Fixed point theorems and dissipative processes.
NASA Technical Reports Server (NTRS)
Hale, J. K.; Lopes, O.
1973-01-01
Operators of the type considered by Hale et al. (1972) are used to show that under certain conditions there is a fixed point in a dissipative map within a Banach space. The conditions required for the existence of this fixed point are discussed in detail. Several fixed point theorems are formulated and proved.
Fixed point theorems and dissipative processes
NASA Technical Reports Server (NTRS)
Hale, J. K.; Lopes, O.
1972-01-01
The deficiencies of the theories that characterize the maximal compact invariant set of T as asymptotically stable, and that some iterate of T has a fixed point are discussed. It is shown that this fixed point condition is always satisfied for condensing and local dissipative T. Applications are given to a class of neutral functional differential equations.
Fixed point theorems for generalized contractions in ordered metric spaces
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Aliouche, A.
2008-05-01
We prove a common fixed point theorem of Gregus type for four mappings satisfying a generalized contractive condition in metric spaces using the concept of weak compatibility which generalizes theorems of [I. Altun, D. Turkoglu, B.E. Rhoades, Fixed points of weakly compatible mappings satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), article ID 17301; A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378; A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (1) (2007) 31-45; P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15 (2005) 2359-2364; X. Zhang, Common fixed point theorems for some new generalized contractive type mappings, J. Math. Anal. Appl. 333 (2) (2007) 780-786]. We prove also a common fixed point theorem which generalizes Theorem 3.5 of [H.KE Pathak, M.S. Khan, T. Rakesh, A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. 53 (2007) 961-971] and common fixed point theorems of Gregus type using a strict generalized contractive condition, a property (E.A) and a common property (E.A).
Some Extensions of Discrete Fixed Point Theorems and Their Applications to the Game Theory
NASA Astrophysics Data System (ADS)
Kawasaki, Hidefumi
2009-09-01
As is well-known in the game theory, fixed point theorems are useful to show the existence of Nash equilibrium. Since they are mathematical tools in continuous variables, it is expected that discrete fixed point theorems also useful to guarantee the existence of pure-strategy Nash equilibrium. In this talk, we review three types of discrete fixed point theorems, give some extensions, and apply them to non-cooperative games.
A fixed point theorem for certain operator valued maps
NASA Technical Reports Server (NTRS)
Brown, D. R.; Omalley, M. J.
1978-01-01
In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H).
Partial rectangular metric spaces and fixed point theorems.
Shukla, Satish
2014-01-01
The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.
Fixed-point theorems for families of weakly non-expansive maps
NASA Astrophysics Data System (ADS)
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.
Common Coupled Fixed Point Theorems for Two Hybrid Pairs of Mappings under φ-ψ Contraction
Handa, Amrish
2014-01-01
We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2X and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2X and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our results. We improve, extend and generalize several known results. The results of this paper generalize the common fixed point theorems for hybrid pairs of mappings and essentially contain fixed point theorems for hybrid pair of mappings. PMID:27340688
Coupled fixed point theorems in G b -metric space satisfying some rational contractive conditions.
Khomdram, Bulbul; Rohen, Yumnam; Singh, Thokchom Chhatrajit
2016-01-01
In this paper we prove the existence and uniqueness of couple fixed point theorems for three mappings satisfying some new rational contractive conditions. We prove our results in the frame work of G b -metric space which is recently introduced by Aghajani et al. (Filomat 28(6):1087-1101, 2014). Illustrative example is also given to support our result.
Fixed-point and implicit/inverse function theorems for free noncommutative functions
NASA Astrophysics Data System (ADS)
Abduvalieva, Gulnara K.
We establish a fixed-point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping is a free noncommutative function, i.e., if it respects matrix similarities. As a special case, we obtain the corresponding version of the Banach Contraction Mapping Theorem. This result is then applied to prove the existence and uniqueness of a solution of the initial value problem for ODEs in noncommutative spaces. As a by-product of the ideas developed in this paper, we establish a noncommutative version of the principle of nested closed sets. We prove the implicit function theorem and the inverse function theorem in two different settings: for free noncommutative functions over operator spaces and for free noncommutative functions on the set of nilpotent matrices.
Searching for fixed point combinators by using automated theorem proving: A preliminary report
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.
On a sharpened form of the Schauder fixed-point theorem.
Browder, F E
1977-11-01
If K is a compact convex subset of a locally convex topological vector space X, we consider a continuous mapping f of K into X. A fixed-point theorem is proved for such a map f under the assumption that for a given continuous realvalued function p on K x X with p(x,y) convex in y and for each point x in K not fixed by f, there exists a point y in the inward set I(K)(x) generated by K at x with p(x,y - f(x)) less than p(x,x - f(x)). For X a Banach space, in particular, this yields a sharp extension and a drastic simplification of the fixed point theory of weakly inward (and weakly outward) mappings. The result comes close in the domain of mappings of compact convex sets to the thrust of fixed point conditions of the Leray-Schauder type for compact maps of sets with interior in X.
On a sharpened form of the Schauder fixed-point theorem
Browder, Felix E.
1977-01-01
If K is a compact convex subset of a locally convex topological vector space X, we consider a continuous mapping f of K into X. A fixed-point theorem is proved for such a map f under the assumption that for a given continuous realvalued function p on K × X with p(x,y) convex in y and for each point x in K not fixed by f, there exists a point y in the inward set IK(x) generated by K at x with p(x,y - f(x)) less than p(x,x - f(x)). For X a Banach space, in particular, this yields a sharp extension and a drastic simplification of the fixed point theory of weakly inward (and weakly outward) mappings. The result comes close in the domain of mappings of compact convex sets to the thrust of fixed point conditions of the Leray-Schauder type for compact maps of sets with interior in X. PMID:16592465
L-Fuzzy Fixed Points Theorems for L-Fuzzy Mappings via β ℱL-Admissible Pair
Rashid, Maliha; Azam, Akbar
2014-01-01
We define the concept of β ℱL-admissible for a pair of L-fuzzy mappings and establish the existence of common L-fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result. PMID:24688441
Latif, Abdul
2014-01-01
We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph. PMID:24895662
Zegeye, Habtu; Shahzad, Naseer
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
2014-01-01
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. PMID:24757423
NASA Astrophysics Data System (ADS)
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen
2016-06-01
This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.
STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.
A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest...converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)
Point and Circle Configurations; A New Theorem.
ERIC Educational Resources Information Center
Dorwart, Harold L.
1988-01-01
Point and circle configurations are not well known, so Clifford's chain of theorems and Miquel's theorem, whose diagrams exhibit such configurations, are discussed. A new theorem similar to Miquel's is then presented. (MNS)
Fundamental theorem on gauge fixing at the action level
NASA Astrophysics Data System (ADS)
Motohashi, Hayato; Suyama, Teruaki; Takahashi, Kazufumi
2016-12-01
Regardless of the long history of gauge theories, it is not well recognized under which condition gauge fixing at the action level is legitimate. We address this issue from the Lagrangian point of view, and prove the following theorem on the relation between gauge fixing and Euler-Lagrange equations: In any gauge theory, if a gauge fixing is complete, i.e., the gauge functions are determined uniquely by the gauge conditions, the Euler-Lagrange equations derived from the gauge-fixed action are equivalent to those derived from the original action supplemented with the gauge conditions. Otherwise, it is not appropriate to impose the gauge conditions before deriving Euler-Lagrange equations as it may in general lead to inconsistent results. The criterion to check whether a gauge fixing is complete or not is further investigated. We also provide applications of the theorem to scalar-tensor theories and make comments on recent relevant papers on theories of modified gravity, in which there are confusions on gauge fixing and counting physical degrees of freedom.
NASA Astrophysics Data System (ADS)
Bounias, Michel
2000-05-01
A physical space can exist as a collection of closed topologies in the intersections of abstract topological subspaces provided with non-equal dimensions. Furthermore, the ordered sequence of mappings of one to another intersection provides an arrow of time which is shared by all connected systems of closed, involving those of the brain type with other types (i.e., physical objects of all categories). The topology of closed spaces associates fixed points of the Brouwer's type with fixed points of the Banach's type. The former are specific of each closed and the latter drive the information from the outside space to mental images inside a closed, through mappings of Jordan's points. The set of fixed points thus provides the properties of both perception and self in living organisms. Conditions for existence of various kinds of Banach's type fixed points are fulfilled by the mathematical brain, since it is both a discrete finite structure, thus a compact topological space, and provided with a set distance (Δ), thus Δ-complete. Finally, since (i) iterates in a sequence of mappings include at least a surjective component and (ii) not identical (if even existing) fixed points would be generated by the non-surjective property which would characterize reciprocal mappings, in either metric or nonmetric setting, the reversion of biological time would break the direct link of the self with perception functions. Thus, while time could be reversible for physics, it is perceived as irreversible for biology, although physical and biological objects share a common space.
The Euler Line and Nine-Point-Circle Theorems.
ERIC Educational Resources Information Center
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Minimum of a functional in a metric space and fixed points
NASA Astrophysics Data System (ADS)
Arutyunov, A. V.; Gel'Man, B. D.
2009-07-01
The existence of minimizers is examined for a function defined on a metric space. Theorems are proved that assert the existence of minimizers, and examples of the functions for which these theorems are valid are given. Then, these theorems are applied to proving theorems on fixed points of univalent and multivalued mappings of metric spaces. Finally, coincident points of two mappings are examined.
Fixed points of quantum gravity.
Litim, Daniel F
2004-05-21
Euclidean quantum gravity is studied with renormalization group methods. Analytical results for a nontrivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameters in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.
Using Technology to Unify Geometric Theorems about the Power of a Point
ERIC Educational Resources Information Center
Contreras, Jose N.
2011-01-01
In this article, I describe a classroom investigation in which a group of prospective secondary mathematics teachers discovered theorems related to the power of a point using "The Geometer's Sketchpad" (GSP). The power of a point is defines as follows: Let "P" be a fixed point coplanar with a circle. If line "PA" is a secant line that intersects…
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.
Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions
NASA Astrophysics Data System (ADS)
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.
Fixed-point adiabatic quantum search
NASA Astrophysics Data System (ADS)
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.
Anderson Acceleration for Fixed-Point Iterations
Walker, Homer F.
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
NASA Astrophysics Data System (ADS)
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.
On Fixed Points of Strictly Causal Functions
2013-04-08
Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards #0720882 ( CSR -EHS: PRET), #0931843 (CPS: Large...National Science Foundation (NSF awards #0720882 ( CSR -EHS: PRET), #0931843 (CPS: Large: ActionWebs), and #1035672 (CPS: Medium: Ptides)), the Naval Research...For despite the abundance of fixed-point problems in the field , it is almost invariably the fixed-point theory of ordered sets or that of metric
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).
NASA Astrophysics Data System (ADS)
Young, Frederic; Siegel, Edward
Cook-Levin theorem theorem algorithmic computational-complexity(C-C) algorithmic-equivalence reducibility/completeness equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited via Siegel FUZZYICS =CATEGORYICS = ANALOGYICS =PRAGMATYICS/CATEGORY-SEMANTICS ONTOLOGY COGNITION ANALYTICS-Aristotle ``square-of-opposition'' tabular list-format truth-table matrix analytics predicts and implements ''noise''-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics (1987)]-Sipser[Intro.Thy. Computation(`97)] algorithmic C-C: ''NIT-picking''(!!!), to optimize optimization-problems optimally(OOPO). Versus iso-''noise'' power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, ''NIT-picking'' is ''noise'' power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-''science''/SEANCE algorithmic C-C models: Turing-machine, finite-state-models, finite-automata,..., discrete-maths graph-theory equivalence to physics Feynman-diagrams are identified as early-days once-workable valid but limiting IMPEDING CRUTCHES(!!!), ONLY IMPEDE latter-days new-insights!!!
PPF Dependent Fixed Point Results for Triangular α c-Admissible Mappings
Ćirić, Ljubomir; Alsulami, Saud M.; Salimi, Peyman
2014-01-01
We introduce the concept of triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings and establish the existence of PPF dependent fixed (coincidence) point theorems for contraction mappings involving triangular α c-admissible mappings (pair of mappings) with respect to η c nonself-mappings in Razumikhin class. Several interesting consequences of our theorems are also given. PMID:24672352
The algebraic multigrid projection for eigenvalue problems; backrotations and multigrid fixed points
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1994-01-01
The periods of the theorem for the algebraic multigrid projection (MGP) for eigenvalue problems, and of the multigrid fixed point theorem for multigrid cycles combining MGP with backrotations, are presented. The MGP and the backrotations are central eigenvector separation techniques for multigrid eigenvalue algorithms. They allow computation on coarse levels of eigenvalues of a given eigenvalue problem, and are efficient tools in the computation of eigenvectors.
Au Fixed Point Development at NRC
NASA Astrophysics Data System (ADS)
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.
ASIC For Complex Fixed-Point Arithmetic
NASA Technical Reports Server (NTRS)
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
Precise Point Positioning with Partial Ambiguity Fixing.
Li, Pan; Zhang, Xiaohong
2015-06-10
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.
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
Fixed Points and Stability for a Sum of Two Operators in Locally Convex Spaces
topological spaces is formulated in terms of specific topologies on the set of nonlinear operators, and a theorem on the stability of fixed points of a sum of two operators is given. As a byproduct, sufficient conditions for a mapping to be open or to be onto are
Mardanov, M. J.; Mahmudov, N. I.; Sharifov, Y. A.
2014-01-01
We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1. PMID:24782675
Mardanov, M J; Mahmudov, N I; Sharifov, Y A
2014-01-01
We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order α (0 < α ≤ 1) involving the two-point and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case α = 1.
Li, Xia; Guo, Meifang; Su, Yongfu
2016-01-01
In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. Strong convergence theorems for finding a solution of the split common null point problem are derived. This iteration algorithm can accelerate the convergence speed of iterative sequence. The results of this paper improve and extend the recent results of Takahashi and Yao (Fixed Point Theory Appl 2015:87, 2015) and many others .
Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation
Goryainov, V V
2015-01-31
The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution family of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles.
Carbon monoxide fixed point continuous monitor
Not Available
1981-10-01
This instrument is to monitor carbon monoxide concentration in underground mines. A carbon monoxide fixed-point continuous monitor consists of two modules. A line-powered control module is designed to power a remote transducer module; provide continuous readouts, visual and audible alarms, operational checks; and activate fans and equipment shutdown circuits if present CO concentration levels are exceeded. Details are given for the workings of each module. (DP)
Ergostatting and thermostatting at a fixed point
NASA Astrophysics Data System (ADS)
Hüffel, Helmuth; Ilijić, Saša
2016-11-01
We propose an innovative type of ergostats and thermostats for molecular dynamics simulations. A general class of active particle swarm models is considered, where any specific total energy (alternatively any specific temperature) can be provided at a fixed point of the evolution of the swarm. We identify the extended system feedback force of the Nosé-Hoover thermostat with the "internal energy" variable of active Brownian motion.
Fixed points and FLRW cosmologies: Flat case
NASA Astrophysics Data System (ADS)
Awad, Adel
2013-05-01
We use a phase space approach to study possible consequences of fixed points in a single fluid flat Friedmann-Lemaître-Robertson-Walker (FLRW) models with pressure p(H), where H is the Hubble parameter. One of these consequences is that a fluid with a differentiable pressure, i.e., a finite adiabatic speed of sound, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II, and III described by Nojiri, Odintsov, and Tsujikawa [Phys. Rev. D 71, 063004 (2005)]. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent dp/dH, or the speed of sound, is a necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to qualitatively describe the entire behavior of a solution in flat FLRW models. We discuss FLRW models with bulk viscosity η˜ρr, in particular, solutions for r=1 and r=1/4 cases, which can be expressed in terms of the Lambert-W function. The last solution behaves as either a nonsingular phantom fluid or a unified dark fluid. Using causality and stability constraints, we show that the universe must end as a de Sitter space. Relaxing the stability constraint leads to a de Sitter universe, an empty universe, or a turnaround solution that reaches a maximum size and then recollapses.
Fixed Point Implementations of Fast Kalman Algorithms.
1983-11-01
fined point multiply. ve &geete a meatn ’C.- nero. variance N random vector s~t) each time weAfilter is said to be 12 Scaled if udae 8(t+11t0 - 3-1* AS...nl.v by bl ’k rn.b.) 20 AST iA C T ’Cnnin to .- a , o. a ide It .,oco ea ry and Idenuty by block number) In this paper we study scaling rules and round...realized in a -fast form that uses the so-called fast Kalman gain algorithm. The algorithm for the gain is fixed point. Scaling rules and expressions for
New SMU Gallium Fixed-Point Cells
NASA Astrophysics Data System (ADS)
Ranostaj, Juraj; Ďuriš, Stanislav; Knorová, Renáta; Kaskötö, Mariana; Vyskočilová, Irena
2011-08-01
In the framework of the European research project EURAMET 732, the Slovak Institute of Metrology (SMU) built three primary gallium fixed-point cells of different designs. The cells are designed for the calibration of the long-stem SPRT. In regard to the procedure commonly used at SMU when realizing the gallium point, the cells are designed for use in a stirred liquid bath. This article provides information about the cell designs, materials used, method of filling, and results of the performed experiments. The experiments were focused on the study of the cells' metrological characteristics, some effects that could influence the melting-point temperature and the effect of the melted metal fraction on the immersion profile. New cells were compared with the SMU reference gallium cell.
Fixed points and closure operators: Programmological aspects
Bui, D.B.; Red`ko, V.N.
1995-09-01
The present article continues the research of others into the declarative nature of specification languages that describe the properties of objects in the form of solutions of equations with the left-hand side solved for the unknown, i.e., equations of the form x = f(x), x {element_of} D, where D is the data universe and f is an operator on D. The main purpose of this study is to elucidate the essence of the iterative processes that can be used to find the solutions of this equation, i.e., the fixed points of the operator f. In the programmological context, the data universe should be viewed as a data type, i.e., the set of data should be endowed with an appropriate structure. Operating on the lowest level of abstraction, we regard the data universe as a partially ordered set (poset), and thus speak of the first approximation, the next approximation, and so on. The relevant programmological applications also impose certain restrictions on the operators. Specifically, we consider operators that preserve the initial relation on data. Indeed, if x{prime} is an approximation to x, then we naturally stipulate that f(x{prime}) be an approximation to f(x). Moreover, the operators in applications are always effective; and as we know, effectiveness implies monotonicity. Thus, we consider equations of the form x = f(x), x {element_of} D, where D is a poset and f a monotone operator on D. Contrary to other references, where we used direct methods traceable to the work of Tarski, the main instrument in this study are the so-called a-chains of the element a of a poset relative to an operator. This enables us, first, to describe the fixed points of a monotone operator on any poset and, second, to construct the closure operator on the set of fixed points of the initial monotone operator.
Fixed point theorems and existence of equilibrium in discontinuous games
NASA Astrophysics Data System (ADS)
Messaoud, Deghdak
2012-11-01
In this paper, we generalize the existence of Berge's strong equilibrium in Deghdak (see [7]) to discontinuous games in infinite dimensional space of srategy. Moreover, we prove that most of Berge's strong games are essential.
NASA Astrophysics Data System (ADS)
Liu, Xuan-Zuo; Tian, Dong-Ping; Chong, Bo
2016-06-01
Liu et al. [Phys. Rev. Lett. 90(17), 170404 (2003)] proved that the characters of transition probabilities in the adiabatic limit should be entirely determined by the topology of energy levels and the stability of fixed points in the classical Hamiltonian system, according to the adiabatic theorem. In the special case of nonlinear Landau-Zener model, we simplify their results to be that the properties of transition probabilities in the adiabatic limit should just be determined by the attributes of fixed points. It is because the topology of energy levels is governed by the behavior and symmetries of fixed points, and intuitively this fact is represented as a correspondence between energy levels and evolution curves of the fixed points which can be quantitatively described as the same complexity numbers.
Secure Computation with Fixed-Point Numbers
NASA Astrophysics Data System (ADS)
Catrina, Octavian; Saxena, Amitabh
Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.
Circle actions on almost complex manifolds with isolated fixed points
NASA Astrophysics Data System (ADS)
Jang, Donghoon
2017-09-01
In Jang (2014), the author proves that if the circle acts symplectically on a compact, connected symplectic manifold M with three fixed points, then M is equivariantly symplectomorphic to some standard action on CP2. In this paper, we extend the result to a circle action on an almost complex manifold; if the circle acts on a compact, connected almost complex manifold M with exactly three fixed points, then dim M = 4. Moreover, the weights at the fixed points agree with those of a standard circle action on the complex projective plane CP2. Also, we deal with the cases of one fixed point and two fixed points.
Sulfur Hexafluoride: A Novel Fixed Point for Contact Thermometry
NASA Astrophysics Data System (ADS)
Dedyulin, S. N.
2017-05-01
In this paper, we report on the development at NRC of a sulfur hexafluoride ( {SF}_6) fixed-point cell for calibrating long-stem standard platinum resistance thermometers. Discussed in detail are the unique challenges of constructing the high-pressure fixed-point cell and realizing the triple point of {SF}_6 in a commercial stirred liquid bath.
A new compact fixed-point blackbody furnace
Hiraka, K.; Oikawa, H.; Shimizu, T.; Kadoya, S.; Kobayashi, T.; Yamada, Y.; Ishii, J.
2013-09-11
More and more NMIs are realizing their primary scale themselves with fixed-point blackbodies as their reference standard. However, commercially available fixed-point blackbody furnaces of sufficient quality are not always easy to obtain. CHINO Corp. and NMIJ, AIST jointly developed a new compact fixed-point blackbody furnace. The new furnace has such features as 1) improved temperature uniformity when compared to previous products, enabling better plateau quality, 2) adoption of the hybrid fixed-point cell structure with internal insulation to improve robustness and thereby to extend lifetime, 3) easily ejectable and replaceable heater unit and fixed-point cell design, leading to reduced maintenance cost, 4) interchangeability among multiple fixed points from In to Cu points. The replaceable cell feature facilitates long term maintenance of the scale through management of a group of fixed-point cells of the same type. The compact furnace is easily transportable and therefore can also function as a traveling standard for disseminating the radiation temperature scale, and for maintaining the scale at the secondary level and industrial calibration laboratories. It is expected that the furnace will play a key role of the traveling standard in the anticipated APMP supplementary comparison of the radiation thermometry scale.
A temperature fixed point near 58 C
NASA Technical Reports Server (NTRS)
Glicksman, M. E.
1980-01-01
Triple-point cell contrains about 300 g of high-purity succinontrile. Experiments show that lower 4 cm of thermometer well are virtually isothermal, making placement of thermometer not very critical. Bulb at bottom of well helps to prevent solid succinontrile mantel from slipping.
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2010 CFR
2010-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2011 CFR
2011-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations. Private...
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2014 CFR
2014-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2012 CFR
2012-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
47 CFR 101.137 - Interconnection of private operational fixed point-to-point microwave stations.
Code of Federal Regulations, 2013 CFR
2013-10-01
... point-to-point microwave stations. 101.137 Section 101.137 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES FIXED MICROWAVE SERVICES Technical Standards § 101.137 Interconnection of private operational fixed point-to-point microwave stations....
52. Fixed Span, Top Chord at Panel Point 6; diagonal ...
52. Fixed Span, Top Chord at Panel Point 6; diagonal member goes to intermediate connection 7 & then to bottom chord at 8; looking ESE. - Pacific Shortline Bridge, U.S. Route 20,spanning Missouri River, Sioux City, Woodbury County, IA
The Fixed-Point Theory of Strictly Causal Functions
2013-06-09
Software Systems (CHESS) at UC Berkeley, which receives support from the National Science Foundation (NSF awards \\#0720882 ( CSR -EHS: PRET), \\#0931843 (CPS...from the National Science Foundation (NSF awards #0720882 ( CSR -EHS: PRET), #0931843 (CPS: Large: ActionWebs), and #1035672 (CPS: Medium: Ptides)), the...computer science. For despite the abundance of fixed-point problems in the field , it is almost invariably the fixed-point theory of order-preserving
On spurious fixed points of Runge-Kutta methods
Vadillo, V.
1997-03-15
In this paper we investigate the onset of spurious fixed points when Runge-Kutta methods are applied to study the dynamics of differential equations. It is shown computationally that the spurious equilibria of Griffiths et al. are connected at infinity with fixed points inherited from the differential equation. We introduce and study the concept of B-regularity which is in connection to the concept of regularity introduced by Iserles. 32 refs., 9 figs.
Global fixed-point proof of time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Ruggenthaler, M.; van Leeuwen, R.
2011-07-01
We reformulate the uniqueness and existence proofs of time-dependent density-functional theory. The central idea is to restate the fundamental one-to-one correspondence between densities and potentials as a global fixed-point question for potentials on a given time interval. We show that the unique fixed point, i.e. the unique potential generating a given density, is reached as the limiting point of an iterative procedure. The one-to-one correspondence between densities and potentials is a straightforward result provided that the response function of the divergence of the internal forces is bounded. The existence, i.e. the v-representability of a density, can be proven as well provided that the operator norms of the response functions of the members of the iterative sequence of potentials have an upper bound. The densities under consideration have second time-derivatives that are required to satisfy a condition slightly weaker than being square-integrable. This approach avoids the usual restrictions of Taylor-expandability in time of the uniqueness theorem by Runge and Gross (Phys. Rev. Lett., 52 (1984) 997) and of the existence theorem by van Leeuwen (Phys. Rev. Lett., 82 (1999) 3863). Owing to its generality, the proof not only answers basic questions in density-functional theory but also has potential implications in other fields of physics.
Implicit function theorem as a realization of the Lagrange principle. Abnormal points
Arutyunov, A V
2000-02-28
A smooth non-linear map is studied in a neighbourhood of an abnormal (degenerate) point. Inverse function and implicit function theorems are proved. The proof is based on the examination of a family of constrained extremal problems; second-order necessary conditions, which make sense also in the abnormal case, are used in the process. If the point under consideration is normal, then these conditions turn into the classical ones.
Stray thermal influences in zinc fixed-point cells
Rudtsch, S.; Aulich, A.; Monte, C.
2013-09-11
The influence of thermal effects is a major uncertainty contribution to the calibration of Standard Platinum Resistance Thermometers (SPRTs) in fixed-point cells. Axial heat losses strongly depend on the fixed-point temperature, constructional details of cells and SPRTs and the resulting heat transfer between cell, thermometer, furnace and environment. At the zinc point contributions by heat conduction and thermal radiation must be considered. Although the measurement of temperature gradients in the re-entrant well of a fixed-point cell provides very important information about the influence of axial heat losses, further investigations are required for a reliable estimate of the resulting uncertainty contribution. It is shown that specific modifications of a zinc fixed-point cell, following generally accepted principles, may result in systematic deviations of the measured fixed-point temperatures larger than typically stated in the uncertainty budget of National Metrology Institutes (NMIs). The underlying heat transport processes are investigated and the consequences for the construction of zinc cells are discussed.
NASA Astrophysics Data System (ADS)
Xiao, Jian-Zhong; Sun, Jing; Huang, Xuan
2010-02-01
In this paper a k+1-step iterative scheme with error terms involving k+1 asymptotically quasi-nonexpansive mappings is studied. In usual Banach spaces, some sufficient and necessary conditions are given for the iterative scheme to approximate a common fixed point. In uniformly convex Banach spaces, power equicontinuity for a mapping is introduced and a series of new convergence theorems are established. Several known results in the current literature are extended and refined.
