development changes will take a long time to yield concrete results.
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.
Mishra, Puneet; Singla, Sunil Kumar
2013-01-01
In the modern world of automation, biological signals, especially Electroencephalogram (EEG) and Electrocardiogram (ECG), are gaining wide attention as a source of biometric information. Earlier studies have shown that EEG and ECG show versatility with individuals and every individual has distinct EEG and ECG spectrum. EEG (which can be recorded from the scalp due to the effect of millions of neurons) may contain noise signals such as eye blink, eye movement, muscular movement, line noise, etc. Similarly, ECG may contain artifact like line noise, tremor artifacts, baseline wandering, etc. These noise signals are required to be separated from the EEG and ECG signals to obtain the accurate results. This paper proposes a technique for the removal of eye blink artifact from EEG and ECG signal using fixed point or FastICA algorithm of Independent Component Analysis (ICA). For validation, FastICA algorithm has been applied to synthetic signal prepared by adding random noise to the Electrocardiogram (ECG) signal. FastICA algorithm separates the signal into two independent components, i.e. ECG pure and artifact signal. Similarly, the same algorithm has been applied to remove the artifacts (Electrooculogram or eye blink) from the EEG signal.
VLSI Implementation of Fixed-Point Lattice Wave Digital Filters for Increased Sampling Rate
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M. Agarwal
2016-12-01
Full Text Available Low complexity and high speed are the key requirements of the digital filters. These filters can be realized using allpass filters. In this paper, design and minimum multiplier implementation of a fixed point lattice wave digital filter (WDF based on three port parallel adaptor allpass structure is proposed. Here, the second-order allpass sections are implemented with three port parallel adaptor allpass structures. A design-level area optimization is done by converting constant multipliers into shifts and adds using canonical signed digit (CSD techniques. The proposed implementation reduces the latency of the critical loop by reducing the number of components (adders and multipliers. Three design examples are included to analyze the effectiveness of the proposed approach. These are implemented in verilog HDL language and mapped to a standard cell library in a 0.18 μm CMOS process. The functionality of the implementations have been verified by applying number of different input vectors. Results and simulations demonstrate that the proposed design method leads to an efficient lattice WDF in terms of maximum sampling frequency. The cost to pay is small area overhead. The postlayout simulations have been done by HSPICE with CMOS transistors.
Nikazad, Touraj; Abbasi, Mokhtar
2017-04-01
In this paper, we introduce a subclass of strictly quasi-nonexpansive operators which consists of well-known operators as paracontracting operators (e.g., strictly nonexpansive operators, metric projections, Newton and gradient operators), subgradient projections, a useful part of cutter operators, strictly relaxed cutter operators and locally strongly Féjer operators. The members of this subclass, which can be discontinuous, may be employed by fixed point iteration methods; in particular, iterative methods used in convex feasibility problems. The closedness of this subclass, with respect to composition and convex combination of operators, makes it useful and remarkable. Another advantage with members of this subclass is the possibility to adapt them to handle convex constraints. We give convergence result, under mild conditions, for a perturbation resilient iterative method which is based on an infinite pool of operators in this subclass. The perturbation resilient iterative methods are relevant and important for their possible use in the framework of the recently developed superiorization methodology for constrained minimization problems. To assess the convergence result, the class of operators and the assumed conditions, we illustrate some extensions of existence research works and some new results.
Yokoyama, Yoshiaki; Kim, Minseok; Arai, Hiroyuki
At present, when using space-time processing techniques with multiple antennas for mobile radio communication, real-time weight adaptation is necessary. Due to the progress of integrated circuit technology, dedicated processor implementation with ASIC or FPGA can be employed to implement various wireless applications. This paper presents a resource and performance evaluation of the QRD-RLS systolic array processor based on fixed-point CORDIC algorithm with FPGA. In this paper, to save hardware resources, we propose the shared architecture of a complex CORDIC processor. The required precision of internal calculation, the circuit area for the number of antenna elements and wordlength, and the processing speed will be evaluated. The resource estimation provides a possible processor configuration with a current FPGA on the market. Computer simulations assuming a fading channel will show a fast convergence property with a finite number of training symbols. The proposed architecture has also been implemented and its operation was verified by beamforming evaluation through a radio propagation experiment.
Directory of Open Access Journals (Sweden)
Włodarczyk K
2005-01-01
Full Text Available Let be a real Hausdorff topological vector space. In the present paper, the concepts of the transfer positive hemicontinuity and strictly transfer positive hemicontinuity of set-valued maps in are introduced (condition of strictly transfer positive hemicontinuity is stronger than that of transfer positive hemicontinuity and for maps and defined on a nonempty compact convex subset of , we describe how some ideas of K. Fan have been used to prove several new, and rather general, conditions (in which transfer positive hemicontinuity plays an important role that a single-valued map has a zero, and, at the same time, we give various characterizations of the class of those pairs and maps that possess coincidences and fixed points, respectively. Transfer positive hemicontinuity and strictly transfer positive hemicontinuity generalize the famous Fan upper demicontinuity which generalizes upper semicontinuity. Furthermore, a new type of continuity defined here essentially generalizes upper hemicontinuity (the condition of upper demicontinuity is stronger than the upper hemicontinuity. Comparison of transfer positive hemicontinuity and strictly transfer positive hemicontinuity with upper demicontinuity and upper hemicontinuity and relevant connections of the results presented in this paper with those given in earlier works are also considered. Examples and remarks show a fundamental difference between our results and the well-known ones.
Positive circuits and maximal number of fixed points in discrete dynamical systems
Richard, Adrien
2008-01-01
The biologist Ren\\'e Thomas conjectured, twenty years ago, that the presence of a positive circuit in the interaction graph of a dynamical system is a necessary condition for the presence of multiple stable states. Recently, Richard and Comet stated and proved this conjecture for systems whose dynamics is described by the iterations of a map $F$ which operates on the product $X$ of $n$ finite intervals of integers. In this paper, we widely extend the result of Richard and Comet by exhibiting an upper bound on the number of fixed points for $F$ which only depends on $X$ and on the topology of the positive circuits of the interaction graph associated with $F$. Our motivation for this work comes from biology. The maps $F$ we focus on are indeed extensively used to described the behavior of gene regulatory networks, and when such a network is studied, the first reliable data often concern its interaction graph, so that the bound we establish can be used, in practice, to obtain valuable information about the numbe...
Higgs and supersymmetric particle signals at the infrared fixed point of the top quark mass
Carena, M S
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 MSSM. 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 decay rate b\\rightarrow s\\gamma. We consider the low and moderate \\tan \\beta regime, 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 sparticle spectra are completely determined as a function of two soft supersymmetry breaking parameters. In the case of non--universality, instead, the strong correlations between the sparticle masses are relaxed, allowing a richer structure for the precision data variables. We show, however, that the requirement that the low energy theory proceeds from a grand unified theory with a local symm...