Matrix product density operators: Renormalization fixed points and boundary theories
NASA Astrophysics Data System (ADS)
Cirac, J. I.; Pérez-García, D.; Schuch, N.; Verstraete, F.
2017-03-01
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
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Komnik, A.; Saleur, H.
2011-09-01
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.
Komnik, A; Saleur, H
2011-09-02
We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.
Fixed-Rate Compressed Floating-Point Arrays.
Lindstrom, Peter
2014-12-01
Current compression schemes for floating-point data commonly take fixed-precision values and compress them to a variable-length bit stream, complicating memory management and random access. We present a fixed-rate, near-lossless compression scheme that maps small blocks of 4(d) values in d dimensions to a fixed, user-specified number of bits per block, thereby allowing read and write random access to compressed floating-point data at block granularity. Our approach is inspired by fixed-rate texture compression methods widely adopted in graphics hardware, but has been tailored to the high dynamic range and precision demands of scientific applications. Our compressor is based on a new, lifted, orthogonal block transform and embedded coding, allowing each per-block bit stream to be truncated at any point if desired, thus facilitating bit rate selection using a single compression scheme. To avoid compression or decompression upon every data access, we employ a software write-back cache of uncompressed blocks. Our compressor has been designed with computational simplicity and speed in mind to allow for the possibility of a hardware implementation, and uses only a small number of fixed-point arithmetic operations per compressed value. We demonstrate the viability and benefits of lossy compression in several applications, including visualization, quantitative data analysis, and numerical simulation.
Measurement of thermodynamic temperature of high temperature fixed points
Gavrilov, V. R.; Khlevnoy, B. B.; Otryaskin, D. A.; Grigorieva, I. A.; Samoylov, M. L.; Sapritsky, V. I.
2013-09-11
The paper is devoted to VNIIOFI's measurements of thermodynamic temperature of the high temperature fixed points Co-C, Pt-C and Re-C within the scope of the international project coordinated by the Consultative Committee for Thermometry working group 5 'Radiation Thermometry'. The melting temperatures of the fixed points were measured by a radiance mode radiation thermometer calibrated against a filter radiometer with known irradiance spectral responsivity via a high temperature black body. This paper describes the facility used for the measurements, the results and estimated uncertainties.
Fixed points and the spontaneous breaking of scale invariance
NASA Astrophysics Data System (ADS)
Litim, Daniel F.; Marchais, Edouard; Mati, Péter
2017-06-01
We investigate critical N -component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalization. Global and local renormalization group flows are solved analytically in the infinite N limit to establish the exact phase diagram of the theory including the Wilson-Fisher fixed point and a line of asymptotically safe UV fixed points. We also study the Bardeen-Moshe-Bander phenomenon of spontaneously broken scale invariance and the stability of the vacuum for general regularization. Our findings clarify a long-standing puzzle about the apparent unboundedness of the effective potential. Implications for other theories are indicated.
Relative equilibria of point vortices and the fundamental theorem of algebra
NASA Astrophysics Data System (ADS)
Aref, Hassan
2010-11-01
The fundamental theorem of algebra implies that every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted with its multiplicity. This result may be applied to the generating polynomial for a relative equilibrium of point vortices and used to derive differential equations for this polynomial in various situations, e.g., when the vortices are on a line or all on a circle. The derivations thus obtained are quite elegant and compact compared to the corresponding derivations found in the literature. A new formula that provides the basis for application of the fundamental theorem to vortex equilibria is outlined and a number of the further derivations demonstrated.
Common fixed point result by using weak commutativity
NASA Astrophysics Data System (ADS)
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.
Fixed Point Problems for Linear Transformations on Pythagorean Triples
ERIC Educational Resources Information Center
Zhan, M.-Q.; Tong, J.-C.; Braza, P.
2006-01-01
In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…
Fixed Point Problems for Linear Transformations on Pythagorean Triples
ERIC Educational Resources Information Center
Zhan, M.-Q.; Tong, J.-C.; Braza, P.
2006-01-01
In this article, an attempt is made to find all linear transformations that map a standard Pythagorean triple (a Pythagorean triple [x y z][superscript T] with y being even) into a standard Pythagorean triple, which have [3 4 5][superscript T] as their fixed point. All such transformations form a monoid S* under matrix product. It is found that S*…
Renormalization group fixed points of foliated gravity-matter systems
NASA Astrophysics Data System (ADS)
Biemans, Jorn; Platania, Alessia; Saueressig, Frank
2017-05-01
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"- direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d g d λ . We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.
Fixed-rate compressed floating-point arrays
Lindstrom, P.
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; Liu, Xiao; Mulligan, Michael; /Stanford U., Phys. Dept. /SLAC
2008-11-05
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 {yields} {lambda}{sup z}t, x {yields} {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.
Fluctuation theorem for a double quantum dot coupled to a point-contact electrometer
Golubev, D.; Utsumi, Y.; Marthaler, M.; Schön, G.
2013-12-04
Motivated by recent experiments on the real-time single-electron counting through a semiconductor GaAs double quantum dot (DQD) by a nearby quantum point contact (QPC), we develop the full-counting statistics of coupled DQD and QPC system. By utilizing the time-scale separation between the dynamics of DQD and QPC, we derive the modified master equation with tunneling rates depending on the counting fields, which fulfill the detailed fluctuation theorem. Furthermore, we derive universal relations between the non-linear corrections to the current and noise, which can be verified in experiments.
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemblemore » forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.« less
Thermal analysis on the realization of the tin fixed point
NASA Astrophysics Data System (ADS)
Tsai, S. F.
2013-09-01
A study on the thermal analysis of a new tin fixed-point open cell within a new three-zone furnace was carried out. The stability at the setting temperatures of liquid-solid coexisting together with some degree Celsius lower and higher than the tin fixed point; and the axial uniformity of furnace while tin is still in solid phase were investigated and analyzed. The impurities effect on the depression in temperature was investigated in terms of ΔT (Tobserved-T1/F=0) and the inverse of the melted fraction (1/F) relationship during the melting and the following freezing realizations at various temperature settings of furnace. These thermal analysis results were also compared with those estimated by the CCT-WG1 recommended SIE (sum of individual estimates) method, which leads to a temperature correction along with a corresponding uncertainty through the individual impurity content detected by GDMS (glow discharge mass spectrometry).
Fixed points, stable manifolds, weather regimes, and their predictability
Deremble, Bruno; D'Andrea, Fabio; Ghil, Michael
2009-10-27
In a simple, one-layer atmospheric model, we study the links between low-frequency variability and the model’s fixed points in phase space. The model dynamics is characterized by the coexistence of multiple ''weather regimes.'' To investigate the transitions from one regime to another, we focus on the identification of stable manifolds associated with fixed points. We show that these manifolds act as separatrices between regimes. We track each manifold by making use of two local predictability measures arising from the meteorological applications of nonlinear dynamics, namely, ''bred vectors'' and singular vectors. These results are then verified in the framework of ensemble forecasts issued from clouds (ensembles) of initial states. The divergence of the trajectories allows us to establish the connections between zones of low predictability, the geometry of the stable manifolds, and transitions between regimes.
Averaging schemes for solving fixed point and variational inequality problems
Magnanti, T.L.; Perakis, G.
1994-12-31
In this talk we develop and study averaging schemes for solving fixed point and variational inequality problems. Typically, researchers have established convergence results for methods that solve these problems by establishing contractive estimates for the underlying algorithmic maps. In this talk we establish global convergence results using nonexpansive estimates. After first establishing convergence for a general iterative scheme for computing fixed points, we consider applications to projection and relaxation algorithms for solving variational inequality problems and to a generalized steepest descent method for solving systems of equations. As part of our development, we also establish a new interpretation of a norm condition typically used for establishing convergence of linearization schemes, by associating it with a strong-f-monotonicity condition. We conclude by applying these results to congested transportation networks.
The Influence of Impurities on the Zinc Fixed Point
NASA Astrophysics Data System (ADS)
Rudtsch, Steffen; Aulich, Antje
2017-02-01
Impurities are considered to be the most significant source of uncertainty for the realization of the International Temperature Scale of 1990 by means of metal fixed points. The determination and further reduction in this uncertainty require a traceable chemical analysis of dissolved impurities in the fixed-point metal and accurate knowledge of the specific temperature change caused by impurities (slope of the liquidus line). We determined the slope of the liquidus line for three binary systems and present results and conclusions from the chemical analysis of zinc with a nominal purity of 7N. For the Fe-Zn system, we determined a liquidus slope of (-0.91± 0.14) mK / (μ g{\\cdot } g^{-1}) from the evaluation of freezing plateaus and (-0.76 ± 0.20) mK / (μ g{\\cdot } g^{-1}) from the evaluation of melting plateaus; for the Pb-Zn system, the corresponding results are (-0.27 ± 0.05) mK / (μ g{\\cdot } g^{-1}) and (-0.26 ± 0.05) mK / (μ g{\\cdot } g^{-1}). Although for the Sb-Zn system, we determined a liquidus slope of about -0.8 mK / (μ g{\\cdot } g^{-1}), our investigations showed that a correction of the influence of antimony is highly questionable because antimony can be found in zinc in a fully dissolved state or precipitated as an insoluble compound. Iron is the only impurity where a correction of the fixed-point temperature was possible. For the realization of the zinc fixed point at PTB, this correction is between 2 μ K and 16 μ K depending on the batch of zinc used. The influence of the sum of all impurities was estimated by means of the OME method. The resulting uncertainty contribution is between 12 μK and 48 μK.
Pseudocontractions in the intermediate sense: Fixed and best proximity points
NASA Astrophysics Data System (ADS)
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.
TCP over OBS - fixed-point load and loss.
Cameron, Craig; Le Vu, Hai; Choi, Jung; Bilgrami, Syed; Zukerman, Moshe; Kang, Minho
2005-11-14
The sending rate of commonly used TCP protocols is tightly coupled to packet loss within the network: a high rate of packet loss will cause a sender to slow down, thereby reducing the network load and decreasing subsequent packet loss rates. In this paper, we combine a widely verified source rate TCP model with an Optical Burst Switching (OBS) loss model, to find fixed-point input loads and loss rates for an OBS link carrying TCP traffic. In doing so, we show that if OBS networks are to be efficiently used to carry TCP traffic, many wavelengths with full wavelength conversion are required.
Maximal Points of Head's Zone in Fixed Drug Eruption
Lee, Sang Sin; Hong, Dong Kyun; Im, Myung; Lee, Young; Seo, Young Joon
2011-01-01
The principles determining the primary localization of lesions in fixed drug eruption (FDE) are still unknown. Studies investigating the predilection areas in FDE have indicated drug-related, trauma-related, or inflammation-related specific site involvement, as well as visceracutaneous reflex-related specific site involvement. The importance of viscerocutaneous reflexes for the location of dermatoses was first recognized in the 1960s. Head's zones are viscerocutaneous reflex projection fields on the skin that extend over certain dermatomes and possess a reflex-associated maximal point. Recently, in a Turkish collective of patients, three women with the primary location of FDE lesions on the maximal points of Head's zones were presented. We also experienced 3 cases with FDE where the lesions were located at specific sites (buttocks), the so-called maximal points of Head's zones, which are known to be the most active dermatomal areas of an underlying visceral pathology. An underlying internal disturbance (ureter stone, pyelonephritis and chronic pelvic inflammatory disease) was found in all 3 patients, corresponding to the organ-related maximal point of Head's zones in each case. In conclusion, the primary location of FDE lesions on the maximal points of Head's zones revealed relevant organ disorders with corresponding projection fields. PMID:22346284
Maximal Points of Head's Zone in Fixed Drug Eruption.
Lee, Sang Sin; Hong, Dong Kyun; Im, Myung; Lee, Young; Seo, Young Joon; Lee, Jeung Hoon
2011-12-01
The principles determining the primary localization of lesions in fixed drug eruption (FDE) are still unknown. Studies investigating the predilection areas in FDE have indicated drug-related, trauma-related, or inflammation-related specific site involvement, as well as visceracutaneous reflex-related specific site involvement. The importance of viscerocutaneous reflexes for the location of dermatoses was first recognized in the 1960s. Head's zones are viscerocutaneous reflex projection fields on the skin that extend over certain dermatomes and possess a reflex-associated maximal point. Recently, in a Turkish collective of patients, three women with the primary location of FDE lesions on the maximal points of Head's zones were presented. We also experienced 3 cases with FDE where the lesions were located at specific sites (buttocks), the so-called maximal points of Head's zones, which are known to be the most active dermatomal areas of an underlying visceral pathology. An underlying internal disturbance (ureter stone, pyelonephritis and chronic pelvic inflammatory disease) was found in all 3 patients, corresponding to the organ-related maximal point of Head's zones in each case. In conclusion, the primary location of FDE lesions on the maximal points of Head's zones revealed relevant organ disorders with corresponding projection fields.
Chiral-scale perturbation theory about an infrared fixed point
NASA Astrophysics Data System (ADS)
Crewther, R. J.; Tunstall, Lewis C.
2014-06-01
We review the failure of lowest order chiral SU(3)L ×SU(3)R 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 image orthorectification algorithms for reduced computational cost
NASA Astrophysics Data System (ADS)
French, Joseph Clinton
Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation
Epidemiological study of fixed drug eruption in Pointe-Noire.
Ognongo-Ibiaho, A N; Atanda, H L
2012-11-01
A prospective study was conducted over a 27 month period in order to determine the epidemiological profile of fixed drug eruption (FDE) observed during a dermatological consultation at Pointe-Noire. During the study period 54 out of 9,070 persons consulting (0.6%) suffered from clinically diagnosed FDE. The variables studied were: age, sex, medicine and point of sale. The average age of onset was 30 years. The frequency of onset was higher in males (38 patients) than in females (16 patients). The incriminated medicines were: the sulfamides (48 patients) including Cotrimoxazole (45 patients ) and Sulfadoxine and Pyremethamine (3 patients) Coartem(®) + Doliprane(®) (1 patient), Chloramphenicol(®) (1 patient), Amidol(®) (1 patient), Duocotexin(®) + Paracetamol(®) (1 patient), Surquina(®) (1 patient), Amodiaquine(®) (1 patient). The point of sale was illicit (peddlers, markets) for 44 patients; for 10 patients it was a lawful outlet (pharmacies). This study shows that cotrimoxazole bought at illicit points of sale is the main etiology of FDE in the department, confirming that these medicines are counterfeit. The involvement of dermatologists in the fight against the illicit sale of medicines should be made a priority. © 2012 The International Society of Dermatology.
Noether's theorems and conserved currents in gauge theories in the presence of fixed fields
NASA Astrophysics Data System (ADS)
Tóth, Gábor Zsolt
2017-07-01
We extend the standard construction of conserved currents for matter fields in general relativity to general gauge theories. In the original construction, the conserved current associated with a spacetime symmetry generated by a Killing field hμ is given by √{-g }Tμ νhν , where Tμ ν is the energy-momentum tensor of the matter. We show that if in a Lagrangian field theory that has gauge symmetry in the general Noetherian sense some of the elementary fields are fixed and are invariant under a particular infinitesimal gauge transformation, then there is a current Bμ that is analogous to √{-g }Tμ νhν and is conserved if the nonfixed fields satisfy their Euler-Lagrange equations. The conservation of Bμ can be seen as a consequence of an identity that is a generalization of ∇μTμ ν=0 and is a consequence of the gauge symmetry of the Lagrangian. This identity holds in any configuration of the fixed fields if the nonfixed fields satisfy their Euler-Lagrange equations. We also show that Bμ differs from the relevant canonical Noether current by the sum of an identically conserved current and a term that vanishes if the nonfixed fields are on shell. For an example, we discuss the case of general, possibly fermionic, matter fields propagating in fixed gravitational and Yang-Mills background. We find that in this case the generalization of ∇μTμ ν=0 is the Lorentz law ∇μTμ ν-Fa ν λJa λ=0 , which holds as a consequence of the diffeomorphism, local Lorentz and Yang-Mills gauge symmetry of the matter Lagrangian. For a second simple example, we consider the case of general fields propagating in a background that consists of a gravitational and a real scalar field.
Fixed Point Transformations Based Iterative Control of a Polymerization Reaction
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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
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.
NASA Astrophysics Data System (ADS)
Gutlé, Claudine
2017-05-01
Incomplete spaces are investigated for solving the Schrödinger equation under the Born-Oppenheimer approximation. It is shown that the Hellmann-Feynman theorem cannot be used for computing the electronic force exerted on a nucleus, when a variational wavefunction with floating centers is used, if multicenter polynomial components are added in order to describe the polarization effects through the chemical bond. This is because the minimum of the potential energy surface is not a stationary point in the direction of the float parameter. Such a failure can be fixed by considering a molecular model with finite size nuclei, as defined herein. The classical electronic force is computed for that model, as compared with the standard point charge approximation, and it is applied to the { {H}_2}^+ molecular ion. As a result, the former model is found more accurate by several orders of magnitude.
Composite Higgs model at a conformal fixed point
NASA Astrophysics Data System (ADS)
Brower, R. C.; Hasenfratz, A.; Rebbi, C.; Weinberg, E.; Witzel, O.
2016-04-01
We propose to construct a chirally broken model based on the infrared fixed point of a conformal system by raising the mass of some flavors while keeping the others massless. In the infrared limit, the massive fermions decouple, and the massless fermions break chiral symmetry. The running coupling of this system "walks," and the energy range of walking can be tuned by the mass of the heavy flavors. Renormalization group considerations predict that the spectrum of such a system shows hyperscaling. We have studied a model with four light and eight heavy flavors coupled to S U (3 ) gauge fields and verified the above expectations. We determined the mass of several hadronic states and found that some of them are in the 2-3 TeV range if the scale is set by the pseudoscalar decay constant Fπ≈250 GeV . The 0++ scalar state behaves very differently from the other hadronic states. In most of our simulations, it is nearly degenerate with the pion, and we estimate its mass to be less than half of the vector resonance mass.
Fundamental flavours, fields and fixed points: a brief account
NASA Astrophysics Data System (ADS)
Kundu, Arnab; Kundu, Nilay
2017-03-01
In this article we report on a preliminary study, via Holography, of infrared fixed points in a putative strongly coupled SU( N c ) gauge theory, with N f fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently effective or a bottom up approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: {AdS}_m× R^n -type, which has appeared in the literature before; and AdS m ×EAdS n -type, where m and n are suitable integers. Both these classes of solutions are non-perturbative in back-reaction. The AdS m ×EAdS n -type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS5 ultraviolet to both an AdS2 and an AdS3 IR.
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.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Ryttov, Thomas A.
2016-08-01
We suggest how to consistently calculate the anomalous dimension γ* of the ψ ¯ 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 (Δfn) , where Δf=N¯ f-Nf , Nf is the number of flavors, and 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 Δf. We then compute γ* through O (Δf2) 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 (Δf3) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ* are observed for a large range of flavors.
The Fundamental Basis Theorem of Geometry from an algebraic point of view
NASA Astrophysics Data System (ADS)
Bekbaev, U.
2017-03-01
An algebraic analog of the Fundamental Basis Theorem of geometry is offered with a pure algebraic proof involving the famous Waring’s problem for polynomials. Unlike the geometry case the offered system of invariant differential operators is commuting, which is a new result even in the classical geometry of surfaces. Moreover the algebraic analog works in more general settings then does the Fundamental Basis Theorem of geometry.
Schaefer type theorem and periodic solutions of evolution equations
NASA Astrophysics Data System (ADS)
Liu, Yicheng; Li, Zhixiang
2006-04-01
Two fixed point theorems for the sum of contractive and compact operators are obtained in this paper, which generalize and improve the corresponding results in [H. Schaefer, Uber die methode der a priori-Schranken, Math. Ann. 129 (1955) 415-416; T.A. Burton, Integral equations, implicit functions and fixed points, Proc. Amer. Math. Soc. 124 (1996) 2383-2390; V.I. Istratescu, Fixed Point Theory, an Introduction, Reidel, Dordrecht, 1981; T.A. Burton, K. Colleen, A fixed point theorem of Krasnoselskii-Schaefer type, Math. Nachr. 189 (1998) 23-31; D.R. Smart, Fixed Point Theorems, Cambridge Univ. Press, Cambridge, 1980]. As the applications for the results, we obtain the existence of periodic solutions for some evolution equations with delay, which extend the corresponding results in [T.A. Burton, B. Zhang, Periodic solutions of abstract differential equations with infinite delay, J. Differential Equations 90 (1991) 357-396].
Shen, Chongfei; Liu, Hongtao; Xie, Xb; Luk, Keith Dk; Hu, Yong
2007-01-01
Adaptive noise canceller (ANC) has been used to improve signal to noise ratio (SNR) of somsatosensory evoked potential (SEP). In order to efficiently apply the ANC in hardware system, fixed-point algorithm based ANC can achieve fast, cost-efficient construction, and low-power consumption in FPGA design. However, it is still questionable whether the SNR improvement performance by fixed-point algorithm is as good as that by floating-point algorithm. This study is to compare the outputs of ANC by floating-point and fixed-point algorithm ANC when it was applied to SEP signals. The selection of step-size parameter (micro) was found different in fixed-point algorithm from floating-point algorithm. In this simulation study, the outputs of fixed-point ANC showed higher distortion from real SEP signals than that of floating-point ANC. However, the difference would be decreased with increasing micro value. In the optimal selection of micro, fixed-point ANC can get as good results as floating-point algorithm.
NASA Astrophysics Data System (ADS)
Lin, Lai-Jiu; Du, Wei-Shih
2006-11-01
In this paper, we introduce the concept of [tau]-function which generalizes the concept of w-distance studied in the literature. We establish a generalized Ekeland's variational principle in the setting of lower semicontinuous from above and [tau]-functions. As applications of our Ekeland's variational principle, we derive generalized Caristi's (common) fixed point theorems, a generalized Takahashi's nonconvex minimization theorem, a nonconvex minimax theorem, a nonconvex equilibrium theorem and a generalized flower petal theorem for lower semicontinuous from above functions or lower semicontinuous functions in the complete metric spaces. We also prove that these theorems also imply our Ekeland's variational principle.
Composition analysis of large samples with PGNAA using a fixed point iteration
NASA Astrophysics Data System (ADS)
Akkurt, Hatice
2002-09-01
The composition problem in large sample prompt gamma neutron activation analysis (PGNAA) is a nonlinear inverse problem. The basic form of the nonlinear inverse composition problem is presented. This problem is then formulated in a general way, as a fixed point problem, without addressing any specific application or sample type or linearization approach. This approach of formulating the problem as a fixed point problem suggested a natural fixed point iteration. The algorithm of the fixed point iteration solves the nonlinear composition problem using a combination of measured and computed data. The effectiveness of the fixed point iteration for composition analysis is demonstrated using purely numerical experiments. These numerical experiments showed that the fixed point iteration can be successfully applied to find the bulk composition of large samples, with excellent agreement between the estimated and true composition of the samples, in a few iterations, independent of the initial guess. In order to test the fixed point iteration using real experimental data, a series of large sample PGNAA measurements were performed at ANL-W. These experiments are described and the measured spectra for the samples are presented. Then, the fixed point iteration is applied for these real experiments to find the composition of the samples. In all of the cases, except borated polyethylene, the composition of the large samples are found in a few iterations with errors less than +/-1.3%. The effectiveness of the fixed point iteration is thus demonstrated with many proof-of-principle measurements. While testing the fixed point iteration algorithm, published values of the source spectrum and relative detector efficiencies are used. The sensitivity of the fixed point iteration to source spectrum is investigated and it is shown that the estimated composition results are not very sensitive to the change in the source spectrum. The reason behind the slow convergence for the borated
Triple point of e-deuterium as an accurate thermometric fixed point
Pavese, F.; McConville, G.T.
1986-01-01
The triple point of deuterium (18.7/sup 0/K) is the only possibility for excluding vapor pressure measurements in the definition of a temperature scale based on fixed points between 13.81 and 24.562/sup 0/K. This paper reports an investigation made at the Istituto di Metrologia and Mound Laboratory, using extremely pure deuterium directly sealed at the production plant into small metal cells. The large contamination by HD of commercially available gas, that cannot be accounted and corrected for due to its increase in handling, was found to be very stable with time after sealing in IMGC cells. HD contamination can be limited to less than 100 ppM in Monsanto cells, both with n-D/sub 2/ and e-D/sub 2/, when filled directly from the thermal diffusion column and sealed at the factory. e-D/sub 2/ requires a special deuterated catalyst. The triple point temperature of e-D/sub 2/ has been determined to be: T(NPL-IPTS-68) = 18.7011 +- 0.002/sup 0/K. 20 refs., 3 figs., 2 tabs.
Area law for fixed points of rapidly mixing dissipative quantum systems
Brandão, Fernando G. S. L.; Cubitt, Toby S.; Lucia, Angelo; Michalakis, Spyridon; Perez-Garcia, David
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.
Asymptotic behavior of two algorithms for solving common fixed point problems
NASA Astrophysics Data System (ADS)
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.
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.
van Maanen, Leendert; Couto, Joaquina; Lebreton, Mael
2016-01-01
The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied-for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes.
Fixed Points of Belief Propagation - An Analysis via Polynomial Homotopy Continuation.
Knoll, Christian; Mehta, Dhagash; Chen, Tianran; Pernkopf, Franz
2017-09-07
Belief propagation (BP) is an iterative method to perform approximate inference on arbitrary graphical models. Whether BP converges and if the solution is a unique fixed point depends on both the structure and the parametrization of the model. To understand this dependence it is interesting to find all fixed points.
Miniature Fixed Points as Temperature Standards for In Situ Calibration of Temperature Sensors
NASA Astrophysics Data System (ADS)
Hao, X. P.; Sun, J. P.; Xu, C. Y.; Wen, P.; Song, J.; Xu, M.; Gong, L. Y.; Ding, L.; Liu, Z. L.
2017-06-01
Miniature Ga and Ga-In alloy fixed points as temperature standards are developed at National Institute of Metrology, China for the in situ calibration of temperature sensors. A quasi-adiabatic vacuum measurement system is constructed to study the phase-change plateaus of the fixed points. The system comprises a high-stability bath, a quasi-adiabatic vacuum chamber and a temperature control and measurement system. The melting plateau of the Ga fixed point is longer than 2 h at 0.008 W. The standard deviation of the melting temperature of the Ga and Ga-In alloy fixed points is better than 2 mK. The results suggest that the melting temperature of the Ga or Ga-In alloy fixed points is linearly related with the heating power.
NASA Astrophysics Data System (ADS)
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.
Comparison of realizations of Re-C fixed points filled and measured at NPL and NRC
NASA Astrophysics Data System (ADS)
Todd, A. D. W.; Lowe, D. H.; Dong, W.; Woods, D. J.
2013-09-01
A Re-C fixed point was filled at the National Physical Laboratory (NPL), UK and its melting temperature compared to a fixed point that had been filled previously at NPL. Both of these fixed points were of the hybrid type and used a purified graphite foil between the sacrificial graphite sleeve and the outer crucible. The melting temperatures of these two fixed points were compared and found to agree within the comparison uncertainties. Another Re-C fixed point was filled at the National Research Council (NRC), Canada. This fixed point was also of the hybrid type but contained carbon-composite sheet as the liner between the sleeve and the outer crucible. The melting temperatures of the fixed point filled at NPL and the one filled at NRC were compared and found to agree within the uncertainties of the comparison. When the ITS-90 temperatures at the Re-C melting point (˜ 2474 °C) measured at NPL were compared to those measured at NRC they were also found to agree within the uncertainties of their respective scales.
Explicit results for the anomalous three point function and non-renormalization theorems
NASA Astrophysics Data System (ADS)
Jegerlehner, F.; Tarasov, O. V.
2006-08-01
Two-loop corrections for the < VVA > correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein [A. Vainshtein, Phys. Lett. B 569 (2003) 187] and Knecht et al. [M. Knecht, S. Peris, M. Perrottet, E. de Rafael, JHEP 0403 (2004) 035]. We find that as in the one-loop case also at two loops the < VVA > correlator has only three independent form-factors instead of four. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C2 (R)αs / π in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non-anomalous transversal amplitudes. The finite overall αs dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity [ < VV ∂ A > correlator]. Our observations, together with known facts, suggest that in perturbation theory the < VVA > correlator is proportional to the one-loop term to all orders and that the non-renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.
NASA Astrophysics Data System (ADS)
Dittmore, Andrew; Trail, Collin; Olsen, Thomas; Wiener, Richard J.
2003-11-01
We have previously demonstrated the experimental control of chaos in a Modified Taylor-Couette system with hourglass geometry( Richard J. Wiener et al), Phys. Rev. Lett. 83, 2340 (1999).. Identifying fixed points susceptible to algorithms for the control of chaos is key. We seek to learn about this process in the accessible numerical model of the damped, driven pendulum. Following Baker(Gregory L. Baker, Am. J. Phys. 63), 832 (1995)., we seek points susceptible to the OGY(E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64), 1196 (1990). algorithm. We automate the search for fixed points that are candidates for control. We present comparisons of the space of candidate fixed points with the bifurcation diagrams and Poincare sections of the system. We demonstrate control at fixed points which do not appear on the attractor. We also show that the control algorithm may be employed to shift the system between non-communicating branches of the attractor.
Implementation Considerations for Automotive Vision Systems on a Fixed-Point DSP
NASA Astrophysics Data System (ADS)
Nikolić, Zoran
In this chapter we evaluate numerical requirements for implementation of camera-based lateral position detection algorithms, such as lane keep assistant (LKA) and lane departure warning (LDW) on a fixed-point DSP. We first present methods that address the challenges and requirements of fixed-point design process. The flow proposed is targeted at converting C/C++ code with floating-point operations into C code with integer operations that can then be fed through the native C compiler for a fixed-point DSP. Advanced code optimization and an implementation by DSP-specific, fixed-point C code generation are introduced. We then demonstrate the conversion flow on tracking example (extended Kalman filter) using synthetically generated data, and we analyze trade-offs for algorithm implementation in fixed-point arithmetic. By using the techniques described in this chapter speed can be increased by a factor of up to 10 compared to floating-point emulation on fixed-point hardware.
Revisiting the dilatation operator of the Wilson-Fisher fixed point
NASA Astrophysics Data System (ADS)
Liendo, Pedro
2017-07-01
We revisit the order-ε dilatation operator of the Wilson-Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.
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.
QCD fixed points: Banks-Zaks scenario or dynamical gluon mass generation?
NASA Astrophysics Data System (ADS)
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.
A sealed He-4 superfluid-transition fixed-point device
NASA Astrophysics Data System (ADS)
Duncan, R. V.; Ahlers, G.
The superfluid transition in pure He-4 under its saturated vapor pressure provides an ideal fixed-point reference for thermometry near 2 K. In practice, the transition may be located to within a few nanokelvin, and it is virtually immune to drift. Here we first review the properties of He-4 very near the transition which may affect the performance of this fixed-point reference. Then we report on the construction and use of a sealed fixed-point device that requires no external capillaries or valves. It is as easily used in a vacuum cryostat as are superconductive fixed-point devices. Unlike superconductors, it is virtually unaffected by magnetic fields and material purity.
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data
Couto, Joaquina; Lebreton, Mael
2016-01-01
The notion of “mixtures” has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture data, applied–for instance- to response times. In that case, the fixed-point property entails that response time distributions obtained in an experiment in which the mixture proportion is manipulated would have a common density point. In the current article, we discuss the application of the fixed-point property and identify three boundary conditions under which the fixed-point property will not be interpretable. In Boundary condition 1, a finding in support of the fixed-point will be mute because of a lack of difference between conditions. Boundary condition 2 refers to the case in which the extreme conditions are so different that a mixture may display bimodality. In this case, a mixture hypothesis is clearly supported, yet the fixed-point may not be found. In Boundary condition 3 the fixed-point may also not be present, yet a mixture might still exist but is occluded due to additional changes in behavior. Finding the fixed-property provides strong support for a dual-process account, yet the boundary conditions that we identify should be considered before making inferences about underlying psychological processes. PMID:27893868
Analysis of fixed point FFT for Fourier domain optical coherence tomography systems.
Ali, Murtaza; Parlapalli, Renuka; Magee, David P; Dasgupta, Udayan
2009-01-01
Optical coherence tomography (OCT) is a new imaging modality gaining popularity in the medical community. Its application includes ophthalmology, gastroenterology, dermatology etc. As the use of OCT increases, the need for portable, low power devices also increases. Digital signal processors (DSP) are well suited to meet the signal processing requirements of such a system. These processors usually operate on fixed precision. This paper analyzes the issues that a system implementer faces implementing signal processing algorithms on fixed point processor. Specifically, we show the effect of different fixed point precisions in the implementation of FFT on the sensitivity of Fourier domain OCT systems.
NASA Astrophysics Data System (ADS)
Konvalinka, Ira; Quddus, Azhar; Asraf, Daniel
2009-05-01
Today there is no direct path for the conversion of a floating-point algorithm implementation to an optimized fixed-point implementation. This paper proposes a novel and efficient methodology for Floating-point to Fixed-point Conversion (FFC) of biometric Fingerprint Algorithm Library (FAL) on fixed-point DaVinci processor. A general FFC research task is streamlined along smaller tasks which can be accomplished with lower effort and higher certainty. Formally specified in this paper is the optimization target in FFC, to preserve floating-point accuracy and to reduce execution time, while preserving the majority of algorithm code base. A comprehensive eight point strategy is formulated to achieve that target. Both local (focused on the most time consuming routines) and global optimization flow (to optimize across multiple routines) are used. Characteristic phases in the FFC activity are presented using data from employing the proposed FFC methodology to FAL, starting with target optimization specification, to speed optimization breakthroughs, finalized with validation of FAL accuracy after the execution time optimization. FAL implementation resulted in biometric verification time reduction for over a factor of 5, with negligible impact on accuracy. Any algorithm developer facing the task of implementing his floating-point algorithm on DaVinci DSP is expected to benefit from this presentation.
NASA Astrophysics Data System (ADS)
Viesca, R. C.
2014-12-01
A fault's transition from slow creep to the propagation of an earthquake-generating dynamic rupture is thought to start as a quasi-static slip instability. Here we examine how such an instability develops on a sliding interface whose strength is governed by a slip rate- and state-dependent friction, where the state variable evolves according to the aging law. We find that the development occurs as the attraction of a dynamical system to a fixed point. The fixed points are such that the state of slip and the rate at which velocity diverges (and its spatial distribution) are known. The fixed points are independent of the manner of external forcing and the values of slip rate and state before the onset of instability. For a fault under uniform normal stress and frictional properties, the sole parameter that determines the fixed point (to within a translational invariance) is the ratio of the frictional parameters, a/b (where, for steady-state rate weakening, 0fixed points are asymptotically stable; however, stability is lost for a/b above that value. Increasing a/b above this critical value leads to a series of Hopf bifurcations. This cascade of bifurcations signals a quasi-periodic route to chaos, implying the existence of a second, larger, critical value of a/b (corresponding to the value at which the third Hopf bifurcation occurs), above which the slip instability may develop in a chaotic fashion. The fixed-point solutions, as well as the critical thresholds concerning their stability, depend on the configuration of slip (e.g., in/anti-plane or mixed-mode slip) and the elastic environment in which the interface is embedded (e.g., a slip surface between elastic half-spaces or one lying below and parallel to a free surface); solving for a fixed point reduces to the solution of an equivalent problem of an equilibrium slip-weakening fracture; and fixed-point stability is determined by linear stability analysis. Solutions of
Implementation of Fixed-point Neuron Models with Threshold, Ramp and Sigmoid Activation Functions
NASA Astrophysics Data System (ADS)
Zhang, Lei
2017-07-01
This paper presents the hardware implementation of single-neuron models with three types of activation functions using fixed-point data format on Field Programmable Gate Arrays (FPGA). Activation function defines the transfer behavior of a neuron model and consequently the Artificial Neural Network (ANN) constructed using it. This paper compared single neuron models designed with bipolar ramp, threshold and sigmoid activation functions. It is also demonstrated that the FPGA hardware implementation performance can be significantly improved by using 16-bit fixed-point data format instead of 32-bit floating-point data format for the neuron model with sigmoid activation function.
NASA Astrophysics Data System (ADS)
Edler, F.; Baratto, A. C.
2006-12-01
Three nickel-carbon (Ni-C) and three iron-carbon (Fe-C) eutectic fixed points cells of a new design, meeting the requirements for reliable applications and being suitable for the calibration of thermocouples, were constructed at PTB and Inmetro. Their melting temperatures were compared by using the high-temperature furnace of PTB (HTF-R) and two platinum/palladium (Pt/Pd) thermocouples. The measured emfs of the Ni-C eutectic fixed point cells at the inflection points of the melting curves agree within a temperature equivalent of about 0.29 °C, compared with an agreement of about 0.09 °C found for the Fe-C cells. Additional comparison measurements of two Fe-C eutectic fixed point cells in a second high-temperature furnace (HTF-M, Inmetro) demonstrate the applicability of the Fe-C eutectic cells as transfer standards for the dissemination of temperatures.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
NASA Astrophysics Data System (ADS)
Rinaldi, Massimiliano
2015-10-01
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 an autonomous 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.
Dark energy as a fixed point of the Einstein Yang-Mills Higgs equations
Rinaldi, Massimiliano
2015-10-01
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 an autonomous 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.
Side Effects in Time Discounting Procedures: Fixed Alternatives Become the Reference Point
2016-01-01
Typical research on intertemporal choice utilizes a two-alternative forced choice (2AFC) paradigm requiring participants to choose between a smaller sooner and larger later payoff. In the adjusting-amount procedure (AAP) one of the alternatives is fixed and the other is adjusted according to particular choices made by the participant. Such a method makes the alternatives unequal in status and is speculated to make the fixed alternative a reference point for choices, thereby affecting the decision made. The current study shows that fixing different alternatives in the AAP influences discount rates in intertemporal choices. Specifically, individuals’ (N = 283) choices were affected to just the same extent by merely fixing an alternative as when choices were preceded by scenarios explicitly imposing reference points. PMID:27768759
Side Effects in Time Discounting Procedures: Fixed Alternatives Become the Reference Point.
Sawicki, Przemysław; Białek, Michał
2016-01-01
Typical research on intertemporal choice utilizes a two-alternative forced choice (2AFC) paradigm requiring participants to choose between a smaller sooner and larger later payoff. In the adjusting-amount procedure (AAP) one of the alternatives is fixed and the other is adjusted according to particular choices made by the participant. Such a method makes the alternatives unequal in status and is speculated to make the fixed alternative a reference point for choices, thereby affecting the decision made. The current study shows that fixing different alternatives in the AAP influences discount rates in intertemporal choices. Specifically, individuals' (N = 283) choices were affected to just the same extent by merely fixing an alternative as when choices were preceded by scenarios explicitly imposing reference points.
NASA Astrophysics Data System (ADS)
Nezir, Veysel; Mustafa, Nizami
2017-04-01
In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.
One-parameter semigroups of analytic functions, fixed points and the Koenigs function
NASA Astrophysics Data System (ADS)
Goryainov, Victor V.; Kudryavtseva, Olga S.
2011-07-01
Analogues of the Berkson-Porta formula for the infinitesimal generator of a one-parameter semigroup of holomorphic maps of the unit disc into itself are obtained in the case when, along with a Denjoy-Wolff point, there also exist other fixed points. With each one-parameter semigroup a so-called Koenigs function is associated, which is a solution, common for all elements of the one-parameter semigroup, of a certain functional equation (Schröder's equation in the case of an interior Denjoy-Wolff point and Abel's equation in the case of a boundary Denjoy-Wolff point). A parametric representation for classes of Koenigs functions that takes account of the Denjoy-Wolff point and other fixed points of the maps in the one-parameter semigroup is presented. Bibliography: 19 titles.
One-parameter semigroups of analytic functions, fixed points and the Koenigs function
Goryainov, Victor V; Kudryavtseva, Olga S
2011-07-31
Analogues of the Berkson-Porta formula for the infinitesimal generator of a one-parameter semigroup of holomorphic maps of the unit disc into itself are obtained in the case when, along with a Denjoy-Wolff point, there also exist other fixed points. With each one-parameter semigroup a so-called Koenigs function is associated, which is a solution, common for all elements of the one-parameter semigroup, of a certain functional equation (Schroeder's equation in the case of an interior Denjoy-Wolff point and Abel's equation in the case of a boundary Denjoy-Wolff point). A parametric representation for classes of Koenigs functions that takes account of the Denjoy-Wolff point and other fixed points of the maps in the one-parameter semigroup is presented. Bibliography: 19 titles.
Holographic non-relativistic fermionic fixed point and bulk dipole coupling
NASA Astrophysics Data System (ADS)
Li, Wei-Jia; Zhang, Hongbao
2011-11-01
Inspired by the recently discovered non-relativistic fermionic fixed points, we investigate how the presence of bulk dipole coupling modifies the spectral function at one of these novel fixed points. As a result, although the infinite flat band is always visible in the presence of the bulk dipole coupling as well as chemical potential, the band is modified in a remarkable way at small momenta up to the order of magnitude of bulk dipole coupling. On the other hand, like a phoenix, a new Fermi surface sprouts from the formed gap when the bulk dipole coupling is pushed up further such as to overshadow the charge parameter, which is obviously different from what is found at the relativistic fixed points.
Miniature Fixed-Point Cell Approaches for Monitoring of Thermocouple Stability
NASA Astrophysics Data System (ADS)
Failleau, G.; Elliott, C. J.; Deuzé, T.; Pearce, J. V.; Machin, G.; Sadli, M.
2014-07-01
In the framework of the European Metrology Research Project ENG08 "MetroFission," LNE-Cnam and NPL have undertaken cooperative research into the development of temperature measurement solutions for the next generation of nuclear fission power plants. Currently, in-pile temperature monitoring is usually performed with nickel-based (Type K or N) thermocouples. When these thermocouples are exposed to a neutron flux, the thermoelements transmute, leading to large and unknown drifts in output. In addition, it is impossible to routinely recalibrate the thermocouples after irradiation for obvious reasons of safety. To alleviate this problem, both LNE-Cnam and NPL have developed, via differing approaches, in situ calibration methods for the thermocouples. The self-validating thermocouple methodologies are based on the principle of a miniature fixed-point cell to be co-located with the thermocouple measurement junction in use. The drift of the thermocouple can be monitored and corrected for by regular determination of the output at the phase transition of the fixed-point material: in effect performing regular in situ calibration checks. The two institutes have constructed miniature fixed-point cells for use at three different temperatures; the freezing point of silver ; LNE-Cnam), the freezing point of copper ; LNE-Cnam and NPL), and the melting point of Fe-C (; NPL). This paper introduces the construction and validation of the miniature fixed-point cells prior to use, to ensure traceability to the ITS-90. A comparison of the performance of the two cell designs is discussed, where typical industrial Type N thermocouples have been used for measurement of the fixed-point cells. Such initial measurements demonstrate the feasibility of each of these two approaches.
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.
The four fixed points of scale invariant single field cosmological models
Xue, BingKan
2012-10-01
We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new models and discuss constraints from strong coupling and superluminality.
Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA
de Souza, Alisson C. D.; Fernandes, Marcelo A. C.
2014-01-01
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. PMID:25268918
Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology
NASA Astrophysics Data System (ADS)
Mori, Fumito; Mochizuki, Atsushi
2017-07-01
Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.
A New Infinite-Randomness Fixed Point in an Interacting Majorana Chain
NASA Astrophysics Data System (ADS)
Vijay, S.; Fu, Liang
We perform a real-space renormalization group (RG) study of an interacting chain of Majorana fermions with strong randomness. Our theory naturally describes the interacting, disordered edge of a weak topological superconductor in the BDI symmetry class of fermion topological phases. Our RG scheme reveals a new infinite-randomness fixed-point, governed by flow equations for the probability distribution of couplings. A numerical implementation of our real-space RG yields critical exponents governing susceptibilities and correlation functions near the fixed-point.
Infinite disorder and correlation fixed point in the Ising model with correlated disorder
NASA Astrophysics Data System (ADS)
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.
Parameter estimation by fixed point of function of information processing intensity
NASA Astrophysics Data System (ADS)
Jankowski, Robert; Makowski, Marcin; Piotrowski, Edward W.
2014-12-01
We present a new method of estimating the dispersion of a distribution which is based on the surprising property of a function that measures information processing intensity. It turns out that this function has a maximum at its fixed point. Fixed-point equation is used to estimate the parameter of the distribution that is of interest to us. The main result consists in showing that only part of available experimental data is relevant for the parameters estimation process. We illustrate the estimation method by using the example of an exponential distribution.
Mukherji, Sutapa
2011-03-01
Boundary-induced phase transitions in a driven diffusive process can be studied through a phase-plane analysis of the boundary-layer equations. In this paper, we generalize this approach further to show how various shapes including multishocks and downward shocks in the bulk particle density profile can be understood by studying the dependence of the fixed points of the boundary-layer equation on an appropriate parameter. This is done for a particular driven interacting particle system as a prototypical example. The present analysis shows the special role of a specific bifurcation of the fixed points in giving rise to different kinds of shocks.
Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces
Arshad, Muhammad; Ahmad, Jamshaid
2013-01-01
Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results. PMID:24062629
Fixed-point distributions of short-range Ising spin glasses on hierarchical lattices
NASA Astrophysics Data System (ADS)
Almeida, Sebastião T. O.; Nobre, Fernando D.
2015-03-01
Fixed-point distributions for the couplings of Ising spin glasses with nearest-neighbor interactions on hierarchical lattices are investigated numerically. Hierarchical lattices within the Migdal-Kadanoff family with fractal dimensions in the range 2.58 ≤D ≤7 , as well as a lattice of the Wheatstone-Bridge family with fractal dimension D ≈3.58 are considered. Three initial distributions for the couplings are analyzed, namely, the Gaussian, bimodal, and uniform ones. In all cases, after a few iterations of the renormalization-group procedure, the associated probability distributions approached universal fixed shapes. For hierarchical lattices of the Migdal-Kadanoff family, the fixed-point distributions were well fitted either by stretched exponentials, or by q -Gaussian distributions; both fittings recover the expected Gaussian limit as D →∞ . In the case of the Wheatstone-Bridge lattice, the best fit was found by means of a stretched-exponential distribution.
A test of fixed and moving reference point control in posture.
Lee, I-Chieh; Pacheco, Matheus M; Newell, Karl M
2017-01-01
This study investigated two contrasting assumptions of the regulation of posture: namely, fixed and moving reference point control. These assumptions were tested in terms of time-dependent structure and data distribution properties when stability is manipulated. Fifteen male participants performed a tightrope simulated balance task that is, maintaining a tandem stance while holding a pole. Pole length (and mass) and the standing support surface (fixed surface/balance board) were manipulated so as to mechanically change the balance stability. The mean and standard deviation (SD) of COP length were reduced with pole length increment but only in the balance board surface condition. Also, the SampEn was lower with greater pole length for the balance board but not the fixed surface. More than one peak was present in the distribution of COP in the majority of trials. Collectively, the findings provide evidence for a moving reference point in the maintenance of postural stability for quiet standing.
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.
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
Fixed-point arithmetic for mobile devices: a fingerprinting verification case study
NASA Astrophysics Data System (ADS)
Moon, Yiu S.; Luk, Franklin T.; Ho, Ho C.; Tang, T. Y.; Chan, Kit C.; Leung, C. W.
2002-12-01
Mobile devices use embedded processors with low computing capabilities to reduce power consumption. Since floating-point arithmetic units are power hungry, computationally intensive jobs must be accomplished with either digital signal processors or hardware co-processors. In this paper, we propose to perform fixed-point arithmetic on an integer hardware unit. We illustrate the advantages of our approach by implementing fingerprint verification on mobile devices.
Fixed Points of Contractive Mappings in b-Metric-Like Spaces
Hussain, Nawab; Roshan, Jamal Rezaei
2014-01-01
We discuss topological structure of b-metric-like spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in b-metric-like spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results. PMID:25143980
Establishment of the Co-C Eutectic Fixed-Point Cell for Thermocouple Calibrations at NIMT
NASA Astrophysics Data System (ADS)
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.
Code of Federal Regulations, 2010 CFR
2010-10-01
... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be operated... internal system from the transmitter control circuit or to close the system......
Code of Federal Regulations, 2011 CFR
2011-10-01
... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be operated... internal system from the transmitter control circuit or to close the system......
Intermediate fixed point in a Luttinger liquid with elastic and dissipative backscattering
NASA Astrophysics Data System (ADS)
Altland, Alexander; Gefen, Yuval; Rosenow, Bernd
2015-08-01
In a recent work [A. Altland, Y. Gefen, and B. Rosenow, Phys. Rev. Lett. 108, 136401 (2012), 10.1103/PhysRevLett.108.136401], we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed point landscape, and scaling near those fixed points. Our analysis is nonperturbative in the elastic tunneling amplitudes, employing an instanton calculation in one or two of the available elastic tunneling channels. Our analysis accounts for nontrivial Klein factors, which represent anyonic or fermionic statistics. These Klein factors need to be taken into account due to the fact that higher-order tunneling processes take place. In particular, we find a stable fixed point, where an incoming current is split 1/2 -1/2 between a forward and a backward scattered beams. This intermediate fixed point, between complete backscattering and full forward scattering, is stable for the Luttinger parameter g <1 .
A MAP fixed-point, packing-unpacking routine for the IBM 7094 computer
Robert S. Helfman
1966-01-01
Two MAP (Macro Assembly Program) computer routines for packing and unpacking fixed point data are described. Use of these routines with Fortran IV Programs provides speedy access to quantities of data which far exceed the normal storage capacity of IBM 7000-series computers. Many problems that could not be attempted because of the slow access-speed of tape...
Analyzing fixed points of intracellular regulation networks with interrelated feedback topology
2012-01-01
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. PMID:22672785
Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
NASA Astrophysics Data System (ADS)
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
Scalar-tensor cosmologies: Fixed points of the Jordan frame scalar field
Jaerv, Laur; Kuusk, Piret; Saal, Margus
2008-10-15
We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System parametrized post-Newtonian (PPN) constraints. The phase space structure should also carry over to the Einstein frame as long as the transformation between the frames is regular which however is not the case for the latter (PPN compatible) fixed point.
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.
Fixed-Radius Point Counts in Forests: Factors Influencing Effectiveness and Efficiency
Daniel R. Petit; Lisa J. Petit; Victoria A. Saab; Thomas E. Martin
1995-01-01
The effectiveness of fixed-radius point counts in quantifying abundance and richness of bird species in oak-hickory, pine-hardwoods, mixed-mesophytic, beech-maple, and riparian cottonwood forests was evaluated in Arkansas, Ohio, Kentucky, and Idaho. Effects of count duration and numbers of stations and visits per stand were evaluated in May to July 1991 by conducting...
NASA Astrophysics Data System (ADS)
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.
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
Convergence theorems for generalized nonexpansive multivalued mappings in hyperbolic spaces.
Kim, Jong Kyu; Pathak, Ramesh Prasad; Dashputre, Samir; Diwan, Shailesh Dhar; Gupta, Rajlaxmi
2016-01-01
In this paper, we establish the existence of a fixed point for generalized nonexpansive multivalued mappings in hyperbolic spaces and we prove some [Formula: see text]-convergence and strong convergence theorems for the iterative scheme proposed by Chang et al. (Appl Math Comp 249:535-540, 2014) to approximate a fixed point for generalized nonexpansive multivalued mapping under suitable conditions. Our results are the extension and improvements of the recent well-known results announced in the current literature.
NASA Astrophysics Data System (ADS)
Bojkovski, J.; Veliki, T.; Zvizdić, D.; Drnovšek, J.
2011-08-01
The objective of project EURAMET 1127 (Bilateral comparison of triple point of mercury and melting point of gallium) in the field of thermometry is to compare realization of a triple point of mercury (-38.8344 °C) and melting point of gallium (29.7646 °C) between the Slovenian national laboratory MIRS/UL-FE/LMK and the Croatian national laboratory HMI/FSB-LPM using a long-stem 25 Ω standard platinum resistance thermometer (SPRT). MIRS/UL/FE-LMK participated in a number of intercomparisons on the level of EURAMET. On the other hand, the HMI/LPM-FSB laboratory recently acquired new fixed-point cells which had to be evaluated in the process of intercomparisons. A quartz-sheathed SPRT has been selected and calibrated at HMI/LPM-FSB at the triple point of mercury, the melting point of gallium, and the water triple point. A second set of measurements was made at MIRS/UL/FE-LMK. After its return, the SPRT was again recalibrated at HMI/LPM-FSB. In the comparison, the W value of the SPRT has been used. Results of the bilateral intercomparison confirmed that the new gallium cell of the HMI/LPM-FSB has a value that is within uncertainty limits of both laboratories that participated in the exercise, while the mercury cell experienced problems. After further research, a small leakage in the mercury fixed-point cell has been found.
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.
Canet, Léonie; Delamotte, Bertrand; Wschebor, Nicolás
2016-06-01
We investigate the regime of fully developed homogeneous and isotropic turbulence of the Navier-Stokes (NS) equation in the presence of a stochastic forcing, using the nonperturbative (functional) renormalization group (NPRG). Within a simple approximation based on symmetries, we obtain the fixed-point solution of the NPRG flow equations that corresponds to fully developed turbulence both in d=2 and 3 dimensions. Deviations to the dimensional scalings (Kolmogorov in d=3 or Kraichnan-Batchelor in d=2) are found for the two-point functions. To further analyze these deviations, we derive exact flow equations in the large wave-number limit, and show that the fixed point does not entail the usual scale invariance, thereby identifying the mechanism for the emergence of intermittency within the NPRG framework. The purpose of this work is to provide a detailed basis for NPRG studies of NS turbulence; the determination of the ensuing intermittency exponents is left for future work.
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.
Bilateral ITS-90 comparison at WC-C peritectic fixed point between NIM and NPL
NASA Astrophysics Data System (ADS)
Dong, W.; Lowe, D. H.; Lu, X.; Machin, G.; Yuan, Z.; Wang, T.; Bloembergen, P.; Xiao, C.
2013-09-01
The WC-C peritectic fixed point, nominal melting and freezing temperature 2747 °C, shows extremely good metrological potential. Elsewhere, we published a prototype scale comparison of the ITS-90 between NPL, NIM and CEM, using high temperature eutectic fixed points (HTFPs) of Co-C (1324 °C), Pt-C (1738 °C), and Re-C (2474 °C). In this paper we present the further results of the bilateral comparison of the ITS-90 at an even higher temperature, 2747 °C, between NIM and NPL using WC-C peritectic fixed points. A NIM single zone high temperature furnace, model Chino IR-80, was modified to extend its temperature to 2800 °C. Then, an NPL researcher, on secondment to NIM, filled two WC-C cells in the modified furnace in a vertical position. The two WC-C cells were then realized in the same furnace, in an horizontal position. Their melting temperatures, defined by the inflection point of the melting curves, were measured by a linear pyrometer, model NIM-PSP. NIM's ITS-90 scale was assigned to the two cells, which were then transported to NPL. The realization of NPL's ITS-90 was then assigned to the two cells by using a model HT9500 Thermogauge furnace to realize the fixed points and a linear pyrometer, model LP3, to determine their temperature. The difference from the mean value of the NIM and NPL ITS-90 values for the WC-C points was derived. This allowed us to compare ITS-90 as realized by the two institutes and to determine the uncertainty in the scale comparison.
NASA Astrophysics Data System (ADS)
Machin, G.; Teixeira, R.; Lu, X.; Lowe, D.
2015-03-01
There is an on-going requirement to perform scale comparisons above the silver point with reduced uncertainties. Previous comparisons have been performed with high stability lamps or radiation thermometers, neither of which were able to achieve the required uncertainty. Ideally a set of driftless unknown temperature fixed points would be used to compare scales, but up to now such artifacts did not exist. This study develops blind high-temperature comparison artifacts based on doped versions of the high-temperature fixed point (HTFP) Ni-C (nominal temperature ). At INMETRO three HTFP blackbodies were constructed, one of pure Ni-C and two doped with different levels of Cu. To ascertain the effect of doping on the transition temperature, the cells were compared to the reference pure Ni-C cell. The doped cells were then transported to NPL and their temperatures measured. NPL was not informed of the INMETRO result ensuring that the measurements remained blind. The cells were then returned to INMETRO and re-measured to establish their stability. The temperatures measured at INMETRO and NPL were then compared and showed very good equivalence of the scale at the fixed-point temperatures. The results of the comparison of the NPL and INMETRO temperature scale, at nominally , are reported, along with evidence of the stability of the artifacts determined from repeat measurements. These promising results indicate that it may be possible to make HTFPs with altered temperatures which are stable enough to serve as comparison artifacts.
Comparisons between transect and fixed point in a oceanic turbulent flow: statistical analyses
NASA Astrophysics Data System (ADS)
Koziol, Lucie; Schmitt, Francois G.; Artigas, Felipe; Lizon, Fabrice
2016-04-01
Oceanological processes possess important fluctuations over large ranges of spatial and temporal scales. These fluctuations are related with the turbulence of the ocean. Usually, in turbulence, one considers fixed point Eulerian measurements, or Lagrangian measurements following an elements of fluid. On the other hand, in oceanography, measurements are often done from a boat operating over a transect, where the boat is moving in the medium at a fixed speed (relative to the flow). Here the aim of our study is to consider if such moving reference frame is modifying the statistics of the measurements. For this we compare two type of measurements at high frequency: fixed point measurements, and transect measurements, where the boat is moving at a fixed speed relative to the flow. 1 Hz fluorometer measurements are considered in both cases. Measurements have been done the same day, under similar conditions. Power spectra of time series are considered, as well as local mean and variance measurements along each transect. It is found that the spectral scaling slope of the measurement is not modified, but the variance is very different, being much larger for the moving frame. Such result needs theoretical understanding and has potential important consequence regarding the measurement that are done at high frequency on moving frames in oceanography.
The fixed point formulation for large sample PGNAA—Part 2: experimental demonstration
NASA Astrophysics Data System (ADS)
Akkurt, H.; Holloway, J. P.; Smith, L. E.
2004-04-01
We present composition estimation results using fixed point iteration compared to the true composition of sample for prompt gamma measurements. The analysis showed that the fixed point iteration algorithm converges very rapidly to true composition of the sample independent of the initial guess when there is no significant background contribution. Even in the presence of significant background contribution, the true composition of the sample was estimated with high precision but with slower convergence. Although approximate data for neutron source spectrum and relative efficiency of the detector was used for analysis, the results showed that the method is not very sensitive to the details of the model since it is based on ratios. Despite the approximate data used for computations, the composition estimation results are in excellent agreement with chemical analysis.
The fixed point formulation for large sample PGNAA—Part 1: theory
NASA Astrophysics Data System (ADS)
Holloway, J. P.; Akkurt, H.
2004-04-01
The determination of large sample composition via prompt gamma measurements is examined as a non-linear inverse problem. We show that this non-linear problem can be formulated as a fixed point problem that always has a physically meaningful solution, even in the presence of significant contributions to photopeak area from gammas emitted by the surroundings. The formulation involves only ratios of measured photopeak areas, and, separately, ratios of modeled photopeak areas. It therefore does not require the absolute comparison of measured or modeled quantities. The proof of the existence of meaningful solutions relies on very simple and natural hypotheses of positivity and continuity. The natural fixed point iteration is examined, and certain physical limits where its global convergence can be guaranteed are examined. Several computational examples are presented.
Alignment Solution for CT Image Reconstruction using Fixed Point and Virtual Rotation Axis
NASA Astrophysics Data System (ADS)
Jun, Kyungtaek; Yoon, Seokhwan
2017-01-01
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 better quality of reconstructions. 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. An advanced physical concept of Center of Attenuation (CA) was also introduced to figure out how this fixed point is applied to the reconstruction of image having errors we categorized in this article. Our technique showed a promising performance in restoring images having translation and vertical tilt errors.
Alignment Solution for CT Image Reconstruction using Fixed Point and Virtual Rotation Axis
Jun, Kyungtaek; Yoon, Seokhwan
2017-01-01
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 better quality of reconstructions. 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. An advanced physical concept of Center of Attenuation (CA) was also introduced to figure out how this fixed point is applied to the reconstruction of image having errors we categorized in this article. Our technique showed a promising performance in restoring images having translation and vertical tilt errors. PMID:28120881
NASA Astrophysics Data System (ADS)
Martín-Hernando, Yolanda; Rodríguez-Ramos, Luis F.; Garcia-Talavera, Marcos R.
2008-07-01
Most computers in the past have been equipped with floating point processing capabilities, allowing an easy and brute-force solution for the machine computation errors, not requiring any specific tailoring of the computation in nearly hundred percent of situations. However, the computation needed for the adaptive optics real-time control in 30-50 meter telescopes is big enough to cause trouble to conventional von-Neumann processors, even if Moore's Law is valid for the next years. Field Programmable Gate Array (FPGAs) have been proposed as a viable alternative to cope with such computation needs[1,2], but--at least today's chips--will require fixed-point arithmetic to be used instead. It is then important to evaluate up to what point the accuracy and stability of the control system will be affected by this limitation. This paper presents the simulation and laboratory results of the comparison between both arithmetics, specifically evaluated in an adaptive optics system. The real-time controller has been modeled as black box having as input the wavefront sensor camera digital output data, providing a digital output to the actuators of the deformable mirror, and with the task of internally computing all outputs from the inputs. MATLAB fixed-point library has been used to evaluate the effect of different precision lengths (5-10 fractional bits) in the computation of the Shack-Hartmann subaperture centroid, in comparison with the reference 64-bit floating-point arithmetic and with the noise floor of the real system, concluding that the effect of the limited precision can be overcome by adequately selecting the number of fractional bits used in the representation, and tailoring that number with the needs at every step of the algorithm.
Modified van der Pauw method based on formulas solvable by the Banach fixed point method
NASA Astrophysics Data System (ADS)
Cieśliński, Jan L.
2012-11-01
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).
Another limitation of DFC when stabilizing unstable fixed points of continuous chaotic systems
NASA Astrophysics Data System (ADS)
Chen, Mao-Yin; Han, Zheng-Zhi; Shang, Yun
2003-05-01
Using stability theory of delayed differential equation (DDE), we show that there exists another limitation of delayed feedback control (DFC) with arbitrary delayed time when stabilizing unstable fixed points (UFPs) of continuous chaotic systems. This limitation is called by zero real part limitation, that is, if Jacobian matrix at a UFP has a characteristic exponent with zero real part, the UFP cannot be stabilized by linear DFC with arbitrary delayed time.
NASA Astrophysics Data System (ADS)
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.
Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
NASA Astrophysics Data System (ADS)
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.
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.
Long-Term Monitoring of Thermocouple Stability with Miniature Fixed-Point Cells
NASA Astrophysics Data System (ADS)
Elliott, C. J.; Failleau, G.; Deuzé, T.; Sadli, M.; Pearce, J. V.; Machin, G.
2014-04-01
In the framework of the European Metrology Research Programme ENG08 "MetroFission" project, two National Measurement Institutes, LNE-Cnam (France) and NPL (UK), have cooperatively developed methods of in situ validation of thermocouple output for application in next-generation nuclear fission power plants. Miniature fixed-point cells for use at three temperatures were constructed in the first step of this project: at the freezing point of silver (), the freezing point of copper (), and the melting point of the iron-carbon eutectic (). This paper reports the results of a second step in the study, where the robustness of the self-validation method has been investigated. Typical industrial Type N thermocouples have been employed with each of the miniature fixed-point devices installed, and repeatedly thermally cycled through the melting and freezing transitions of the fixed-point ingots. The devices have been exposed to a total of up to 90 h in the molten state. Furthermore, the LNE-Cnam devices were also subjected to fast cool-down rates, on five occasions, where the rate is estimated to have been between and . The devices are shown to be repeatable, reliable, and robust over the course of these tests. The drift of the Type N thermocouple has been identified separately to the behavior of the device. A reliable method for improving thermocouple performance and process control is therefore demonstrated. Requirements for implementation and the advantages of each approach for monitoring and correcting thermocouple drift are discussed, and an uncertainty budget for self-validation is presented.
Fixed points of the SRG evolution and the on-shell limit of the nuclear force
NASA Astrophysics Data System (ADS)
Arriola, E. Ruiz; Szpigel, S.; Timóteo, V. S.
2016-08-01
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 λ → 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 λ → 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 celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A = 2 , 3 , 4 systems are investigated and related to the occurrence of a Tjon-line which emerges as the minimum of an avoided crossing between Eα = 4Et - 3Ed and Eα = 2Et. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S-waves.
Nonthermal fixed points in quantum field theory beyond the weak-coupling limit
NASA Astrophysics Data System (ADS)
Berges, Jürgen; Wallisch, Benjamin
2017-02-01
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 have relied 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 interaction strengths. 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 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 overoccupied and of strong-field initial conditions, we find that nonthermal fixed points are not restricted to parameter ranges suitable for classical-statistical simulations but extend also to couplings of order 1. While the infrared behavior is found to be insensitive to the differences in the initial conditions, we demonstrate that transport phenomena to higher momenta depend on the presence or absence of a symmetry-breaking field expectation value.
Design of high-performance fixed-point transforms using the common factor method
NASA Astrophysics Data System (ADS)
Hinds, Arianne T.
2010-08-01
Fixed-point implementations of transforms such as the Discrete Cosine Transform (DCT) remain as fundamental building blocks of state-of-the-art video coding technologies. Recently, the 16x16 DCT has received focus as a transform suitable for the high efficiency video coding project currently underway in the Joint Collaboration Team - Video Coding. By its definition, the 16x16 DCT is inherently more complex than transforms of traditional sizes such as 4x4 or 8x8 DCTs. However, scaled architectures such as the one employed in the design of the 8x8 DCTs specified in ISO/IEC 23002-2 can also be utilized to mitigate the complexity of fixed-point approximations of higher-order transforms such as the 16x16 DCT. This paper demonstrates the application of the Common Factor method to design two scaled implementations of the 16x16 DCT. One implementation can be characterized by its exceptionally low complexity, while the other can be characterized by its relatively high precision. We review the Common Factor method as a method to arrive at fixed-point implementations that are optimized in terms of complexity and precision for such high performance transforms.
NASA Astrophysics Data System (ADS)
Wähmer, M.; Anhalt, K.; Hollandt, J.; Klein, R.; Taubert, R. D.; Thornagel, R.; Ulm, G.; Gavrilov, V.; Grigoryeva, I.; Khlevnoy, B.; Sapritsky, V.
2017-10-01
Absolute spectral radiometry is currently the only established primary thermometric method for the temperature range above 1300 K. Up to now, the ongoing improvements of high-temperature fixed points and their formal implementation into an improved temperature scale with the mise en pratique for the definition of the kelvin, rely solely on single-wavelength absolute radiometry traceable to the cryogenic radiometer. Two alternative primary thermometric methods, yielding comparable or possibly even smaller uncertainties, have been proposed in the literature. They use ratios of irradiances to determine the thermodynamic temperature traceable to blackbody radiation and synchrotron radiation. At PTB, a project has been established in cooperation with VNIIOFI to use, for the first time, all three methods simultaneously for the determination of the phase transition temperatures of high-temperature fixed points. For this, a dedicated four-wavelengths ratio filter radiometer was developed. With all three thermometric methods performed independently and in parallel, we aim to compare the potential and practical limitations of all three methods, disclose possibly undetected systematic effects of each method and thereby confirm or improve the previous measurements traceable to the cryogenic radiometer. This will give further and independent confidence in the thermodynamic temperature determination of the high-temperature fixed point's phase transitions.
Small Multiple Fixed-Point Cell as Calibration Reference for a Dry Block Calibrator
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas
NASA Astrophysics Data System (ADS)
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.
Scaling in the vicinity of the four-state Potts fixed point
NASA Astrophysics Data System (ADS)
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.
Study on the Impurity Effect in the Realization of Silver Fixed Point
NASA Astrophysics Data System (ADS)
Tsai, S. F.
2016-03-01
The application of a thermal analysis model to estimate the temperature depression from the ideal fixed-point temperature is important, especially when the chemical analysis of the sample in a cell is insufficient or the cell might have been contaminated during fabrication. This study extends previous work, on thermal analysis with the tin point, to an investigation of the impurity dependence of the silver-point temperature. Close agreement was found between the temperature depression (-0.36 mK) inferred from the thermal analysis of the measured fixed-point plateau and the temperature depression (-0.32 mK) inferred using the sum of individual estimates (SIE) method with an impurity analysis based on glow discharge mass spectrometry. Additionally, the results of the thermal analysis manifest no significant dependence on the rate of solidification, and the scatter of observed gradients was within 0.36 mK among five plateaux with different temperature settings of the furnace. Although the results support the application of both the SIE method and thermal analysis for the silver point, further experiments with cell-to-cell comparisons linked to thermal analysis, a study of the thermometer-furnace systematic effects, the oxygen effect, and the locus of the freezing plateau should be investigated to reach a firm conclusion.
Robust Optimization of Fixed Points of Nonlinear Discrete Time Systems with Uncertain Parameters
NASA Astrophysics Data System (ADS)
Kastsian, Darya; Monnigmann, Martin
2010-01-01
This contribution extends the normal vector method for the optimization of parametrically uncertain dynamical systems to a general class of nonlinear discrete time systems. Essentially, normal vectors are used to state constraints on dynamical properties of fixed points in the optimization of discrete time dynamical systems. In a typical application of the method, a technical dynamical system is optimized with respect to an economic profit function, while the normal vector constraints are used to guarantee the stability of the optimal fixed point. We derive normal vector systems for flip, fold, and Neimark-Sacker bifurcation points, because these bifurcation points constitute the stability boundary of a large class of discrete time systems. In addition, we derive normal vector systems for a related type of critical point that can be used to ensure a user-specified disturbance rejection rate in the optimization of parametrically uncertain systems. We illustrate the method by applying it to the optimization of a discrete time supply chain model and a discretized fermentation process model.
Is that Really Hidden? The Presence of Complex Fixed-Points in Chaotic Flows with No Equilibria
NASA Astrophysics Data System (ADS)
Pham, Viet-Thanh; Jafari, Sajad; Volos, Christos; Wang, Xiong; Golpayegani, S. Mohammad Reza Hashemi
In this letter we investigate the role of complex fixed-points in finding hidden attractors in chaotic flows with no equilibria. If these attractors could be found by starting the trajectory in the neighborhood of complex fixed-points, maybe it would be better not to call them hidden.
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
NASA Astrophysics Data System (ADS)
Hinds, Arianne T.
2011-09-01
Spatial transformations whose kernels employ sinusoidal functions for the decorrelation of signals remain as fundamental components of image and video coding systems. Practical implementations are designed in fixed precision for which the most challenging task is to approximate these constants with values that are both efficient in terms of complexity and accurate with respect to their mathematical definitions. Scaled architectures, for example, as used in the implementations of the order-8 Discrete Cosine Transform and its corresponding inverse both specified in ISO/IEC 23002-2 (MPEG C Pt. 2), can be utilized to mitigate the complexity of these approximations. That is, the implementation of the transform can be designed such that it is completed in two stages: 1) the main transform matrix in which the sinusoidal constants are roughly approximated, and 2) a separate scaling stage to further refine the approximations. This paper describes a methodology termed the Common Factor Method, for finding fixed-point approximations of such irrational values suitable for use in scaled architectures. The order-16 Discrete Cosine Transform provides a framework in which to demonstrate the methodology, but the methodology itself can be employed to design fixed-point implementations of other linear transformations.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Chen, Peijun; Huang, Jianguo; Zhang, Xiaoqun
2013-02-01
Recently, the minimization of a sum of two convex functions has received considerable interest in a variational image restoration model. In this paper, we propose a general algorithmic framework for solving a separable convex minimization problem from the point of view of fixed point algorithms based on proximity operators (Moreau 1962 C. R. Acad. Sci., Paris I 255 2897-99). Motivated by proximal forward-backward splitting proposed in Combettes and Wajs (2005 Multiscale Model. Simul. 4 1168-200) and fixed point algorithms based on the proximity operator (FP2O) for image denoising (Micchelli et al 2011 Inverse Problems 27 45009-38), we design a primal-dual fixed point algorithm based on the proximity operator (PDFP2Oκ for κ ∈ [0, 1)) and obtain a scheme with a closed-form solution for each iteration. Using the firmly nonexpansive properties of the proximity operator and with the help of a special norm over a product space, we achieve the convergence of the proposed PDFP2Oκ algorithm. Moreover, under some stronger assumptions, we can prove the global linear convergence of the proposed algorithm. We also give the connection of the proposed algorithm with other existing first-order methods. Finally, we illustrate the efficiency of PDFP2Oκ through some numerical examples on image supper-resolution, computerized tomographic reconstruction and parallel magnetic resonance imaging. Generally speaking, our method PDFP2O (κ = 0) is comparable with other state-of-the-art methods in numerical performance, while it has some advantages on parameter selection in real applications.
Dry Block Calibrator with Improved Temperature Field and Integrated Fixed-Point Cells
NASA Astrophysics Data System (ADS)
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.
Uncertainty due to non-linearity in radiation thermometers calibrated by multiple fixed points
Yamaguchi, Y.; Yamada, Y.
2013-09-11
A new method to estimate the uncertainty due to non-linearity is described on the n= 3 scheme basis. The expression of uncertainty is mathematically derived applying the random walk method. The expression is simple and requires only the temperatures of the fixed points and a relative uncertainty value for each flux-doubling derived from the non-linearity measurement. We also present an example of the method, in which the uncertainty of temperature measurement by a radiation thermometer is calculated on the basis of non-linearity measurement.
Fixed-point methods for computing the equilibrium composition of complex biochemical mixtures.
Kuzmic, P
1998-01-01
The fixed-point algebraic method [Storer and Cornish-Bowden (1976) Biochem. J. 159, 1-5] for computing the concentrations at equilibrium of complex biochemical mixtures fails for many binding stoichiometries, especially those that include molecular self-association. A typical example is the monomer-dimer-tetramer equilibrium. This paper reports two main results. First, the above algorithm is analysed theoretically to predict for which binding stoichiometries it succeeds and for which it will fail. Secondly, an alternative algorithm is described for self-associating biochemical systems. Illustrative examples are based on the dimeric proteinase from HIV. PMID:9531499
Standard map in magnetized relativistic systems: Fixed points and regular acceleration
Sousa, M. C. de; Steffens, F. M.; Pakter, R.; Rizzato, F. B.
2010-08-15
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.
Thermodynamics of a field theory with an infrared fixed point from gauge/gravity duality
Alanen, J.; Kajantie, K.
2010-02-15
We use gauge/gravity duality to study the thermodynamics of a field theory with asymptotic freedom in the ultraviolet and a fixed point in the infrared. We find a high temperature quark-gluon phase and a low T conformal unparticle phase. The phase transition between the phases is of first order or continuous, depending on the ratio of the radii of asymptotic anti-de Sitter spaces at T=0 and T={infinity}. This is a prediction from a model of gauge/gravity duality, not yet verified on the field theory side.
Isotopic effects in the neon fixed point: uncertainty of the calibration data correction
NASA Astrophysics Data System (ADS)
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.
Development of a new radiometer for the thermodynamic measurement of high temperature fixed points
Dury, M. R.; Goodman, T. M.; Lowe, D. H.; Machin, G.; Woolliams, E. R.
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.
Woolliams, E R; Anhalt, K; Ballico, M; Bloembergen, P; Bourson, F; Briaudeau, S; Campos, J; Cox, M G; del Campo, D; Dong, W; Dury, M R; Gavrilov, V; Grigoryeva, I; Hernanz, M L; Jahan, F; Khlevnoy, B; Khromchenko, V; Lowe, D H; Lu, X; Machin, G; Mantilla, J M; Martin, M J; McEvoy, H C; Rougié, B; Sadli, M; Salim, S G R; Sasajima, N; Taubert, D R; Todd, A D W; Van den Bossche, R; van der Ham, E; Wang, T; Whittam, A; Wilthan, B; Woods, D J; Woodward, J T; Yamada, Y; Yamaguchi, Y; Yoon, H W; Yuan, Z
2016-03-28
The thermodynamic temperature of the point of inflection of the melting transition of Re-C, Pt-C and Co-C eutectics has been determined to be 2747.84 ± 0.35 K, 2011.43 ± 0.18 K and 1597.39 ± 0.13 K, respectively, and the thermodynamic temperature of the freezing transition of Cu has been determined to be 1357.80 ± 0.08 K, where the ± symbol represents 95% coverage. These results are the best consensus estimates obtained from measurements made using various spectroradiometric primary thermometry techniques by nine different national metrology institutes. The good agreement between the institutes suggests that spectroradiometric thermometry techniques are sufficiently mature (at least in those institutes) to allow the direct realization of thermodynamic temperature above 1234 K (rather than the use of a temperature scale) and that metal-carbon eutectics can be used as high-temperature fixed points for thermodynamic temperature dissemination. The results directly support the developing mise en pratique for the definition of the kelvin to include direct measurement of thermodynamic temperature.
Influence of Impurities and Filling Protocol on the Aluminum Fixed Point
NASA Astrophysics Data System (ADS)
Renaot, E.; Valin, M. H.; Elgourdou, M.
2008-06-01
To improve the uncertainty of the aluminum fixed point, a study was launched by LNE-INM/CNAM in the framework of the EUROMET Project 732 “Toward more accurate temperature fixed points” (Coordinating laboratory: LNE-INM/CNAM, 17 partner countries). A new open cell was filled with aluminum of 99.99995% purity. A French laboratory carried out elemental analysis of the sample using glow discharge-mass spectrometry (GD-MS). The values of the equilibrium distribution coefficient k and of the derivative {δ T_{{l}}/δ ci_{{l}}} of the temperature of the liquidus line with respect to the concentration of impurity i will be obtained through collaboration with a French physical and chemical laboratory. In the past, some aluminum cells were opened after several melts and freezes. The aluminum ingot was sticking to the graphite crucible, indicating that physicochemical reactions had likely occurred between Al and C. To avoid this reaction, an effort was made to draw benefit from the Al2O3 film that appears immediately on the surface of the aluminum ingot when it is exposed to oxygen. The open aluminum cell was tested in different furnaces and with different thermal insulator arrangements inside the fixed-point assembly. The observed drifts of the plateaux were always larger than the expected values. The cell was opened to inspect the aluminum ingot. The ingot was extracted easily, since no sticking to the crucible had occurred. The aluminum showed a very bright surface, but the presence of many “craters” throughout the thickness of the ingot was surprising. In some cases, the thermometer well was even apparent.
Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...
2016-05-20
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 enablingmore » 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. Finally, 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.« less
Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; Utke, Jean
2016-05-20
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. Finally, 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.
Optimization of the thermogauge furnace for realizing high temperature fixed points
Wang, T.; Dong, W.; Liu, F.
2013-09-11
The thermogauge furnace was commonly used in many NMIs as a blackbody source for calibration of the radiation thermometer. It can also be used for realizing the high temperature fixed point(HTFP). According to our experience, when realizing HTFP we need the furnace provide relative good temperature uniformity to avoid the possible damage to the HTFP. To improve temperature uniformity in the furnace, the furnace tube was machined near the tube ends with a help of a simulation analysis by 'ansys workbench'. Temperature distributions before and after optimization were measured and compared at 1300 °C, 1700°C, 2500 °C, which roughly correspond to Co-C(1324 °C), Pt-C(1738 °C) and Re-C(2474 °C), respectively. The results clearly indicate that through machining the tube the temperature uniformity of the Thermogage furnace can be remarkably improved. A Pt-C high temperature fixed point was realized in the modified Thermogauge furnace subsequently, the plateaus were compared with what obtained using old heater, and the results were presented in this paper.
Stability of cobalt-carbon high temperature fixed points doped with iron and platinum
NASA Astrophysics Data System (ADS)
Kňazovická, L.; Lowe, D.; Machin, G.; Davies, H.; Rani, A.
2015-04-01
High temperature fixed points (HTFPs) are stable and repeatable and make comparison of temperature scales possible at a level of uncertainty not previously possible. However, they potentially lack objectivity if the fixed-point temperature is known. Five HTFPs were constructed, one pure Co-C, two Co-C doped with Fe and two Co-C doped with Pt of differing concentrations. The candidate dopants were identified through thermochemical modelling as likely to give maximum temperature shift with minimum increase in melting range. The temperature differences of the doped systems from the pure system were determined and it was found that the addition of Fe depressed the melting temperature and the addition of Pt elevated the melting temperature, qualitatively in line with the thermochemical modelling. The higher concentration doped HTFPs were then aged for approximately 100 h with continuous melting-freezing cycles and the difference to the undoped Co-C HTFP remeasured. These differences were found to agree with those of the unaged results within the measurement uncertainties, confirming artefact stability. It is clear that the doping of HTFPs is a powerful way of constructing stable and reliable high temperature scale comparison artefacts of unknown temperature.
Calculation of the ``Rotating Wall'' Torque Near a Fixed Point Attractor.
NASA Astrophysics Data System (ADS)
O'Neil, T. M.
2005-10-01
A rotating field asymmetry (the so-called ``rotating wall'') is often used to exert a torque on a non-neutral plasma in a Penning trap, spinning the plasma up to high rotation frequency (and high density). In recent experiments, the plasma state was observed to converge to an attracting fixed point where the applied torque balanced ambient torques.ootnotetextJ.R. Danielson and C.M. Surko, Phys. Rev. Lett. 95, 035001 (2005); also see invited talk by Danielson at this conference. At the fixed point, the nearly uniform plasma rotation frequency differs only slightly from the frequency of the rotating field asymmetry. This paper explains the attractor, using simple dynamical equations for the uniform plasma rotation frequency and temperature.ootnotetextT.M. O'Neil and D.H.E. Dubin, Phys. Plasmas 5, 2163 (1998). Also, the paper calculates the torque due to the rotating field asymmetry near the attractor, that is, for small frequency difference. The calculated torque is consistent with the measured torque.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Wright, James R.
2006-12-01
I present the use of Sherman's Theorem, and a development approach, for optimal solutions to real-time estimation problems that are multidimensional, nonlinear, stochastic, and have random multidimensional forcing function modeling errors that drive the state. Satisfaction of Sherman's Theorem guarantees that the mean-squared state estimate error on each state estimate component is minimized. Sherman's Theorem is not new, but my application of Sherman's Theorem is new. To Malcolm Shuster, who taught me about torque replacement modeling with rate-gyro sensors, and argues fiercely in defense of Maximum Likelihood Estimation (MLE).
NASA Astrophysics Data System (ADS)
Lampitt, Richard; Cristini, Luisa
2014-05-01
The Fixed point Open Ocean Observatory network (FixO3) seeks to integrate the 23 European open ocean fixed point observatories and to improve access to these key installations for the broader community. These will provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Coordinated by the National Oceanography Centre, UK, FixO3 builds on the significant advances achieved through the previous Europe-funded FP7 programmes EuroSITES, ESONET and CARBOOCEAN. Started in September 2013 with a budget of 7 Million Euros over 4 years the project has 29 partners drawn from academia, research institutions and SME's. In addition 12 international experts from a wide range of disciplines comprise an Advisory Board. On behalf of the FixO3 Consortium, we present the programme that will be achieved through the activities of 12 Work Packages: 1. Coordination activities to integrate and harmonise the current procedures and processes. Strong links will be fostered with the wider community across academia, industry, policy and the general public through outreach, knowledge exchange and training. 2. Support actions to offer a) free access to observatory infrastructures to those who do not have such access, and b) free and open data services and products. 3. Joint research activities to innovate and enhance the current capability for multidisciplinary in situ ocean observation. Support actions include Transnational Access (TNA) to FixO3 infrastructure, meaning that European organizations can apply to free-of-charge access to the observatories for research and testing in two international calls during the project lifetime. The first call for TNA opens in summer 2014. More information can be found on FixO3 website (www.fixo3.eu/). Open ocean observation is currently a high priority for European marine and maritime activities. FixO3 will provide important data on environmental products and services to address the Marine Strategy
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
NASA Astrophysics Data System (ADS)
Lampitt, Richard; Cristini, Luisa; Alexiou, Sofia
2015-04-01
The Fixed point Open Ocean Observatory network (FixO3, http://www.fixo3.eu/ ) integrates 23 European open ocean fixed point observatories and improves access to these infrastructures for the broader community. These provide multidisciplinary observations in all parts of the oceans from the air-sea interface to the deep seafloor. Started in September 2013 with a budget of 7 Million Euros over 4 years, the project has 29 partners drawn from academia, research institutions and SME's coordinated by the National Oceanography Centre, UK. Here we present the programme's achievements in the 18 months and the activities of the 12 Work Packages which have the objectives to: • integrate and harmonise the current procedures and processes • offer free access to observatory infrastructures to those who do not have such access, and free and open data services and products • innovate and enhance the current capability for multidisciplinary in situ ocean observation Open ocean observation is a high priority for European marine and maritime activities. FixO3 provides important data and services to address the Marine Strategy Framework Directive and in support of the European Integrated Maritime Policy. FixO3 provides a strong integrated framework of open ocean facilities in the Atlantic from the Arctic to the Antarctic and throughout the Mediterranean, enabling an integrated, regional and multidisciplinary approach to understand natural and anthropogenic change in the ocean.
New Filling Technique and Performance Evaluations of the Cr3C2-C Peritectic Fixed Point
NASA Astrophysics Data System (ADS)
Sasajima, N.; Lowe, D.; Bai, C.; Yamada, Y.; Ara, C.
2011-12-01
The Cr3C2-C peritectic fixed point was investigated to test its capability to serve as a practical high-temperature fixed point. An improved filling technique where C/C sheet works as a wick and graphite paper as a hopper was applied successfully, and the long-term stability of the peritectic cell was evaluated by means of radiation thermometry. The repeatability of the melting point in one day was 7 mK with a melting range of approximately 100 mK. The cell was aged for 7 days, and the evaluated 56 melting temperatures during this period all fall within 90 mK, with a standard deviation of 19 mK. X-ray transmission photos showed that the ingot was filled uniformly in the crucible. After the evaluation of long-term stability, no clear degradation of the ingot shape and no leakage of molten metal were observed. From these results, it can be concluded that the Cr3C2-C peritectic cell has good stability and robustness, and the new filling technique was established. The impurity effect on the Cr3C2-C peritectic cell was also investigated by adding tungsten powder to another cell as the impurity component. After the observation of melting and freezing plateaux, the cell was cut in half to analyze the microstructure by means of electron probe microanalysis (EPMA) and laser ablation inductively coupled plasma mass spectrometer (LA-ICP-MS). The high concentration of impurity was observed in the area of the chromium-rich domain (eutectic mixture of Cr7C3 and Cr3C2), which suggests that impurities were rejected from the Cr3C2 peritectic phase during the peritectic freezing and were accumulated in the Cr7C3-Cr3C2 eutectic phase. This explains why the impurity effect is more severe for the Cr7C3-Cr3C2 eutectic point than for the Cr3C2-C peritectic point.
Fixed points and stability in the two-network frustrated Kuramoto model
NASA Astrophysics Data System (ADS)
Kalloniatis, Alexander C.; Zuparic, Mathew L.
2016-04-01
We examine a modification of the Kuramoto model for phase oscillators coupled on a network. Here, two populations of oscillators are considered, each with different network topologies, internal and cross-network couplings and frequencies. Additionally, frustration parameters for the interactions of the cross-network phases are introduced. This may be regarded as a model of competing populations: internal to any one network phase synchronisation is a target state, while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor. We conduct fixed point analyses for two regimes: one, where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other; the second where one part of a population remains fixed in phase in relation to the other population, but where instability may occur within the first population leading to 'fragmentation'. We compare analytic results to numerical solutions for the system at various critical thresholds.
NASA Astrophysics Data System (ADS)
Castro, P.; Machin, G.; Villamañan, M. A.; Lowe, D.
2011-08-01
High-temperature fixed points (HTFPs) based on eutectic and peritectic reactions of metals and carbon are likely to become, in the near term, reference standards at high temperatures. Typically for radiation thermometry applications, these HTFPs are generally formed of a graphite crucible, with a reentrant well, an included 120° cone, and a nominal aperture of 3 mm. It is important to quantify the temperature drop at the back wall of the cavity, and to understand the influence of the crucible configuration and furnace conditions on this drop. In order to study these influences, three different situations have been modeled by means of the finite volume method for numerical analysis. The first investigates the influence of the furnace temperature profile on the temperature drop by simulating four different furnace conditions. The other two study variations in the crucible configuration, namely, the thickness of the graphite back wall and the length of the blackbody tube.
Fixed Points of Wegner-Wilson Flows and Many-Body Localization
NASA Astrophysics Data System (ADS)
Pekker, David; Clark, Bryan K.; Oganesyan, Vadim; Refael, Gil
2017-08-01
Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner-Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a Gaussian white-noise-like distribution in the ergodic phase, a 1 /f law inside the MBL phase, and scale-free distributions in the transition regime.
Point and Fixed Plot Sampling Inventory Estimates at the Savannah River Site, South Carolina.
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.
NASA Technical Reports Server (NTRS)
Shimada, Seiichi; Bock, Yehuda
1992-01-01
Results are presented from temporally dense measurements of crustal deformation associated with the convergence of the Eurasian (EUR), Pacific, North American, and Philippine Sea (PHS) plates, carried out in April 1988 by a 10-station GPS fixed-point network established in central Japan. Using regional orbit relaxation methods, the analysis of the first 17-month data revealed significant horizontal deformation across the Suruga trough. Namely, it was found that a site in the northern tip of PHS plate moved nearly westward with a velocity of 28 +/-5 mm per year, and a site at the southeastern tip of EUR plate moved south-southwestward with a velocity of 18 +/-5 mm per year. A significant vertical uplift with a velocity of 20 mm/yr was detected at a site inland of the Tokai district located in the Akaishi uplift zone and at a site on the Hatsushima Island in Sagami Bay.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Hoyos Velasco, Fredy Edimer; García, Nicolás Toro; Garcés Gómez, Yeison Alberto
In this paper, the output voltage of a buck power converter is controlled by means of a quasi-sliding scheme. The Fixed Point Inducting Control (FPIC) technique is used for the control design, based on the Zero Average Dynamics (ZAD) strategy, including load estimation by means of the Least Mean Squares (LMS) method. The control scheme is tested in a Rapid Control Prototyping (RCP) system based on Digital Signal Processing (DSP) for dSPACE platform. The closed loop system shows adequate performance. The experimental and simulation results match. The main contribution of this paper is to introduce the load estimator by means of LMS, to make ZAD and FPIC control feasible in load variation conditions. In addition, comparison results for controlled buck converter with SMC, PID and ZAD-FPIC control techniques are shown.
Probability distribution of the entanglement across a cut at an infinite-randomness fixed point
NASA Astrophysics Data System (ADS)
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.
Progress report for the CCT-WG5 high temperature fixed point research plan
Machin, G.; Woolliams, E. R.; Anhalt, K.; Bloembergen, P.; Sadli, M.; Yamada, Y.
2013-09-11
An overview of the progress in High Temperature Fixed Point (HTFP) research conducted under the auspices of the CCT-WG5 research plan is reported. In brief highlights are: Provisional long term stability of HTFPs has been demonstrated. Optimum construction methods for HTFPs have been established and high quality HTFPs of Co-C, Pt-C and Re-C have been constructed for thermodynamic temperature assignment. The major sources of uncertainty in the assignment of thermodynamic temperature have been identified and quantified. The status of absolute radiometric temperature measurement has been quantified through the circulation of a set of HTFPs. The measurement campaign to assign low uncertainty thermodynamic temperatures to a selected set of HTFPs will begin in mid-2012. It is envisaged that this will be complete by 2015 leading to HTFPs becoming routine reference standards for radiometry and high temperature metrology.
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.
Fixed-point analysis and realization of a blind beamforming algorithm
NASA Astrophysics Data System (ADS)
Xu, Fan; Fu, Dengwei; Willson, Alan N.
1999-11-01
We present the fixed-point analysis and realization of a blind beamforming algorithm. This maximum-power beamforming algorithm consists of the computation of a correlation matrix and its dominant eigenvector, and we propose that the later be accomplished by the power method. After analyzing the numerical stability of the power method, we derive a division-free form of the algorithm. Based on a block-Toeplitz assumption, we design an FIR filter based system to realize both the correlation computation and the power method. Our ring processor, which is optimized to implement digital filters, is used as the core of the architecture. A special technique for dynamically switching filter inputs is shown to double the system throughput. Finally we discuss the issue of hardware/software hybrid realization.
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.
NASA Astrophysics Data System (ADS)
Mishima, K.; Yamashita, K.
2009-01-01
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.
NASA Astrophysics Data System (ADS)
López-Gómez, Julián; Molina-Meyer, Marcela
In this work a general class of nonlinear abstract equations satisfying a generalized strong maximum principle is considered in order to study the behavior of the bounded components of positive solutions bifurcating from the curve of trivial states (λ,u)=(λ,0) at a nonlinear eigenvalue λ=λ0 with geometric multiplicity one. Since the unilateral theorems of Rabinowitz (J. Funct. Anal. 7 (1971) 487, Theorems 1.27 and 1.40) are not true as originally stated (cf. the very recent counterexample of Dancer, Bull. London Math. Soc. 34 (2002) 533), in order to get our main results the unilateral theorem of López-Gómez (Spectral Theory and Nonlinear Functional Analysis, Research Notes in Mathematics, vol. 426, CRC Press, Boca Raton, FL, 2001, Theorem 6.4.3) is required. Our analysis fills some serious gaps existing is some published papers that were provoked by a direct use of Rabinowitz's unilateral theory. Actually, the abstract theory developed in this paper cannot be covered with the pioneering results of Rabinowitz (1971), since in Rabinowitz's context any component of positive solutions must be unbounded, by a celebrated result attributable to Dancer (Arch. Rational Mech. Anal. 52 (1973) 181).
New Approach in Filling of Fixed-Point Cells: Case Study of the Melting Point of Gallium
NASA Astrophysics Data System (ADS)
Bojkovski, J.; Hiti, M.; Batagelj, V.; Drnovšek, J.
2008-02-01
The typical way of constructing fixed-point cells is very well described in the literature. The crucible is loaded with shot, or any other shape of pure metal, inside an argon-filled glove box. Then, the crucible is carefully slid into a fused-silica tube that is closed at the top with an appropriate cap. After that, the cell is removed from the argon glove box and melted inside a furnace while under vacuum or filled with an inert gas like argon. Since the metal comes as shot, or in some other shape such as rods of various sizes, and takes more volume than the melted material, it is necessary to repeat the procedure until a sufficient amount of material is introduced into the crucible. With such a procedure, there is the possibility of introducing additional impurities into the pure metal with each cycle of melting the material and putting it back into the glove box to fill the cell. Our new approach includes the use of a special, so-called dry-box system, which is well known in chemistry. The atmosphere inside the dry box contains less than 20 ppm of water and less than 3 ppm of oxygen. Also, the size of the dry box allows it to contain a furnace for melting materials, not only for gallium but for higher-temperature materials as well. With such an approach, the cell and all its parts (pure metal, graphite, fused-silica tube, and cap) are constantly inside the controlled atmosphere, even while melting the material and filling the crucible. With such a method, the possibility of contaminating the cell during the filling process is minimized.
Bilateral comparison of tin fixed point cells between INMETRO and NPL
NASA Astrophysics Data System (ADS)
Silva, R. da; Veltcheva, R. I.; Gray, J.; Pearce, J. V.; Machin, G.; Teixeira, R. N.
2013-09-01
In April 2011, a bilateral comparison of tin fixed point cells (231.928 °C) took place at the facilities of the Temperature group at the National Physical Laboratory (NPL). The comparison was with a standard from the Thermal Metrology Division of the National Institute of Metrology, Quality and Technology (INMETRO). It involved two cells: the test cell was an open one constructed in late 2010 at the INMETRO Thermometry Laboratory as part of an MSc research project; the reference cell was a sealed one, constructed in 2000 at NPL, traceable to the UK national standard tin point. The materials employed in the construction of the cells were from different suppliers. The cell design, dimensions and construction procedures were also different. Three standard platinum resistance thermometers (SPRTs), each different models from different manufacturers, were used to undertake the comparison, one from INMETRO and two from NPL. The comparison was performed in quadruplicate, each combination using a different freezing plateau. The differing self-heating behaviour of the different SPRTs was taken into account. The methodology employed in this comparison is detailed in the present paper.
Δ I =1 /2 rule for kaon decays derived from QCD infrared fixed point
NASA Astrophysics Data System (ADS)
Crewther, R. J.; Tunstall, Lewis C.
2015-02-01
This article gives details of our proposal to replace ordinary chiral S U (3 )L×S U (3 )R perturbation theory χ PT3 by three-flavor chiral-scale perturbation theory χ PTσ . In χ PTσ , amplitudes are expanded at low energies and small u ,d ,s quark masses about an infrared fixed point αIR of three-flavor QCD. At αIR , the quark condensate ⟨q ¯ q ⟩vac≠0 induces nine Nambu-Goldstone bosons: π ,K ,η , and a 0++ QCD dilaton σ . Physically, σ appears as the f0(500 ) resonance, a pole at a complex mass with real part ≲ mK . The Δ I =1 /2 rule for nonleptonic K decays is then a consequence of χ PTσ , with a KSσ coupling fixed by data for γ γ →π π and KS→γ γ . We estimate RIR≈5 for the nonperturbative Drell-Yan ratio R =σ (e+e-→hadrons)/σ (e+e-→μ+μ-) at αIR and show that, in the many-color limit, σ /f0 becomes a narrow q q ¯ state with planar-gluon corrections. Rules for the order of terms in χ PTσ loop expansions are derived in Appendix A and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for γ γ channels, partial conservation of the dilatation current is not equivalent to σ -pole dominance.
NASA Astrophysics Data System (ADS)
Teratani, Yoshimichi; Sakano, Rui; Fujiwara, Ryo; Hata, Tokuro; Arakawa, Tomonori; Ferrier, Meydi; Kobayashi, Kensuke; Oguri, Akira
2016-09-01
Carbon nanotube quantum dot has four-fold degenerate one-particle levels, which bring a variety to the Kondo effects taking place in a wide tunable-parameter space. We theoretically study an emergent SU(2) symmetry that is suggested by recent magneto-transport measurements, carried out near two electrons filling. It does not couple with the magnetic field, and emerges in the case where the spin and orbital Zeeman splittings cancel each other out in two of the one-particle levels among four. This situation seems to be realized in the recent experiment. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs as magnetic field increases at two impurity-electrons filling. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. Furthermore, we consider how the singlet ground state evolves during such a crossover. Specifically, we reexamine the SU(N) Kondo singlet for M impurity-electrons filling in the limit of strong exchange interactions. We find that the nondegenerate Fermi-liquid fixed point of Nozières and Blandin can be described as abosonic Perron-Frobenius vector for M composite pairs, each of which consists of one impurity-electron and one conduction-hole. This interpretation in terms of the Perron-Frobenius theorem can also be extended to the Fermi-liquid fixed-point without the SU(N) symmetry.
Evaluation of a new furcation stent as a fixed reference point for class II furcation measurements.
Laxman, Vandana K; Khatri, Manish; Devaraj, C G; Reddy, Kranti; Reddy, Ramesh
2009-03-01
To date probing of the furcation using sounding has been one of the reliable methods to assess horizontal component of furcation in multirooted teeth. A more precise and reliable measurement of this horizontal component of furcation involves using a fixed reference point providing stability and reproducibility of measurements. A custom stent is used to provide a fixed reference point and can be used pre- and post-surgically without re-entry. Therefore, the purposes of this study were to (1) assess the reliability of furcation measurements by direct probing (without stent) and with the use of a newly designed furcation stent and (2) to assess the furcation measurements in relation to gingival margin position pre- and post-operatively. Forty-three chronic periodontitis patients with buccal grade II furcation involvement in maxillary or mandibular molars were included. The furcation involvement was measured by direct probing using a UNC-15 calibrated probe with and without using a custom stent. The furcation involvement and gingival margin position were measured pre- and post-surgically. There was a significant reduction in plaque (PI) and gingival inflammation (GI) during the study period. The reduction in plaque index and gingival index was observed from 1.75 +/- 0.35 to 0.92 +/- 0.30, 1.88 +/- 0.35 to 0.98 +/- 0.29, respectively. Complete agreement was found between the first and the second measurement for about 74% of sites without the custom stent, whereas 86% of the sites measured using the stent had complete agreement. The differences never exceeded 1 mm for any of the sites. There was significant (t = 2.49; p<0.05) difference observed at complete agreement level ('0' difference). It may be concluded the clinical attachment level-H of the furcation involvement using a PCP UNC-15 probe and a custom designed stent provides reproducible information about the furcation depth in multirooted teeth. Use of a simple modified furcation stent has shown greater
Assessment of tungsten/rhenium thermocouples with metal-carbon eutectic fixed points up to 1500°C
Gotoh, M.
2013-09-11
Four Type A thermocouples and two Type C thermocouples were calibrated at the Au fixed point and Co-C and Pd-C eutectic fixed points. The thermocouples were exposed to 1330 °C for a total of 100 hours. The maximum drift due to the exposure was found to be 4.8 °C. The fixed-point calibration EMF of these thermocouples deviated by less than 0.86% from the temperature specified by the standards ASTM E230-2003 for Type C and GOSTR 8.585-2001 for Type A. The length of one of Type A thermocouples A52 is longer than the others by 150mm. Making use of this provision it was possible to place annealed part of A52 to the temperature gradient part of calibration arrangement every time. Therefore observed aging effect was as low as 0.5 °C compared to the other thermocouples.
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-11
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Hao, X.; Yuan, Z.; Wang, J.; Lu, X.
2013-09-01
In this paper, we describe an InGaAs detector based radiation thermometer (IRT) and new design of fixed-point blackbodies, including Sn, Zn, Al and Cu, for the establishment of a temperature scale from 200 °C to 1085 °C at the National Institute of Metrology of China. The construction and calibration of the IRT with the four fixed-point blackbodies are described. Characteristics of the IRT, such as the size-of-source effect, the amplifier performance and its stability are determined. The design of the four fixed-points, with 10 mm diameter of aperture and 0.9999 emissivity, is described. The uncertainty of the scale realization is elaborated.
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
DElia, M.; Farchioni, F.; Papa, A.
1997-02-01
We study the renormalization group evolution up to the fixed point of the lattice topological susceptibility in the 2D O(3) nonlinear {sigma} model. We start with a discretization of the continuum topological charge by a local charge density polynomial in the lattice fields. Among the different choices we propose also a Symanzik-improved lattice topological charge. We check step by step in the renormalization group iteration the progressive dumping of quantum fluctuations, which are responsible for the additive and multiplicative renormalizations of the lattice topological susceptibility with respect to the continuum definition. We find that already after three iterations these renormalizations are negligible and an excellent approximation of the fixed point is achieved. We also check by an explicit calculation that the assumption of slowly varying fields in iterating the renormalization group does not lead to a good approximation of the fixed point charge operator. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
Supersymmetric renormalisation group fixed points and third generation fermion mass predictions
Froggatt, C.D.; Moorhouse, R.G.; Knowles, I.G.
1992-09-01
We present a supersymmetric renormalization group fixed point determination of the third generation fermion masses, in which the large mass ratio between the top and bottom quarks is attributed to a hierarchy in the vacuum expectation values of the two Higgs doublets. Above a supersymmetry breaking scale, M{sub s}, we use the minimal supersymmetric standard model with a transition at M{sub s} to the standard model with only one Higgs- doublet effective. The mass predictions result from renormalization group evolution of large Yukawa couplings at M{sub x} {approximately} 1016 GeV. Averaging over a wide range of these couplings, not subject to any symmetry requirements, gives m{sub t} = 184.3{plus_minus}6.8 GeV, m{sub b} = 4.07{plus_minus}0.33 GeV, m{sub {tau}} = 1.78{plus_minus}0.33 GeV and a light Higgs mass m{sub h}o = 121.8{plus_minus}4.3 GeV for M{sub s} = 1 TeV and {alpha}{sub s} (M{sub z}) = 0.125.
Realization of the WC-C peritectic fixed point at NIM and NMIJ
Wang, T.; Bai, C.; Yuan, Z.; Dong, W.; Lu, X.; Sasajima, N.; Yamada, Y.; Ara, C.
2013-09-11
Three WC-C peritectic fixed point cells, constructed from different sources of tungsten with different nominal purities, were measured at NIM and NMIJ. The three cells were constructed at NMIJ by NIM and NMIJ staffs, and T{sub 90} values of the three cells were measured at NMIJ during the period 31 Aug. to 25 Dec. 2009. Thereafter, the three cells were then transported to NIM, and T{sub 90} values of these cells were measured from 7 Dec. 2011 to 9 Jan. 2012. The results showed that T{sub 90} values of the three cells measured at the two institutes agreed within 0.4 °C with the combined scale comparison uncertainty of 1.7 °C (k= 2). The main component of the uncertainty is not the uncertainty due to impurities of the cells but the scale uncertainty and the stability of the measurement system. From these results it can be concluded that the WC-C cell is stable enough to provide new means of international high-temperature scale comparison above 3000 K.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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 to calibrate type B thermocouples (Pt30 %Rh/Pt6 %Rh). A critical point by using miniature fixed points with small amounts of fixed-point material is the analysis of the melting curves, which are characterized by significant slopes during the melting process compared to flat melting plateaus obtainable using conventional fixed-point cells. The method of the extrapolated starting point temperature using straight line approximation of the melting plateau was applied to analyze the melting curves. This method allowed an unambiguous determination of an electromotive force (emf) assignable as melting temperature. The strict consideration of two constraints resulted in a unique, repeatable and objective method to determine the emf at the melting temperature within an uncertainty of about 0.1 μ V. The lifetime and long-term stability of the miniature fixed points was investigated by performing more than 100 melt/freeze cycles for each crucible of the different ceramic materials. No failure of the crucibles occurred indicating an excellent mechanical stability of the investigated miniature cells. The consequent limitation of heating rates to values below {± }3.5 K min^{-1} above 1100° C and the carefully and completely filled crucibles (the liquid palladium occupies the whole volume of the crucible) are the reasons for successfully preventing the crucibles from breaking. The thermal stability of the melting temperature of palladium was excellent when using the crucibles made of Al2O3(86 %)+ZrO2(14 %) and ZrO2. Emf drifts over the total duration of the long-term investigation were below a temperature equivalent of about 0.1 K-0.2 K.
NASA Technical Reports Server (NTRS)
Alefeld, Goetz; Koshelev, Misha; Mayer, Guenter
1997-01-01
At first glance. it may seem that reconstructing the past is, in general, easier than predicting the future, because the past has already occurred and it has already left its traces, while the future is still yet to come, and so no traces of the future are available. However, in many real life situations, including problems from geophysics and celestial mechanics, reconstructing the past is much more computationally difficult than predicting the future. In this paper, we give an explanation of this difficulty. This explanation is given both on a formal level (as a theorem) and on the informal level (as a more intuitive explanation).
NASA Astrophysics Data System (ADS)
Ragay-Enot, Monalisa; Lee, Young Hee; Kim, Yong-Gyoo
2017-07-01
A mini multi-fixed-point cell (length 118 mm, diameter 33 mm) containing three materials (In-Zn eutectic (mass fraction 3.8% Zn), Sn and Pb) in a single crucible was designed and fabricated for the easy and economical fixed-point calibration of industrial platinum resistance thermometers (IPRTs) for use in industrial temperature measurements. The melting and freezing behaviors of the metals were investigated and the phase transition temperatures were determined using a commercial dry-block calibrator. Results showed that the melting plateaus are generally easy to realize and are reproducible, flatter and of longer duration. On the other hand, the freezing process is generally difficult, especially for Sn, due to the high supercooling required to initiate freezing. The observed melting temperatures at optimum set conditions were 143.11 °C (In-Zn), 231.70 °C (Sn) and 327.15 °C (Pb) with expanded uncertainties (k = 2) of 0.12 °C, 0.10 °C and 0.13 °C, respectively. This multi-fixed-point cell can be treated as a sole reference temperature-generating system. Based on the results, the realization of melting points of the mini multi-fixed-point cell can be recommended for the direct calibration of IPRTs in industrial applications without the need for a reference thermometer.
NASA Astrophysics Data System (ADS)
Fahr, M.; Cundy, D. S.
2015-08-01
Impurities are still among the primary concerns regarding the realization of many fixed points of the International Temperature Scale (ITS-90). Several methods have been suggested to correct for these effects. The most promising strategy, with regard to the achievable uncertainty level, is the `sum of the individual estimates' (SIE) method. It involves a chemical analysis of the material and a calculation of each of the detected chemical species' effect on the phase-transition temperature of the fixed-point substance. This correction can be accurate only if all the detected impurities are completely dissolved. Given the recent evidence for insoluble impurities in metal fixed points, this strategy needs to be modified; otherwise, it may lead to an inaccurate estimation of the impurity-related effect on the fixed-point temperature. In this article, a correction method is set out that reflects the crucial distinction between soluble, insoluble, and partially soluble impurities. This `sum of the individual estimates for the dissolved species' (SIEDS) method starts from a chemical analysis but takes into account only the dissolved particles. For this purpose, different types of substances are considered as possible dissolved impurities and are discussed from a chemical point of view. For those impurities where data are insufficient, only an uncertainty estimation is possible. For this purpose, the `overall maximum estimate of the dissolved species' (OMEDS) method is derived from the SIEDS method as the new counterpart to the well-known `overall maximum estimate' (OME) method.
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
Analysis of gene network robustness based on saturated fixed point attractors.
Li, Genyuan; Rabitz, Herschel
2014-03-20
The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or -1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network is
Analysis of gene network robustness based on saturated fixed point attractors
2014-01-01
The analysis of gene network robustness to noise and mutation is important for fundamental and practical reasons. Robustness refers to the stability of the equilibrium expression state of a gene network to variations of the initial expression state and network topology. Numerical simulation of these variations is commonly used for the assessment of robustness. Since there exists a great number of possible gene network topologies and initial states, even millions of simulations may be still too small to give reliable results. When the initial and equilibrium expression states are restricted to being saturated (i.e., their elements can only take values 1 or −1 corresponding to maximum activation and maximum repression of genes), an analytical gene network robustness assessment is possible. We present this analytical treatment based on determination of the saturated fixed point attractors for sigmoidal function models. The analysis can determine (a) for a given network, which and how many saturated equilibrium states exist and which and how many saturated initial states converge to each of these saturated equilibrium states and (b) for a given saturated equilibrium state or a given pair of saturated equilibrium and initial states, which and how many gene networks, referred to as viable, share this saturated equilibrium state or the pair of saturated equilibrium and initial states. We also show that the viable networks sharing a given saturated equilibrium state must follow certain patterns. These capabilities of the analytical treatment make it possible to properly define and accurately determine robustness to noise and mutation for gene networks. Previous network research conclusions drawn from performing millions of simulations follow directly from the results of our analytical treatment. Furthermore, the analytical results provide criteria for the identification of model validity and suggest modified models of gene network dynamics. The yeast cell-cycle network
NASA Astrophysics Data System (ADS)
Castro, P.; Machin, G.; Bloembergen, P.; Lowe, D.; Whittam, A.
2014-07-01
This study forms part of the European Metrology Research Programme project implementing the New Kelvin to assign thermodynamic temperatures to a selected set of high-temperature fixed points (HTFPs), Cu, Co-C, Pt-C, and Re-C. A realistic thermal model of these HTFPs, developed in finite volume software ANSYS FLUENT, was constructed to quantify the uncertainty associated with the temperature drop across the back wall of the cell. In addition, the widely applied software package, STEEP3 was used to investigate the influence of cell emissivity. The temperature drop, , relates to the temperature difference due to the net loss of heat from the aperture of the cavity between the back wall of the cavity, viewed by the thermometer, defining the radiance temperature, and the solid-liquid interface of the alloy, defining the transition temperature of the HTFP. The actual value of can be used either as a correction (with associated uncertainty) to thermodynamic temperature evaluations of HTFPs, or as an uncertainty contribution to the overall estimated uncertainty. In addition, the effect of a range of furnace temperature profiles on the temperature drop was calculated and found to be negligible for Cu, Co-C, and Pt-C and small only for Re-C. The effective isothermal emissivity is calculated over the wavelength range from 450 nm to 850 nm for different assumed values of surface emissivity. Even when furnace temperature profiles are taken into account, the estimated emissivities change only slightly from the effective isothermal emissivity of the bare cell. These emissivity calculations are used to estimate the uncertainty in the temperature assignment due to the uncertainty in the emissivity of the blackbody.
NASA Astrophysics Data System (ADS)
Mehta, Dhagash; Kastner, Michael
2011-06-01
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.
NASA Astrophysics Data System (ADS)
Phaneendra, T.; Swatmaram
2012-10-01
We obtain a common fixed point for two pairs of self-maps on a complete metric space, one of which is reciprocally continuous and compatible, while the other weakly compatible, where all the four maps satisfy a generalized inequality. Our result is a significant generalization of that of Singh and Mishra.
Weak convergence theorems for a countable family of Lipschitzian mappings
NASA Astrophysics Data System (ADS)
Nilsrakoo, Weerayuth; Saejung, Satit
2009-08-01
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9 (2008) 37-43], Tada-Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359-370], and Plubtieng-Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions.
Mehta, Dhagash; Kastner, Michael
2011-06-15
Research Highlights: > Exact results for all stationary points of some high-dimensional function are given. > They are interpreted as Gribov copies of a lattice Landau gauge fixing functional. > The Gribov ambiguity and the Neuberger problem in compact U(1) are illustrated. > Stationary points are used to discuss a criterion on the absence of phase transitions. - Abstract: We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics. An analytic solution of all stationary points is derived for lattices with an odd number of lattice sites and periodic boundary conditions. In the context of lattice gauge theory, these stationary points and their indices are used to compute the gauge fixing partition function, making reference in particular to the Neuberger problem. Interpreted as stationary points of the one-dimensional XY Hamiltonian, the solutions and their Hessian determinants allow us to evaluate a criterion which makes predictions on the existence of phase transitions and the corresponding critical energies in the thermodynamic limit.
NASA Astrophysics Data System (ADS)
Mishima, Kenji; Yamashita, Koichi
2009-03-01
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. Our theory can not only achieve high transition probabilities but also determine exact temporal duration of the laser pulses. As a demonstration, our theory is applied to entanglement generation in rotational modes of NaCl-NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Using the tailored laser pulses, we discuss the fidelity of entanglement distillation and quantum teleportation. Our method will significantly be useful for the quantum control of non-local interaction such as entangling interaction, and other time-sensitive general quantum dynamics, chemical reactions.
2012-01-01
A lumped model of neural activity in neocortex is studied to identify regions of multi-stability of both steady states and periodic solutions. Presence of both steady states and periodic solutions is considered to correspond with epileptogenesis. The model, which consists of two delay differential equations with two fixed time lags is mainly studied for its dependency on varying connection strength between populations. Equilibria are identified, and using linear stability analysis, all transitions are determined under which both trivial and non-trivial fixed points lose stability. Periodic solutions arising at some of these bifurcations are numerically studied with a two-parameter bifurcation analysis. PMID:22655859
Formalin Fixed Paraffin Embedded Tissue as a Starting Point for PrPSc Detection by ELISA
USDA-ARS?s Scientific Manuscript database
Introduction: Formalin fixed paraffin embedded tissue are regularly employed in TSE diagnosis by IHC, the standard by which all other diagnostic protocols are currently judged. While IHC affords advantages over diagnostic approaches that typically utilize fresh or frozen tissue, such as Western blot...
Competition Between Transients in the Rate of Approach to a Fixed Point
NASA Astrophysics Data System (ADS)
Day, Judy; Rubin, Jonathan E.; Chow, Carson C.
2009-01-01
The goal of this paper is to provide and apply tools for analyzing a specific aspect of transient dynamics not covered by previous theory. The question we address is whether one component of a perturbed solution to a system of differential equations can overtake the corresponding component of a reference solution as both converge to a stable node at the origin, given that the perturbed solution was initially farther away and that both solutions are nonnegative for all time. We call this phenomenon tolerance, for its relation to a biological effect. We show using geometric arguments that tolerance will exist in generic linear systems with a complete set of eigenvectors and in excitable nonlinear systems. We also define a notion of inhibition that may constrain the regions in phase space where the possibility of tolerance arises in general systems. However, these general existence theorems do not not yield an assessment of tolerance for specific initial conditions. To address that issue, we develop some analytical tools for determining if particular perturbed and reference solution initial conditions will exhibit tolerance.
Influence of the Opening of a Blackbody Cavity Measured at the Ag and Cu ITS-90 Fixed Points
NASA Astrophysics Data System (ADS)
Bourson, F.; Sadli, M.; Rougié, B.; Briaudeau, S.; Kozlova, O.
2014-04-01
The International Temperature Scale of 1990 blackbody fixed points are commonly composed of a graphite crucible containing a pure metal enclosing a radiating blackbody cavity. The shape of the cavity is determined to behave as much as possible as a perfect blackbody; however, the opening from which the radiance is measured induces radiative losses. The measured temperature is therefore underestimated by a few tens of millikelvins at C, compared to that of a perfect blackbody. The difference is due, on the one hand, to the drop of emissivity caused by the opening, and on the other hand, to the temperature drop between the solid/liquid interface and the inner wall of the cavity, observed by the radiation thermometer. The temperature drop is generally estimated by modeling the emissivity and the temperature difference across the cavity wall. This approach is relevant as long as the temperature distribution along the cavity and the graphite properties are known, but in many cases, the lack of data does not allow precise determination of the corrections. The corrections for the temperature drop and emissivity drop, which both depend on the cavity opening, can be determined experimentally with a low uncertainty by measuring the temperature of a fixed point for different cavity openings. To be significant, the measurement requires a source stable within a few millikelvins. In this study, this constraint has been solved by changing the cavity opening during the phase transition of the fixed point, with a rotating wheel supporting apertures of different dimensions. Measurements have been performed at the Ag and Cu fixed points during the freezing plateaus. Experimental results are presented and compared to those obtained by modeling.
Laurie, M.; Vlahovic, L.; Rondinella, V.V.; Sadli, M.; Failleau, G.; Fuetterer, M.; Lapetite, J.M.; Fourrez, S.
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)
NASA Astrophysics Data System (ADS)
Sadli, Mohamed; Bourson, Frédéric; Diril, Ahmet; Journeau, Christophe; Lowe, Dave; Parga, Clemente
2014-08-01
Among the activities of the European Metrology Research Programme (EMRP) project HiTeMS one work package is devoted to the development and testing of industrial solutions for long-standing temperature measurement problems at the highest temperatures. LNE-Cnam, NPL, TUBITAK-UME have worked on the design of high temperature fixed points (HTFP) suitable for in-situ temperature monitoring to be implemented in the facilities of CEA (Commissariat à l'énergie atomique et aux énergies alternatives). Several high temperature fixed point cells were constructed in these three national metrology institutes (NMIs) using a rugged version of cells based on the hybrid design of the laboratory HTFP developed and continuously improved at LNE-Cnam during the last years. The fixed points of interest were Co-C, Ru-C and Re-C corresponding to melting temperatures of 1324 °C, 1953 °C and 2474 °C respectively. The cells were characterised at the NMIs after their construction. Having proved robust enough, they were transported to CEA and tested in an induction furnace and cycled from room temperature to temperatures much above the melting temperatures (> +400 °C) with extremely high heating and cooling rates (up to 10 000 K/h). All the cells withstood the tests and the melting plateaus could be observed in all cases.
Starting points in plant-bacteria nitrogen-fixing symbioses: intercellular invasion of the roots.
Ibáñez, Fernando; Wall, Luis; Fabra, Adriana
2017-04-01
Agricultural practices contribute to climate change by releasing greenhouse gases such as nitrous oxide that are mainly derived from nitrogen fertilizers. Therefore, understanding biological nitrogen fixation in farming systems is beneficial to agriculture and environmental preservation. In this context, a better grasp of nitrogen-fixing systems and nitrogen-fixing bacteria-plant associations will contribute to the optimization of these biological processes. Legumes and actinorhizal plants can engage in a symbiotic interaction with nitrogen-fixing rhizobia or actinomycetes, resulting in the formation of specialized root nodules. The legume-rhizobia interaction is mediated by a complex molecular signal exchange, where recognition of different bacterial determinants activates the nodulation program in the plant. To invade plants roots, bacteria follow different routes, which are determined by the host plant. Entrance via root hairs is probably the best understood. Alternatively, entry via intercellular invasion has been observed in many legumes. Although there are common features shared by intercellular infection mechanisms, differences are observed in the site of root invasion and bacterial spread on the cortex reaching and infecting a susceptible cell to form a nodule. This review focuses on intercellular bacterial invasion of roots observed in the Fabaceae and considers, within an evolutionary context, the different variants, distribution and molecular determinants involved. Intercellular invasion of actinorhizal plants and Parasponia is also discussed. © The Author 2016. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved. For permissions, please email: journals.permissions@oup.com.
NASA Astrophysics Data System (ADS)
Temesvári, T.
2017-07-01
The asymptotical behavior of physical quantities, like the order parameter, the replicon, and longitudinal masses, is studied around the zero-field spin-glass transition point when a small external magnetic field is applied. An effective field theory to model this asymptotics contains a small perturbation in its Lagrangian which breaks the zero-field symmetry. A first-order renormalization group supplemented by perturbational results provides the scaling functions. The perturbative zero of the scaling function for the replicon mass defines a generic Almeida-Thouless surface stemming from the zero-field fixed point.
The EuroSITES network: Integrating and enhancing fixed-point open ocean observatories around Europe
NASA Astrophysics Data System (ADS)
Lampitt, Richard S.; Larkin, Kate E.; EuroSITES Consortium
2010-05-01
EuroSITES is a 3 year (2008-2011) EU collaborative project (3.5MEuro) with the objective to integrate and enhance the nine existing open ocean fixed point observatories around Europe (www.eurosites.info). These observatories are primarily composed of full depth moorings and make multidisciplinary in situ observations within the water column as the European contribution to the global array OceanSITES (www.oceansites.org). In the first 18 months, all 9 observatories have been active and integration has been significant through the maintenance and enhancement of observatory hardware. Highlights include the enhancement of observatories with sensors to measure O2, pCO2, chlorophyll, and nitrate in near real-time from the upper 1000 m. In addition, some seafloor missions are also actively supported. These include seafloor platforms currently deployed in the Mediterranean, one for tsunami detection and one to monitor fluid flow related to seismic activity and slope stability. Upcoming seafloor science missions in 2010 include monitoring benthic biological communities and associated biogeochemistry as indicators of climate change in both the Northeast Atlantic and Mediterranean. EuroSITES also promotes the development of innovative sensors and samplers in order to progress capability to measure climate-relevant properties of the ocean. These include further developing current technologies for autonomous long-term monitoring of oxygen consumption in the mesopelagic, pH and mesozooplankton abundance. Many of these science missions are directly related to complementary activities in other European projects such as EPOCA, HYPOX and ESONET. In 2010 a direct collaboration including in situ field work will take place between ESONET and EuroSITES. The demonstration mission MODOO (funded by ESONET) will be implemented in 2010 at the EuroSITES PAP observatory. Field work will include deployment of a seafloor lander system with various sensors which will send data to shore in real
Two-stage fixed-bed gasifier with selectable middle gas off-take point
Strickland, Larry D.; Bissett, Larry A.
1992-01-01
A two-stage fixed bed coal gasifier wherein an annular region is in registry with a gasification zone underlying a devolatilization zone for extracting a side stream of high temperature substantially tar-free gas from the gasifier. A vertically displaceable skirt means is positioned within the gasifier to define the lower portion of the annular region so that vertical displacement of the skirt means positions the inlet into the annular region in a selected location within or in close proximity to the gasification zone for providing a positive control over the composition of the side stream gas.
Mishima, K; Yamashita, K
2009-07-07
We develop monotonically convergent free-time and fixed end-point optimal control theory (OCT) in the density-matrix representation to deal with quantum systems showing dissipation. Our theory is more general and flexible for tailoring optimal laser pulses in order to control quantum dynamics with dissipation than the conventional fixed-time and fixed end-point OCT in that the optimal temporal duration of laser pulses can also be optimized exactly. To show the usefulness of our theory, it is applied to the generation and maintenance of the vibrational entanglement of carbon monoxide adsorbed on the copper (100) surface, CO/Cu(100). We demonstrate the numerical results and clarify how to combat vibrational decoherence as much as possible by the tailored shapes of the optimal laser pulses. It is expected that our theory will be general enough to be applied to a variety of dissipative quantum dynamics systems because the decoherence is one of the quantum phenomena sensitive to the temporal duration of the quantum dynamics.
NASA Astrophysics Data System (ADS)
Göttel, Stefan; Reininghaus, Frank; Schoeller, Herbert
2015-07-01
We study a pseudo-spin-1/2 quantum dot in the cotunneling regime close to the particle-hole symmetric point. For a generic tunneling matrix we find a fixed point with interesting nonequilibrium properties, characterized by effective reservoirs with compensating spin orientation vectors weighted by the polarizations and the tunneling rates. At large bias voltage we study the magnetic field dependence of the dot magnetization and the current. The fixed point can be clearly identified by analyzing the magnetization of the dot. We characterize the universal properties for the case of two reservoirs and discuss deviations from the fixed point model in experimentally realistic situations.
Chen, Feinian; Curran, Patrick J.; Bollen, Kenneth A.; Kirby, James; Paxton, Pamela
2009-01-01
This article is an empirical evaluation of the choice of fixed cutoff points in assessing the root mean square error of approximation (RMSEA) test statistic as a measure of goodness-of-fit in Structural Equation Models. Using simulation data, the authors first examine whether there is any empirical evidence for the use of a universal cutoff, and then compare the practice of using the point estimate of the RMSEA alone versus that of using it jointly with its related confidence interval. The results of the study demonstrate that there is little empirical support for the use of .05 or any other value as universal cutoff values to determine adequate model fit, regardless of whether the point estimate is used alone or jointly with the confidence interval. The authors' analyses suggest that to achieve a certain level of power or Type I error rate, the choice of cutoff values depends on model specifications, degrees of freedom, and sample size. PMID:19756246
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
1982-05-15
Data MM—*0 REPORT DOCUMENTATION PAGE f REPORT NUMBER T-465 a. OOVT ACCESSION NO 4. TITLE Cnd SuMlla) CLASSICAL AND BAYSIAN APPROACHES TO...IS. KEY WOROS (Contlmtm on nr«H •!*• II nxmmmmr mit immMr *r NMt • CHANGE POINT, BAYSIAN SEQUENTIAL DETECTION, SURVEY PAPER SO. ABSTRACT
Kleinert, H; Pelster, A; Bachmann, M
1999-09-01
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating functionals are calculated explicitly for the harmonic oscillator with time-dependent frequency, and used to derive a smearing formula for correlation functions of polynomial and nonpolynomial functions of time-dependent positions and momenta. This formula summarizes the effect of quantum fluctuations, and serves to derive generalized Wick rules and Feynman diagrams for perturbation expansions of nonpolynomial interactions.
NASA Astrophysics Data System (ADS)
Hefner, B. Todd; Walker, James S.
1999-12-01
Position-space renormalization-group methods are used to derive exact results for an Ising model on a fractal lattice. The model incorporates both nearest-neighbor and long-range interactions. The long-range interactions, which span all length scales on the lattice, can be thought of as resulting from fractal periodic boundary conditions. We present exact phase diagrams and specific heats in terms of these two interactions, and show that a “hall of mirrors” fixed-point imaging mechanism leads to an infinite number of phase transitions.
NASA Astrophysics Data System (ADS)
Kafri, H. Q.; Khuri, S. A.; Sayfy, Ali
2016-12-01
This article introduces a new numerical approach to solve the equation that models a rectangular purely convecting fin with temperature-dependent thermal conductivity. The algorithm embeds an integral operator, defined in terms of Green's function, into Krasnoselskii-Mann's fixed point iteration scheme. The validity of the method is demonstrated by a number of examples that consist of a range of values of the parameters that appear in the model. In addition, the evaluation of the fin efficiency is presented. The residual error computations show that the current method provides highly accurate approximations.
Moisset de Espanés, P; Osses, A; Rapaport, I
2016-12-01
Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random Boolean networks (RBNs). In this paper we explore how the topology affects the distribution of the number of fixed points in randomly generated networks. We also study the size of the basins of attraction of these fixed points if we assume the α-asynchronous dynamics (where every node is updated independently with probability 0≤α≤1). It is well-known that asynchrony avoids the cyclic attractors into which parallel dynamics tends to fall. We observe the remarkable property that, in all our simulations, if for a given RBN with Barabási-Albert topology and α-asynchronous dynamics an initial configuration reaches a fixed point, then every configuration also reaches a fixed point. By contrast, in the parallel regime, the percentage of initial configurations reaching a fixed point (for the same networks) is dramatically smaller. We contrast the results of the simulations on Barabási-Albert networks with the classical Erdös-Rényi model of random networks. Everything indicates that Barabási-Albert networks are extremely robust. Finally, we study the mean and maximum time/work needed to reach a fixed point when starting from randomly chosen initial configurations. Copyright Â© 2016 Elsevier Ireland Ltd. All rights reserved.
Kainz, K; Prah, D; Ahunbay, E; Li, X
2014-06-01
Purpose: A novel modulated arc therapy technique, mARC, enables superposition of step-and-shoot IMRT segments upon a subset of the optimization points (OPs) of a continuous-arc delivery. We compare two approaches to mARC planning: one with the number of OPs fixed throughout optimization, and another where the planning system determines the number of OPs in the final plan, subject to an upper limit defined at the outset. Methods: Fixed-OP mARC planning was performed for representative cases using Panther v. 5.01 (Prowess, Inc.), while variable-OP mARC planning used Monaco v. 5.00 (Elekta, Inc.). All Monaco planning used an upper limit of 91 OPs; those OPs with minimal MU were removed during optimization. Plans were delivered, and delivery times recorded, on a Siemens Artiste accelerator using a flat 6MV beam with 300 MU/min rate. Dose distributions measured using ArcCheck (Sun Nuclear Corporation, Inc.) were compared with the plan calculation; the two were deemed consistent if they agreed to within 3.5% in absolute dose and 3.5 mm in distance-to-agreement among > 95% of the diodes within the direct beam. Results: Example cases included a prostate and a head-and-neck planned with a single arc and fraction doses of 1.8 and 2.0 Gy, respectively. Aside from slightly more uniform target dose for the variable-OP plans, the DVHs for the two techniques were similar. For the fixed-OP technique, the number of OPs was 38 and 39, and the delivery time was 228 and 259 seconds, respectively, for the prostate and head-and-neck cases. For the final variable-OP plans, there were 91 and 85 OPs, and the delivery time was 296 and 440 seconds, correspondingly longer than for fixed-OP. Conclusion: For mARC, both the fixed-OP and variable-OP approaches produced comparable-quality plans whose delivery was successfully verified. To keep delivery time per fraction short, a fixed-OP planning approach is preferred.
NASA Astrophysics Data System (ADS)
Liang, Yanfeng; Naqvi, Syed Mohsen; Chambers, Jonathon A.
2012-12-01
Fast fixed-point independent vector analysis (FastIVA) is an improved independent vector analysis (IVA) method, which can achieve faster and better separation performance than original IVA. As an example IVA method, it is designed to solve the permutation problem in frequency domain independent component analysis by retaining the higher order statistical dependency between frequencies during learning. However, the performance of all IVA methods is limited due to the dimensionality of the parameter space commonly encountered in practical frequency-domain source separation problems and the spherical symmetry assumed with the source model. In this article, a particular permutation problem encountered in using the FastIVA algorithm is highlighted, namely the block permutation problem. Therefore a new audio video based fast fixed-point independent vector analysis algorithm is proposed, which uses video information to provide a smart initialization for the optimization problem. The method cannot only avoid the ill convergence resulting from the block permutation problem but also improve the separation performance even in noisy and high reverberant environments. Different multisource datasets including the real audio video corpus AV16.3 are used to verify the proposed method. For the evaluation of the separation performance on real room recordings, a new pitch based evaluation criterion is also proposed.
Mass Measurement Using the Fixed Point of a Spring-Mass System with a Dynamic Vibration Absorber
NASA Astrophysics Data System (ADS)
Yamamoto, Satoru; Ishino, Yuji; Takasaki, Masaya; Mizuno, Takeshi
A vibration-type measurement system characterized by the use of an undamped dynamic vibration absorber has been developed. However, inevitable damping in the absorber may cause measurement error. A new method of measuring mass is proposed to overcome this problem. The measurement system utilizes the fixed point of a mass-spring system with a dynamic vibration absorber so that the mass is estimated regardless of damping in the absorber. A phase-looked loop (PLL) is used to achieve tuning. The principle of measurement is described on the basis of a mathematical model. A measuring apparatus was designed and fabricated, and several of its basic characteristics were studied experimentally. Damping of the primary system was found to affect fixed point formation. By reducing the damping of the primary system by a voice coil motor, the measurement conditions were achieved. The efficacy of the apparatus was studied both analytically and experimentally. The measurement conditions were realized automatically by the PLL. Mass measurement was performed while the PLL was operated; the average measurement error was within 0.21 [%].
NASA Astrophysics Data System (ADS)
Defenu, Nicoló; Trombettoni, Andrea; Codello, Alessandro
2015-11-01
We study, by renormalization group methods, O (N ) models with interactions decaying as power law with exponent d +σ . When only the long-range momentum term pσ is considered in the propagator, the critical exponents can be computed from those of the corresponding short-range O (N ) models at an effective fractional dimension Deff. Neglecting wave function renormalization effects the result for the effective dimension is Deff=2/d σ , which turns to be exact in the spherical model limit (N →∞ ) . Introducing a running wave function renormalization term the effective dimension becomes instead Deff=(2/-ηSR)d σ . The latter result coincides with the one found using standard scaling arguments. Explicit results in two and three dimensions are given for the exponent ν . We propose an improved method to describe the full theory space of the models where both short- and long-range propagator terms are present and no a priori choice among the two in the renormalization group flow is done. The eigenvalue spectrum of the full theory for all possible fixed points is drawn and a full description of the fixed-point structure is given, including multicritical long-range universality classes. The effective dimension is shown to be only approximate, and the resulting error is estimated.
NASA Astrophysics Data System (ADS)
Pearce, J. V.; Machin, G.; Ford, T.; Wardle, S.
2008-02-01
Improvement of energy efficiency of jet aircraft is achieved by operating gas turbine engines at higher temperatures. To facilitate this, gas turbine engine manufacturers are continuously developing new alloys for hot-zone turbine blades that will withstand the increased in-service temperatures. A critical part of the manufacture of these blades is heat treatment to ensure that they attain the necessary metallurgical characteristics. Current heat-treatment temperature-control requirements are at the limit of what is achievable with conventional thermocouple calibrations. A project that will allow thermocouple manufacturer CCPI Europe Ltd. to realize uncertainties of ± 1°C, or better, in the calibration of its noble metal thermocouples is described. This will be realized through implementing a Co C eutectic fixed point in CCPI’s calibration chain. As this melts at 1,324°C, very close to the heat-treatment temperatures required, low uncertainties will be obtained. This should yield an increase in effectiveness of the heat-treatment process performed by Bodycote Heat Treatments Ltd., allowing them to respond effectively to the increasingly stringent demands of engine manufacturers. Outside the current project, there is a strong requirement by industry for lower uncertainties at and above 1,300°C. Successful implementation of the current fixed point in an industrial setting is likely to result in rapid take-up by other companies, probably through the supply of ultra-low uncertainty thermocouples, looking to improve their high-temperature processes.
NASA Astrophysics Data System (ADS)
Slamnoiu, G.; Radu, O.; Surdu, G.; Roşca, V.; Damian, R.; Pascu, C.; Curcă, E.; Rădulescu, A.
2016-08-01
The paper has as its main objectives the presentation and the analysis of the numerical analysis results for the study of a fixed point anchoring system for a hydroacoustic sensor when measuring the hydroacoustic signature of divers and ships in real sea conditions. The study of the mechanical behavior of this system has as main objectives the optimization of the shape and weight of the anchorage ballast for the metallic structure while considering the necessity to maintain the sensor in a fixed point and the analysis of the sensor movements and the influences on the measurements caused by the sea current streams. The study was focused on the 3D model of metallic structure design; numerical modeling of the water flow around the sensor anchoring structure using volume of fluid analysis and the analysis of the forces and displacements using FEM when needed for the study. In this paper we have used data for the sea motion dynamics and in particular the velocity of the sea current streams as determined by experimental measurements that have been conducted for the western area of the Black Sea.
The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
NASA Astrophysics Data System (ADS)
Gliozzi, Ferdinando; Guerrieri, Andrea L.; Petkou, Anastasios C.; Wen, Congkao
2017-04-01
We describe in detail the method used in our previous work arXiv:1611.10344 https://arxiv.org/abs/1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ɛ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O( N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.
Construction of Home-Made Tin Fixed-Point Cell at TUBITAK UME
NASA Astrophysics Data System (ADS)
Kalemci, M.; Arifovic, N.; Bağçe, A.; Aytekin, S. O.; Ince, A. T.
2015-08-01
TUBITAK UME Temperature Laboratory initiated a new study which focuses on the construction of a tin freezing-point cell as a primary temperature standard. The design is an open-cell type similar to the National Institute of Standards and Technology design. With this aim, a brand new vacuum and filling line employing an oil diffusion pump and two cold traps (liquid nitrogen and dry ice) was set-up. The graphite parts (crucible, thermometer well, etc.) have been baked at high temperature under vacuum. Each cell was filled with approximately 1 kg of high-purity tin (99.9999 %) in a three-zone furnace. Then several melting and freezing curves were obtained to assess the quality of the home-made cell, and also the new cell was compared with the existing reference cell of the laboratory. The results obtained are very close to the reference cell of UME, indicating that the method used for fabrication was promising and satisfactory and also seems to meet the requirements to have a primary level temperature standard.
The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
Gliozzi, Ferdinando; Guerrieri, Andrea L.; Petkou, Anastasios C.; ...
2017-04-11
Here, we describe in detail the method used in our previous work arXiv:1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We also compute, to the first non-trivial order in the ε-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When availablemore » we agree with older results, but we also produce a wealth of new ones. Furthermore, unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.« less
The g-theorem and quantum information theory
NASA Astrophysics Data System (ADS)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
2016-10-01
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
A Phase-Field Solidification Model of Almost Pure ITS-90 Fixed Points
NASA Astrophysics Data System (ADS)
Large, M. J.; Pearce, J. V.
2014-07-01
A two-dimensional axisymmetric phase-field model of thermo-solutal solidification in freezing-point cells used for calibrating standard platinum resistance thermometers for realization and dissemination of the International Temperature Scale of 1990 is presented. The cell is essentially a graphite crucible containing an ingot of very pure metal (of order 99.9999 %). A graphite tube is inserted along the axis of the ingot to enable immersion of the thermometer in the metal. In this study, the metal is tin (freezing temperature of ). During the freezing of these cells, a steady, reproducible temperature is realized, with a defined temperature that can be used to calibrate thermometers with uncertainties mK. The model is applied to understand the effect of experimental parameters, such as initiation technique and furnace homogeneity, on the measured freezing curve. Results show that freezing curves whose behavior is consistent with the Scheil theory of solidification can be obtained with a specific furnace temperature profile, and provided that the freeze is of a long duration, the results are consistent with previous one-dimensional models and experiments. Morphological instability is observed with the inner interface initiation technique, causing the interface to adopt a cellular structure. This elevates the measured temperature, in accordance with the Gibbs-Thomson effect. In addition, the influence of initiation techniques on the solidification behavior is examined. The model indicates that an initially smooth inner mantle can `de-wet' from the thermometer well-forming agglomerated solid droplets, following recalescence, under certain conditions. This manifests as a measured temperature depression due to the Gibbs-Thomson effect, with a magnitude of to in simulations. The temperature rises to that of the stable outer mantle as freezing progresses and the droplets re-melt. It is demonstrated that the effect occurs below a critical mantle thickness. A physical
Selbig, William R.; Bannerman, Roger T.
2011-01-01
The U.S Geological Survey, in cooperation with the Wisconsin Department of Natural Resources (WDNR) and in collaboration with the Root River Municipal Stormwater Permit Group monitored eight urban source areas representing six types of source areas in or near Madison, Wis. in an effort to improve characterization of particle-size distributions in urban stormwater by use of fixed-point sample collection methods. The types of source areas were parking lot, feeder street, collector street, arterial street, rooftop, and mixed use. This information can then be used by environmental managers and engineers when selecting the most appropriate control devices for the removal of solids from urban stormwater. Mixed-use and parking-lot study areas had the lowest median particle sizes (42 and 54 (u or mu)m, respectively), followed by the collector street study area (70 (u or mu)m). Both arterial street and institutional roof study areas had similar median particle sizes of approximately 95 (u or mu)m. Finally, the feeder street study area showed the largest median particle size of nearly 200 (u or mu)m. Median particle sizes measured as part of this study were somewhat comparable to those reported in previous studies from similar source areas. The majority of particle mass in four out of six source areas was silt and clay particles that are less than 32 (u or mu)m in size. Distributions of particles ranging from 500 (u or mu)m were highly variable both within and between source areas. Results of this study suggest substantial variability in data can inhibit the development of a single particle-size distribution that is representative of stormwater runoff generated from a single source area or land use. Continued development of improved sample collection methods, such as the depth-integrated sample arm, may reduce variability in particle-size distributions by mitigating the effect of sediment bias inherent with a fixed-point sampler.
Bell's theorem and Bayes' theorem
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-12-01
Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin- 1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables
NASA Astrophysics Data System (ADS)
Thianwan, Sornsak
2009-02-01
In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space.
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Noether’s second theorem and Ward identities for gauge symmetries
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-04
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s second theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.
Noether’s second theorem and Ward identities for gauge symmetries
Avery, Steven G.; Schwab, Burkhard U. W.
2016-02-04
Recently, a number of new Ward identities for large gauge transformations and large diffeomorphisms have been discovered. Some of the identities are reinterpretations of previously known statements, while some appear to be genuinely new. We present and use Noether’s second theorem with the path integral as a powerful way of generating these kinds of Ward identities. We reintroduce Noether’s second theorem and discuss how to work with the physical remnant of gauge symmetry in gauge fixed systems. We illustrate our mechanism in Maxwell theory, Yang-Mills theory, p-form field theory, and Einstein-Hilbert gravity. We comment on multiple connections between Noether’s secondmore » theorem and known results in the recent literature. Finally, our approach suggests a novel point of view with important physical consequences.« less
NASA Astrophysics Data System (ADS)
Iwase, R.; Naoi, J.; Kikuchi, T.; Mizutani, K.
2005-12-01
A method of fix point displacement measurement on seafloor by utilizing phase conjugate underwater acoustic wave is proposed and is examined by a simulation. Phase conjugation is a well-known process in the field of optics. The primary feature is cancellation of propagation distortion. When we consider a phase conjugate mirror which generates phase conjugate wave and assume that the spatial property of the propagating medium is stationary over the time needed for a round trip, a phase conjugate wave reflected at that mirror propagates opposite direction of the original incident wave showing time-reversed signature. In case of a spherical wave transmitted from a point source, the reflected phase conjugate wave converges to the original source point. Recently these phenomena of phase conjugation are also demonstrated experimentally for underwater acoustic waves, such as in Kuperman et al. (1998). In underwater acoustics, a source-receiver transponder is used for an original source, and a vertical transducer array, which retransmits time-reversed acoustic pulses generated from received ones that were transmitted from the source transponder, works as a phase conjugate mirror. In this case, the retransmitted pulses also converge to the original source transponder in original shapes by interfering one another. As the feature of the phase conjugation, this process is not affected by frequency of the pulses and property of the medium, such as water depth, topography of seafloor and thermal structure of seawater, as far as the property is stable enough for a round trip time. In long term, however, the retransmitted pulse may not be converged at the source because of the change of propagating condition that includes distance between the source and the array. The collapse of phase conjugation can be detected by observing the acoustic field at the source. Acoustic amplitude structure at the source is less affected by propagating condition. On the other hand, acoustic phase
Miks, Antonin; Novak, Jiri
2014-11-03
This work performs a paraxial analysis of three-component zoom lens with a fixed position of image-space focal point and a distance between object and image points, which is composed of three tunable-focus elements. Formulas for the calculation of paraxial parameters of such optical systems are derived and the calculation is presented on examples.
Fogle, W.E.; Hornung, E.W.; Mayberry, M.C.; Phillips, N.E.
1981-08-01
Comparison of a powdered CMN thermometer with an NBS fixed point device demonstrates an internal inconsistency in the T/sub c/'s assigned to the fixed point device. T/sub c/'s between 100 and 200 mK are in excellent agreement with a temperature scale interpolated between He vapor pressure temperatures and nuclear orientation temperatures, but there is a discrepancy of 8% at the 15 mK point. Evidence for different susceptibility-temperature relations for superficially similar CMN thermometers is also presented.
The essence of the generalized Newton binomial theorem
NASA Astrophysics Data System (ADS)
Liu, Cheng-shi
2010-10-01
Under the frame of the homotopy analysis method, Liao gives a generalized Newton binomial theorem and thinks it as a rational base of his theory. In the paper, we prove that the generalized Newton binomial theorem is essentially the usual Newton binomial expansion at another point. Our result uncovers the essence of generalized Newton binomial theorem as a key of the homotopy analysis method.
The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem
NASA Astrophysics Data System (ADS)
Avksentyev, E. A.
2015-11-01
The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.
NASA Astrophysics Data System (ADS)
Zhang, Weinian; Ge, Shuzhi Sam
2006-01-01
Control system design for non-affine systems is a difficult problem because of the lack of mathematical tools. The key to the problem is solving for an implicit function but the known results for implicit functions are not applicable for higher dimensional systems except for single-input and single-output systems. In this paper, a new version of a global implicit function theorem in higher dimension is presented and proved. This result can be applied to show the controllability of a class of non-affine multi-input and multi-output (MIMO) system so that approximation based control system design can be applied with ease.
NASA Astrophysics Data System (ADS)
Dong, W.; Machin, G.; Bloembergen, P.; Lowe, D.; Wang, T.
2016-11-01
Extensive studies of platinum-carbon eutectic alloy based high temperature fixed point cells have shown that this alloy has extremely good metrological potential as a temperature reference. However, it’s possible adoption as an accepted reference standard means that its eutectic temperature value will soon be agreed with an uncertainty less than most radiation thermometry scales at that temperature. Thus it will lack credibility if used as a future scale comparison artefact. To avoid this, the fixed-point cell can be deliberately doped with an impurity to change its transition temperature by an amount sufficient to test the accuracy of the scales of the institutes, involved in the comparison. In this study dopants of palladium and iridium were added to platinum-carbon to produce ternary alloy and quaternary alloy fixed-point cells. The stability of these artefacts was demonstrated and the fixed-point cells were used to compare the ITS-90 scales of NIM and NPL. It was found that the fixed point temperatures could be changed by an appreciable amount while retaining the stability and repeatability required for comparison artefacts.
Design and Investigation of Pd-C Eutectic Fixed-Point Cells for Thermocouple Calibration at NMIA
NASA Astrophysics Data System (ADS)
Jahan, F.; Ogura, H.; Ballico, M. J.; van der Ham, E. W. M.; Sasajima, N.
2017-05-01
The calibration of Pt/Rh thermocouples up to 1560°C at NMIA currently uses the conventional `melt-wire technique' to realize Gold (Au) and Palladium (Pd) melting points, resulting in the loss of 20 mm of wire from the junction end for each calibration. To avoid this loss, NMIA intends to replace the melt-wire technique with the use of miniature fixed-point cells. NMIA has established Copper (Cu) and Cobalt-Carbon (Co-C) eutectic cells for calibration of thermocouples to 1324°C. To extend the calibration up to 1500°C, miniature Palladium-Carbon (Pd-C) eutectic cells (1492°C) have been constructed and tested in collaboration with NMIJ, AIST. Although these cells are made of high-purity reference materials, careful consideration must be given to contamination introduced during the manufacture and filling of the crucibles and by their long-term use. These issues can only be assessed by measurement of cell-to-cell temperature differences within the ensemble of cells traceable to ITS-90. In the work presented here, 3 NMIA-design mini Pd-C cells were constructed: 1 at NMIA and 2 at NMIJ. These cells were compared, together with a "large" NMIJ Pd-C cell, using type-R, type-B and Pt/Pd thermocouples and radiation thermometry. Although the cells are found to be stable and repeatable, significant problems arising from migration of Pd to the thermocouples were identified.
Pointing losses in single-axis and fixed-mount earth-station antennas due to satellite movement
NASA Astrophysics Data System (ADS)
Buchsbaum, L. M.
1986-06-01
There are substantial cost advantages in the use of single-axis or fixed-mount earth-station antennas, thus reducing or eliminating the need for autotracking in earth-stations operating with quasi-stationary satellites. Such cost advantages are more relevant in small antennas where the tracking system represents a larger percentage of the overall cost. In addition, small antennas are particularly suitable to be operated without autotracking, owing to their wider half-power beamwidth. This paper describes a model for calculating the antenna pointing loss as a function of the antenna diameter, operating frequency band, satellite station-keeping tolerances, and the relative geometry between the earth-station and the satellite. The model has been extensively used in the development of Intelsat's IBS and VISTA services as well as in domestic leases. Although the model has been developed based on orbital mechanics equations, its emphasis is towards earth-station and systems engineering applications. Some example calculations and results obtained through an HP-41 CV programmable calculator are also provided.
NASA Astrophysics Data System (ADS)
Siegel, J.; Siegel, Edward Carl-Ludwig
2011-03-01
Cook-Levin computational-"complexity"(C-C) algorithmic-equivalence reduction-theorem reducibility equivalence to renormalization-(semi)-group phase-transitions critical-phenomena statistical-physics universality-classes fixed-points, is exploited with Gauss modular/clock-arithmetic/model congruences = signal X noise PRODUCT reinterpretation. Siegel-Baez FUZZYICS=CATEGORYICS(SON of ``TRIZ''): Category-Semantics(C-S) tabular list-format truth-table matrix analytics predicts and implements "noise"-induced phase-transitions (NITs) to accelerate versus to decelerate Harel [Algorithmics(1987)]-Sipser[Intro. Theory Computation(1997) algorithmic C-C: "NIT-picking" to optimize optimization-problems optimally(OOPO). Versus iso-"noise" power-spectrum quantitative-only amplitude/magnitude-only variation stochastic-resonance, this "NIT-picking" is "noise" power-spectrum QUALitative-type variation via quantitative critical-exponents variation. Computer-"science" algorithmic C-C models: Turing-machine, finite-state-models/automata, are identified as early-days once-workable but NOW ONLY LIMITING CRUTCHES IMPEDING latter-days new-insights!!!
NASA Astrophysics Data System (ADS)
Qiu, Mo; Yu, Simin; Wen, Yuqiong; Lü, Jinhu; He, Jianbin; Lin, Zhuosheng
In this paper, a novel design methodology and its FPGA hardware implementation for a universal chaotic signal generator is proposed via the Verilog HDL fixed-point algorithm and state machine control. According to continuous-time or discrete-time chaotic equations, a Verilog HDL fixed-point algorithm and its corresponding digital system are first designed. In the FPGA hardware platform, each operation step of Verilog HDL fixed-point algorithm is then controlled by a state machine. The generality of this method is that, for any given chaotic equation, it can be decomposed into four basic operation procedures, i.e. nonlinear function calculation, iterative sequence operation, iterative values right shifting and ceiling, and chaotic iterative sequences output, each of which corresponds to only a state via state machine control. Compared with the Verilog HDL floating-point algorithm, the Verilog HDL fixed-point algorithm can save the FPGA hardware resources and improve the operation efficiency. FPGA-based hardware experimental results validate the feasibility and reliability of the proposed approach.
NASA Astrophysics Data System (ADS)
McEvoy, H. C.; Sadli, M.; Bourson, F.; Briaudeau, S.; Rougié, B.
2013-12-01
The silver and copper fixed-point blackbody sources of NPL were directly compared with those of LNE-Cnam using an IKE LP3 and an IKE LP5 at three wavelengths (650 nm, 795 nm and 903 nm). The two silver fixed points and the two copper fixed points were in excellent agreement with each other, with a difference of 11 mK for the silver and within 16 mK for the copper, with an expanded measurement uncertainty of between 10 mK and 20 mK depending on the pyrometer used. The temperature interval between the silver and copper freezing points was also measured using combinations of all four fixed points. The results with the NPL LP3 gave a value for the silver-copper temperature interval of 122.89 °C with an expanded uncertainty of 30 mK those with the LNE-Cnam LP5 gave a temperature interval of 122.87 °C also with an expanded uncertainty of 30 mK this compares with the ITS-90 value of 122.84 °C.
Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue
2017-01-01
With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array—application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384. PMID:28672813
Yang, Chen; Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue
2017-06-24
With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array-application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
Generalized F-theorem and the ɛ expansion
NASA Astrophysics Data System (ADS)
Fei, Lin; Giombi, Simone; Klebanov, Igor R.; Tarnopolsky, Grigory
2015-12-01
Some known constraints on Renormalization Group flow take the form of inequalities: in even dimensions they refer to the coefficient a of the Weyl anomaly, while in odd dimensions to the sphere free energy F. In recent work [1] it was suggested that the a- and F-theorems may be viewed as special cases of a Generalized F -Theorem valid in continuous dimension. This conjecture states that, for any RG flow from one conformal fixed point to another, {tilde{F}}_{UV}>{tilde{F}}_{IR} , where tilde{F}= sin (π d/2) log {Z}_{S^d} . Here we provide additional evidence in favor of the Generalized F-Theorem. We show that it holds in conformal perturbation theory, i.e. for RG flows produced by weakly relevant operators. We also study a specific example of the Wilson-Fisher O( N) model and define this CFT on the sphere S 4- ɛ , paying careful attention to the beta functions for the coefficients of curvature terms. This allows us to develop the ɛ expansion of tilde{F} up to order ɛ 5. Padé extrapolation of this series to d = 3 gives results that are around 2-3% below the free field values for small N. We also study RG flows which include an anisotropic perturbation breaking the O( N) symmetry; we again find that the results are consistent with {tilde{F}}_{UV}>{tilde{F}}_{IR}.
Hahl, Sayuri K.; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
Hahl, Sayuri K; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
NASA Astrophysics Data System (ADS)
Head, D. I.; Gray, J.; de Podesta, M.
2009-02-01
Ongoing work to improve the uniformity of vertically mounted furnaces, manufactured by Carbolite (e.g., Type TZF12/75—three-zone furnace capable of 1200 °C, with 75 mm inner bore) along the axis and across the working tube and/or equalizing block is reported. This involves adjusting the size of the end zones, the position of the control thermometers, and the use of cascade-control methods. Means regularly used at NPL to reduce electrical noise in some commercially available ac furnaces through a reduction in the voltage used to “fire” the heaters, and better use of thyristor controllers (by extending their cycle time) are described. The need to shield the controllers from local magnetic fields is described. With these measures, the electrical noise from ac furnaces can approach that of dc furnaces, without the large cost of a dc power supply. The application of new data analysis techniques (Allan deviation) will be shown to improve the representation of uninterrupted fixed-point traces (as used in ingot verification rather than PRT calibration). Reduction of statistical noise on the temperature measurements has been achieved for data on the freezing plateau by determining the statistically optimum averaging time. This shows that the statistical uncertainty in the determination of the temperature of a particular freezing plateau is less than 25 μK and that noise (drift) from other sources, possibly due to variations in room temperature, starts to become appreciable over periods longer than a few tens of minutes. The measurement of freezing and melting plateaux at this level is aided by the introduction of new ASL-F900 bridge(s), and quieter/larger standard resistor baths.
G. J. Jordan; M. J. Ducey; J. H. Gove
2004-01-01
We present the results of a timed field trial comparing the bias characteristics and relative sampling efficiency of line-intersect, fixed-area, and point relascope sampling for downed coarse woody material. Seven stands in a managed northern hardwood forest in New Hampshire were inventoried. Significant differences were found among estimates in some stands, indicating...
ERIC Educational Resources Information Center
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of…
2014-01-01
We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle. PMID:24592174
ERIC Educational Resources Information Center
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of…
La, Moonwoo; Park, Sang Min; Kim, Dong Sung
2015-01-01
In this study, a multiple sample dispenser for precisely metered fixed volumes was successfully designed, fabricated, and fully characterized on a plastic centrifugal lab-on-a-disk (LOD) for parallel biochemical single-end-point assays. The dispenser, namely, a centrifugal multiplexing fixed-volume dispenser (C-MUFID) was designed with microfluidic structures based on the theoretical modeling about a centrifugal circumferential filling flow. The designed LODs were fabricated with a polystyrene substrate through micromachining and they were thermally bonded with a flat substrate. Furthermore, six parallel metering and dispensing assays were conducted at the same fixed-volume (1.27 μl) with a relative variation of ±0.02 μl. Moreover, the samples were metered and dispensed at different sub-volumes. To visualize the metering and dispensing performances, the C-MUFID was integrated with a serpentine micromixer during parallel centrifugal mixing tests. Parallel biochemical single-end-point assays were successfully conducted on the developed LOD using a standard serum with albumin, glucose, and total protein reagents. The developed LOD could be widely applied to various biochemical single-end-point assays which require different volume ratios of the sample and reagent by controlling the design of the C-MUFID. The proposed LOD is feasible for point-of-care diagnostics because of its mass-producible structures, reliable metering/dispensing performance, and parallel biochemical single-end-point assays, which can identify numerous biochemical. PMID:25610516
Brückner, Hans-Peter; Spindeldreier, Christian; Blume, Holger
2013-01-01
A common approach for high accuracy sensor fusion based on 9D inertial measurement unit data is Kalman filtering. State of the art floating-point filter algorithms differ in their computational complexity nevertheless, real-time operation on a low-power microcontroller at high sampling rates is not possible. This work presents algorithmic modifications to reduce the computational demands of a two-step minimum order Kalman filter. Furthermore, the required bit-width of a fixed-point filter version is explored. For evaluation real-world data captured using an Xsens MTx inertial sensor is used. Changes in computational latency and orientation estimation accuracy due to the proposed algorithmic modifications and fixed-point number representation are evaluated in detail on a variety of processing platforms enabling on-board processing on wearable sensor platforms.
NASA Astrophysics Data System (ADS)
Nezir, Veysel
2016-04-01
In this paper, we investigate fixed point property for an l1 like subspace in c0 with an equivalent norm and talk about Lorentz-Marcinkiewicz spaces and fixed point property (FPP) for lw,∞ 0 space. It is seen that the subspace given with equivalent norm and Lorentz-Marcinkiewicz space lw,∞ 0 have weak fixed point property (w-FPP) but they both fail the FPP for nonexpansive mappings (n.e.).
Is there a c-theorem in four dimensions?
NASA Astrophysics Data System (ADS)
Cardy, John L.
1988-12-01
The difficulties of extending Zamolodchikov's c-theorem to dimensions d ≠ 2 are discussed. It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably regularized, defines a c-function, which, at least to one loop order, is decreasing along RG trajectories and is stationary at RG fixed points, where it is proportional to the usual conformal anomaly. It is shown that the existence of such a c-function, if it satisfies these properties to all orders, is consistent with the expected behavior of QCD in four dimensions. The author thanks T. Banks, A. Cappelli, A. Coste, D. Friedan, E. Martinec and M. Srednicki for important suggestions and discussions. This work was supported by NSF Grant PHY 86-14185.
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…
The Poincaré-Hopf Theorem for line fields revisited
NASA Astrophysics Data System (ADS)
Crowley, Diarmuid; Grant, Mark
2017-07-01
A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.
Nishiyama, Yoshihiro
2006-07-01
Extending the parameter space of the three-dimensional (d=3) Ising model, we search for a regime of eliminated corrections to finite-size scaling. For that purpose, we consider a real-space renormalization group (RSRG) with respect to a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a criterion of "scale invariance," we determine a location of the nontrivial RSRG fixed point. Subsequent large-scale TM simulation around the fixed point reveals eliminated corrections to finite-size scaling. As anticipated, such an elimination of corrections admits systematic finite-size-scaling analysis. We obtained the estimates for the critical indices as nu=0.6245(28) and y(h)=2.4709(73). As demonstrated, with the aid of the preliminary RSRG survey, the transfer-matrix simulation provides rather reliable information on criticality even for d=3, where the tractable system size is restricted severely.
NASA Astrophysics Data System (ADS)
Pérez Molina, Manuel; Francés Monllor, Jorge; Álvarez López, Mariela; Neipp López, Cristian; Carretero López, Luis
2010-05-01
We develop the Interpolatory Fixed-Point Algorithm (IFPA) to compute efficiently the TE and TM reflectance and transmittance coefficients for arbitrary 1D structures at oblique incidence. For this purpose, we demonstrate that the semi-analytical solutions of the Helmholtz equation provided by the fixed-point method have a polynomial dependence on variables that are related to the essential electromagnetic parameters -incidence angle and wavelength-, which allows a drastic simplification of the required calculations taking the advantage of interpolation for a few parameter values. The first step to develop the IFPA consists of stating the Helmholtz equation and boundary conditions for TE and TM plane incident waves on a 1D finite slab with an arbitrary permittivity profile surrounded by two homogeneous media. The Helmholtz equation and boundary conditions are then transformed into a second-order initial value problem which is written in terms of transfer matrices. By applying the fixed-point method, the coefficients of such transfer matrices are obtained as polynomials on several variables that can be characterized by a reduced set of interpolating parameters. We apply the IFPA to specific examples of 1D diffraction gratings, optical rugate filters and quasi-periodic structures, for which precise solutions for the TE and TM modes are efficiently obtained by computing less than 20 interpolating parameters.
Shimamoto, Akira; Yamashita, Keitaro; Inoue, Hirofumi; Yang, Sung-Mo; Iwata, Masahiro; Ike, Natsuko
2013-04-01
Destructive tests are generally applied to evaluate the fixed strength of spot-welding nuggets of zinc-plated steel (which is a widely used primary structural material for automobiles). These destructive tests, however, are expensive and time-consuming. This paper proposes a nondestructive method for evaluating the fixed strength of the welded joints using surface electrical resistance. A direct current nugget-tester and probes have been developed by the authors for this purpose. The proposed nondestructive method uses the relative decrease in surface electrical resistance, α. The proposed method also considers the effect of the corona bond. The nugget diameter is estimated by two factors: RQuota, which is calculated from variation of resistance, and a constant that represents the area of the corona bond. Since the maximum tensile strength is correlated with the nugget diameter, it can be inferred from the estimated nugget diameter. When appropriate measuring conditions for the surface electrical resistance are chosen, the proposed method can effectively evaluate the fixed strength of the spot-welded joints even if the steel sheet is zinc-plated.
NASA Technical Reports Server (NTRS)
White, M. D.
1944-01-01
Detail calculations are presented of the shifts in stick-fixed neutral point of the Republic XF-12 airplane due to the windmilling propellers and to the fuselage. The results of these calculations differ somewhat from those previously made for this airplane by Republic Aviation Corporation personnel under the direction of Langley flight division personnel. Due to these differences the neutral point for the airplane is predicted to be 37.8 percent mean aerodynamic chord, instead of 40.8 percent mean aerodynamic chord as previously reported.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
On Siegel's linearization theorem for fields of prime characteristic
NASA Astrophysics Data System (ADS)
Lindahl, Karl-Olof
2004-05-01
In 1981, Herman and Yoccoz (1983 Generalizations of some theorems of small divisors to non Archimedean fields Geometric Dynamics (Lecture Notes in Mathematics) ed J Palis Jr, pp 408-47 (Berlin: Springer) Proc. Rio de Janeiro, 1981) proved that Siegel's linearization theorem (Siegel C L 1942 Ann. Math. 43 607-12) is true also for non-Archimedean fields. However, the condition in Siegel's theorem is usually not satisfied over fields of prime characteristic. We consider the following open problem from non-Archimedean dynamics. Given an analytic function f defined over a complete, non-trivial valued field of characteristic p > 0, does there exist a convergent power series solution to the Schröder functional equation (2) that conjugates f to its linear part near an indifferent fixed point? We will give both positive and negative answers to this question, one of the problems being the presence of small divisors. When small divisors are present this brings about a problem of a combinatorial nature, where the convergence of the conjugacy is determined in terms of the characteristic of the state space and the powers of the monomials of f, rather than in terms of the diophantine properties of the multiplier, as in the complex case. In the case that small divisors are present, we show that quadratic polynomials are analytically linearizable if p = 2. We find an explicit formula for the coefficients of the conjugacy, and applying a result of Benedetto (2003 Am. J. Math. 125 581-622), we find the exact size of the corresponding Siegel disc and show that there is an indifferent periodic point on the boundary. In the case p > 2 we give a sufficient condition for divergence of the conjugacy for quadratic maps as well as for a certain class of power series containing a quadratic term (corollary 2.1).
Two-circles theorem, q-periodic functions and entangled qubit states
NASA Astrophysics Data System (ADS)
Pashaev, Oktay K.
2014-03-01
For arbitrary hydrodynamic flow in circular annulus we introduce the two circle theorem, allowing us to construct the flow from a given one in infinite plane. Our construction is based on q-periodic analytic functions for complex potential, leading to fixed scale-invariant complex velocity, where q is determined by geometry of the region. Self-similar fractal structure of the flow with q-periodic modulation as solution of q-difference equation is studied. For one point vortex problem in circular annulus by fixing singular points we find solution in terms of q-elementary functions. Considering image points in complex plane as a phase space for qubit coherent states we construct Fibonacci and Lucas type entangled N-qubit states. Complex Fibonacci curve related to this construction shows reach set of geometric patterns.
Single-Arm Phase II Group Sequential Trial Design with Survival Endpoint at a Fixed Time Point.
Wu, Jianrong; Xiong, Xiaoping
2014-01-01
In this paper, three non-parametric test statistics are proposed to design single-arm phase II group sequential trials for monitoring survival probability. The small-sample properties of these test statistics are studied through simulations. Sample size formulas are derived for the fixed sample test. The Brownian motion property of the test statistics allowed us to develop a flexible group sequential design using a sequential conditional probability ratio test procedure (Xiong, 1995). An example is given to illustrate the trial design by using the proposed method.
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Infrared Fixed Point in the Strong Running Coupling: Unraveling the ΔI = 1/2 Puzzle in K-Decays
NASA Astrophysics Data System (ADS)
Crewther, R. J.; Tunstall, Lewis C.
2013-08-01
In this paper, we present an explanation for the ΔI = 1/2 rule in K-decays based on the premise of an infrared fixed point αIR in the running coupling αs of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate <\\bar {q}q> vac !=q 0 spontaneously breaks scale and chiral SU(3)L×SU(3)R symmetry. Consequently, the low-lying spectrum contains nine Nambu-Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f0(500) resonance and construct a chiral-scale perturbation theory χPTσ for low-energy amplitudes expanded in αs about αIR. The ΔI = 1/2 rule emerges in the leading order of χPTσ through a σ-pole term KS→σ→ππ, with a gKSσ coupling fixed by data on γγ→π0π0 and KS→γγ. We also determine RIR ≈5 for the nonperturbative Drell-Yan ratio at αIR.
Temporal Distributional Limit Theorems for Dynamical Systems
NASA Astrophysics Data System (ADS)
Dolgopyat, Dmitry; Sarig, Omri
2017-02-01
Suppose {T^t} is a Borel flow on a complete separable metric space X, f:X→ R is Borel, and xin X. A temporal distributional limit theorem is a scaling limit for the distributions of the random variables X_T:=int _0^t f(T^s x)ds, where t is chosen randomly uniformly from [0, T], x is fixed, and T→ ∞. We discuss such laws for irrational rotations, Anosov flows, and horocycle flows.
Noether's theorem for dissipative quantum dynamical semi-groups
NASA Astrophysics Data System (ADS)
Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G.
2015-02-01
Noether's theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quantum setting of quantum Markov dynamics. For finite-dimensional Hilbert spaces, we construct a mapping from observables to completely positive maps that leads to the natural analogue of their criterion of commutativity with the infinitesimal generator of the Markov dynamics. Using standard results on the relaxation of states to equilibrium under quantum dynamical semi-groups, we are able to characterise the constants of the motion under quantum Markov evolutions in the infinite-dimensional setting under the usual assumption of existence of a stationary strictly positive density matrix. In particular, the Noether constants are identified with the fixed point of the Heisenberg picture semi-group.
Asymptotic behavior and Denjoy-Wolff theorems for Hilbert metric nonexpansive maps
NASA Astrophysics Data System (ADS)
Lins, Brian C.
We study the asymptotic behavior of fixed point free Hilbert metric nonexpansive maps on bounded convex domains. For such maps, we prove that the omega limit sets are contained in a convex subset of the boundary when the domain is either polyhedral or two dimensional. Similar results are obtained for several classes of positive operators defined on closed cones, including linear maps, affine linear maps, max-min operators, and reproduction-decimation operators. We discuss the relationship between these results and other Denjoy-Wolff type theorems. In particular, we investigate the interaction of nonexpansive maps with the horofunction boundary in the Hilbert geometry and in finite dimensional normed spaces.
NASA Astrophysics Data System (ADS)
Nezir, Veysel; Mustafa, Nizami
2017-04-01
In 2011, Lennard and Nezir showed that very large class of closed bounded convex sets in c0 fails the fixed point property for affine nonexpansive mappings respect to c0's usual norm since they proved that closed convex hull of any asymptotically isometric (ai) c0-summing basis fails the fixed point property for nonexpansive mappings and in fact their class is one of these. Then, Nezir recently worked on these sets and constructed several equivalent norms. In one of his works, he defined the equivalent norm ||| . ||| on c0 by |||x |||:=1/γ1 lim p →∞k ∈ℕ γk(∑j=k∞ |ξ/j|pj ) 1/p+γ1sup j ∈ℕ ∑k=1∞ Qk |ξ *k-α ξ *j| where γ2=γ1,γk↑k1 ,γk +1<γk +2,∀k ∈ℕ, x *:=(ξ*j)j∈ℕis the decreasing rearrangement of x , ∑k=1∞ Qk=1 ,Qk↓k 0 and Qk>Qk +1,∀k ∈ℕ for all x ∈ c0. Then, he studied a subclass of the class S below introduced by Lennard and Nezir and showed that it has the fixed point property for affine ||| . |||-nonexpansive mappings for some α > 1 when Q1>1/-γ1+2 |α | 1 +2 |α | . S := { Eb\\sub c0:Eb={ ∑n=1∞ αn ∑k=1n fk ∀αn≥0 and ∑n=1∞αn =1 } where b ∈(0 ,1 ), f1=b e1,f2=b e2,fn=en for all n ≥3 } . In this paper, we will show that the below larger class G given by Lennard and Nezir that contains S has the fixed point property for affine ||| . |||-nonexpansive mappings for all α > 1 when 1/-γ1+2 |α | 1 +2 |α | . G := { E \\sub; 0:E ={ ∑n=1∞ αn ∑k=1n bkek :∀αn≥0 and ∑n=1∞ αn =1 } where (bn)n∈ℕ∈ℝ with 0
Hasenfratz, Anna
2012-02-10
I investigate an SU(3) gauge model with 12 fundamental fermions. The physically interesting region of this strongly coupled system can be influenced by an ultraviolet fixed point due to lattice artifacts. I suggest to use a gauge action with an additional negative adjoint plaquette term that lessens this problem. I also introduce a new analysis method for the 2-lattice matching Monte Carlo renormalization group technique that significantly reduces finite volume effects. The combination of these two improvements allows me to measure the bare step scaling function in a region of the gauge coupling where it is clearly negative, indicating a positive renormalization group β function and infrared conformality.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
A generalization of Nekhoroshev's theorem
NASA Astrophysics Data System (ADS)
Bates, Larry; Cushman, Richard
2016-11-01
Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville-Arnol'd on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev's theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev's theorem does in the abelian case.
Arnold, Michael; Langenbruch, Tobias; Kroha, Johann
2007-11-02
We propose a physical realization of the two-channel Kondo (2CK) effect, where a dynamical defect in a metal has a unique ground state and twofold degenerate excited states. In a wide range of parameters the interactions with the electrons renormalize the excited doublet downward below the bare defect ground state, thus stabilizing the 2CK fixed point. In addition to the Kondo temperature T(K) the three-state defect exhibits another low-energy scale, associated with ground-to-excited-state transitions, which can be exponentially smaller than T(K). Using the perturbative nonequilibrium renormalization group we demonstrate that this can provide the long-sought explanation of the sharp conductance spikes observed by Ralph and Buhrman in ultrasmall metallic point contacts.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
NASA Astrophysics Data System (ADS)
Renaot, E.; Martin, C.
2011-08-01
In order to improve the uncertainty on the aluminum fixed point, a study was launched by Laboratoire Commun de Métrologie LNE-CNAM in the frame of the EURAMET Project 732 "Toward more accurate temperature fixed points" (coordinating laboratory: France, 17 partner countries). An earlier study completed in this laboratory showed that in regular realization of the melting-freezing plateaus, there is no diffusion of impurities in the thickness of the ingot, or the diffusion is excessively slow and cannot allow a uniform distribution of the impurities. On the other hand, it is frequently noticed that the experimental conditions before the freezing plateau have an impact on its characteristics (value, slope,…). Up to now, no systematic study was performed on the influence of this parameter. So, the objective of the task started recently in this laboratory is to investigate the influence of the time spent in the liquid phase on the phase transition. As a final result, it is demonstrated that in order to reach the equilibrium of the concentration of impurities, it is necessary to ensure that the metal remains in the liquid phase at least 24 h before initiating the freeze. At the end of the process, the aluminum ingot was chemically analyzed. The analyses reveal large contaminations of the surface of the ingot (sodium, sulfur, and phosphorus). One of the important outputs of this study is that the conditions of usage of the cells should be given important attention since large contaminations can be brought by the furnace.
NASA Astrophysics Data System (ADS)
Kiss, László Péter; Szeidl, György
2017-04-01
This paper deals with the vibrations of isotropic, linearly elastic and heterogeneous circular beams given that a vertical force acts at the crown point. The effect of the loading is taken into account via the axial strain it causes. The material parameters, like Young's modulus, can vary arbitrarily over the symmetric, uniform cross-section. Thus, it is possible to simply model composites (not only multi-layered but also functionally graded material distributions). The main objectives are as follows: (1) to derive the equations of motion, (2) to determine the Green function matrix in closed-form both for a tensile force and for a compressive one; (3) to clarify how the load affects the natural frequencies and (4) to develop a numerical model so that we can obtain how the eigenfrequencies are related to the load. The computational results are presented in graphical format.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.
2002-11-01
The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The basic issues were known to Gibbs. Boltzmann conducted a very public debate with Loschmidt and others without a satisfactory resolution. In recent decades there has been no real change in the situation. In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. The relation was derived heuristically and applied to the special case of dissipative non-equilibrium systems subject to constant energy 'thermostatting'. These restrictions meant that the full importance of the Theorem was not immediately apparent. Within a few years, derivations of the Theorem were improved but it has only been in the last few of years that the generality of the Theorem has been appreciated. We now know that the Second Law of Thermodynamics can be derived assuming ergodicity at equilibrium, and causality. We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. Unlike the Boltzmann equation, the FT is completely consistent with Loschmidt's observation that for time reversible dynamics, every dynamical phase space trajectory and its conjugate time reversed 'anti-trajectory', are both solutions of the underlying equations of motion. Indeed the standard proofs of
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
Generalized No-Broadcasting Theorem
NASA Astrophysics Data System (ADS)
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-01
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with “superquantum” correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Non-traditional theorems unfolding
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2015-02-01
The purpose of this paper is to provide examples of 'non-traditional' proof-related activities or theorems that can be explored through paper folding by university and high-school students. These theorems were encountered through playful acts of paper folding by the author. The author used these activities successfully with preservice teachers. The paper contains proof outlines for each theorem.
Benecke, Reiner; Heinze, Axel; Reichel, Gerhard; Hefter, Harald; Göbel, Hartmut
2011-11-01
This was a prospective, randomized, double-blind, placebo-controlled, 12-week, multicenter study to evaluate the efficacy and tolerability of fixed location injections of botulinum type A toxin (BoNT-A, Dysport) in predetermined injection sites in patients with myofascial pain syndrome of the upper back. Patients with moderate-to-severe myofascial pain syndrome affecting cervical and/or shoulder muscles (10 trigger points, disease duration 6-24 months) and moderate-to-severe pain intensity were randomized to BoNT-A (N = 81) or saline (N = 72). Patients received treatment into 10 predetermined fixed injection sites in the head, neck, and shoulder (40 units of BoNT-A per site or saline, a total of 400 units of BoNT-A). The primary efficacy outcome was the proportion of patients with mild or no pain at week 5 (responders). Secondary outcomes included changes in pain intensity and the number of pain-free days per week. At week 5, 49% (37/76) of BoNT-A patients and 38% (27/72) of placebo patients had responded to treatment (P = 0.1873). Duration of daily pain was reduced in the BoNT-A group compared with the placebo group from week 5, with statistically significant differences at weeks 9 and 10 (P = 0.04 for both). Treatment was well tolerated. Fixed-location treatment with BoNT-A of patients with upper back myofascial pain syndrome did not lead to a significant improvement of the main target parameter in week 5 after treatment. Only in week 8 were significant differences found. Several secondary parameters, such as physicians' global assessment and patients' global assessment, significantly favored BoNT-A over placebo at weeks 8 and 12. Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Pavese, Franco
2009-02-01
According to the Guide to the Expression of Uncertainty in Measurement (GUM) on which the expression of uncertainty in the field of metrology is based, since 1995, 'it is assumed that the results of a measurement have been corrected for all recognised significant systematic effects'. Since the International Temperature Scale of 1990 specifies that the substances used for the realization of the 'fixed points' be 'ideally pure', to fully implement the intent of the GUM corrections should be applied for any chemical impurities that affect the value of the measurand. In general, thermometrists' opinion is that significant laboratory research and more literature search are still needed for further progress towards reliable corrections. This paper, reviewing the available literature data, shows that the situation is more favourable in the case of the substances used for the realization of the Scale reference points in the range 13.8 K to 273.16 K based on the use of hydrogen, neon, oxygen and argon. The appendix reports a similar review also for nitrogen. Then the paper discusses the other conditions, physical-chemical and thermal, of the substances inside the thermometric cells, concurring with the chemical impurity effects to the overall state of knowledge of the realized triple point temperature relevant to the solution of the problem of performing the corrections.
NASA Astrophysics Data System (ADS)
Elliott, C. J.; Greenen, A.; Lowe, D.; Pearce, J. V.; Machin, G.
2015-04-01
To categorise thermocouples in batches, manufacturers state an expected operating tolerance for when the thermocouples are as-new. In use, thermocouple behaviour can rapidly change and the tolerance becomes invalid, especially when used at high temperatures (i.e. above 1000 °C) as the processes leading to de-calibration, such as oxidation and contamination, can be very fast and lead to erroneous readings. In-situ thermocouple self-validation provides a method to track the drift and correct the thermocouple reading in real-time, but it must be shown to be reliable. Two miniature temperature fixed-point cells designed at NPL for in-situ thermocouple self-validation, the first containing a Pt-C eutectic alloy and the second containing a Ru-C eutectic alloy, have been exposed to temperatures close to their melting point for 2200 h and 1570 h, respectively, and continuously, for up to three months. Recalibration after this long-term high-temperature exposure, where a tantalum-sheathed thermocouple was always in place, is used to show that no significant change of the temperature reference point (the melting temperature) has occurred in either the Pt-C ingot or the Ru-C ingot, over timescales far longer than previously demonstrated and approaching that required by industry for practical use of the device.
NASA Astrophysics Data System (ADS)
Lu, Min; Rao, Wen-Jia; Narayanan, Rajesh; Wan, Xin; Zhang, Guang-Ming
2016-12-01
Quantum entanglement under an extensive bipartition can reveal the critical boundary theory of a topological phase in a parameter space. In this study we demonstrate that the infinite-randomness fixed point for spin-1/2 degrees of freedom can emerge from an extensive random bipartition of the spin-1 Affleck-Kennedy-Lieb-Tasaki chain. The nested entanglement entropy of the ground state of the reduced density matrix exhibits a logarithmic scaling with an effective central charge c ˜=0.72 ±0.02 ≈ln2 . We further discuss, in the language of bulk quantum entanglement, how to understand all phase boundaries and the surrounding Griffiths phases for the antiferromagnetic Heisenberg spin-1 chain with quenched disorder and dimerization.
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
Grover, Lov K
2005-10-07
The quantum search algorithm consists of an iterative sequence of selective inversions and diffusion type operations, as a result of which it is able to find a state with desired properties (target state) in an unsorted database of size N in only sqrt[N] queries. This is achieved by designing the iterative transformations in a way that each iteration results in a small rotation of the state vector in a two-dimensional Hilbert space that includes the target state; if we choose the right number of iterative steps, we will stop just at the target state. This Letter shows that by replacing the selective inversions by selective phase shifts of pi/3, the algorithm preferentially converges to the target state irrespective of the step size or number of iterations. This feature leads to robust search algorithms and also to new schemes for quantum control and error correction.
Multizone Furnace for Analysis of Fixed-Point Realizations in the Range from 1,000°C to 1,700°C
NASA Astrophysics Data System (ADS)
Hiti, M.; Bojkovski, J.; Batagelj, V.; Drnovšek, J.
2008-02-01
In this article, the development of a laboratory furnace specially designed for analysis of fixed-point plateau realizations in the range from 1,000 °C to 1,700 °C that enables control of various temperature distribution settings along the heating zone length is presented. A total of 13 thermocouples are built into the furnace tube wall to control the temperature as well as to measure the temperature distribution. The furnace is divided into seven independently controlled heating zones. Each heating zone comprises a MoSi2 heating element and its dedicated DC power supply module. The furnace temperature is controlled by manipulating the output voltage of each power supply to control the temperature of each heating element, as estimated from its electrical resistance. The heating power and temperature measurement are fully controlled by a computer using an application written in Lab VIEW, allowing very flexible furnace control. The furnace can be used in air as well as in an inert atmosphere. Measurements of the temperature distribution of the furnace during a melting-point realization are presented.
Oppermann, R; Schmidt, M J
2008-12-01
A scaling theory of replica symmetry breaking (RSB) in the Sherrington-Kirkpatrick (SK) model is presented in the framework of critical phenomena for the scaling regime of large RSB orders kappa , small temperatures T , and small (homogeneous) magnetic fields H . We employ the pseudodynamical picture [R. Oppermann, M. J. Schmidt, and D. Sherrington, Phys. Rev. Lett. 98, 127201 (2007)], where two critical points CP1 and CP2 are associated with the order function's pseudodynamical limits lim_{a-->infinity}q(a)=1 and lim_{a-->0}q(a)=0 at (T=0 , H=0 , 1kappa=0) . CP1 - and CP2 -dominated contributions to the free energy functional F[q(a)] require an unconventional scaling hypothesis. We determine the scaling contributions in accordance with detailed numerical self-consistent solutions for up to 200 orders of RSB. Power laws, scaling functions, and crossover lines are obtained. CP1 -dominated behavior is found for the nonequilibrium susceptibility, which decays like chi_{1}=kappa;{-53}f_{1}(Tkappa;{-53}) , for the entropy, which obeys S(T=0) approximately chi_{1};{2} , and for the subclass of diverging parameters a_{i}=kappa;{53}f_{a_{i}}(Tkappa;{-53}) [describing Parisi box sizes m_{i}(T) identical witha_{i}(T)T ], with f_{1}(zeta) approximately zeta and f_{a_{i}}(zeta) approximately 1zeta for zeta-->infinity , while f(0) is finite. CP2 -dominated behavior, controlled by the magnetic field H while temperature is irrelevant, is retrieved in the plateau height (or width) of the order function q(a) according to q_{pl}(H)=kappa;{-1}f_{pl}(H;{23}kappa;{-1}) with f_{pl}mid R:(zeta)mid R:_{zeta-->infinity} approximately zeta and f_{pl}(0) finite. Divergent characteristic RSB orders kappa_{CP1}(T) approximately T;{-35} and kappa_{CP2}(H) approximately H;{-23} , respectively, describe the crossover from mean field SK- to RSB-critical behavior with rational-valued exponents extracted with high precision from our RSB data. The order function q(a) is obtained as a fixed-point
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-07-08
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Han, Houzeng; Xu, Tianhe; Wang, Jian
2016-01-01
Precise Point Positioning (PPP) makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF) combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD) operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC) algorithm is implemented by integrating PPP with inertial navigation system (INS) using an Extended Kalman filter (EKF). The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies of the height
Duality Theorems in Ergodic Transport
NASA Astrophysics Data System (ADS)
Lopes, Artur O.; Mengue, Jairo K.
2012-11-01
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose σ is the shift acting on Bernoulli space X={1,2,…, d}ℕ, and, consider a fixed continuous cost function c: X× X→ℝ. Denote by Π the set of all Borel probabilities π on X× X, such that, both its x and y marginals are σ-invariant probabilities. We are interested in the optimal plan π which minimizes ∫ c dπ among the probabilities in Π. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan π by convex combinations of plans such that the support projects in periodic orbits.
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
Bayes' theorem in paleopathological diagnosis.
Byers, Steven N; Roberts, Charlotte A
2003-05-01
The utility of Bayes' theorem in paleopathological diagnoses is explored. Since this theorem has been used heavily by modern clinical medicine, its usefulness in that field is described first. Next, the mechanics of the theorem are discussed, along with methods for deriving the prior probabilities needed for its application. Following this, the sources of these prior probabilities and their accompanying problems in paleopathology are considered. Finally, an application using prehistoric rib lesions is presented to demonstrate the utility of this method to paleopathology.
Generalized Kochen-Specker theorem
NASA Astrophysics Data System (ADS)
Aravind, P. K.
2003-11-01
A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)] is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker, and Bell theorems that shed some light on the relationship between these three theorems.
On Leighton's comparison theorem
NASA Astrophysics Data System (ADS)
Ghatasheh, Ahmed; Weikard, Rudi
2017-06-01
We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.
Multidimensional Tauberian theorems for generalized functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.
2016-12-01
This is a brief survey of multidimensional Tauberian theorems for generalized functions. Included are theorems of Hardy-Littlewood type, Tauberian and Abelian comparison theorems of Keldysh type, theorems of Wiener type, and Tauberian theorems for generalized functions with values in Banach spaces. Bibliography: 58 titles.
Widmann, Gerlig; Zangerl, Antoniette; Keiler, Martin; Stoffner, Rudolf; Bale, Reto; Puelacher, Wolfgang
2010-08-01
In edentulous patients, accurate and stable positioning of a surgical template is impeded by the mobile mucosal tissue. The objective was to evaluate the accuracy of flapless computer-assisted template-guided surgery in an edentulous human cadaver specimen using three fixed oral reference points (FRP) for fixation of the registration mouthpiece and the consecutive surgical template. Oral implants were planned on the computed tomography (CT) of an edentulous human cadaver specimen. Surgical templates have been fabricated using a multipurpose navigation system. Both the registration mouthpiece and consecutive surgical template were supported via three FRP. Study implants were inserted through the guide sleeves and the accuracy was evaluated on a post-surgical CT of the cadaver jaws fused with the pre-surgical planning CT. A Matlab script enabled comparison of the planned surgical path with the study implants. In five maxillary and three mandibular edentulous human cadaver specimens, a total of 51 implants (35 implants in the maxilla and 16 implants in the mandible) have been placed. The mean+/-standard deviation total error (Euclidean distance)/lateral error (normal deviation) were 1.1+/-0.6/0.7+/-0.5 mm at the implant base and 1.2+/-0.7/0.9+/-0.7 mm at the implant tip. The mean angular error was 2.8+/-2.2 degrees. Flapless surgery based on FRP-supported image-guided surgical templates may provide similar accuracy as reported for tooth-supported surgical templates or surgical navigation.
NASA Astrophysics Data System (ADS)
Pearce, J. V.; Elliott, C. J.; Lowe, D. H.; Failleau, G.; Deuzé, T.; Bourson, F.; Sadli, M.; Machin, G.
2014-04-01
A series of high-temperature fixed points (HTFPs) Pt-C (1738 , and Ru-C (1953 ) have been constructed at the National Physical Laboratory (NPL) and the Laboratoire National de métrologie et d'Essais and Conservatoire national des arts et métiers (LNE-Cnam). These are required for the calibration of high-temperature thermocouples in the framework of work package 6 of the European Metrology Research Programme IND01 project "HiTeMS." The goal of this work package is to establish a European capability that can determine low-uncertainty reference functions of non-standard high-temperature thermocouples. For reference functions to be widely applicable, measurements must be performed by more than one institute and preferably by more than one method. Due to the high price of the ingot materials, miniature HTFP cells are used. NPL and LNE-Cnam constructed their HTFP cells with different designs; these are described here, together with the performance of the cells using both radiation thermometry and thermocouples. The melting temperature of the Ru-C cells (for thermocouple calibrations) was determined using radiation thermometry at both NPL and LNE-Cnam, and the two results are compared. The suitability of the cells for calibration of W-Re and Rh-Ir thermocouples is evaluated, and some results are presented. Some discussion is given regarding the materials challenges when calibrating Rh-Ir thermocouples up to 2000 C.
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
The Non-Signalling theorem in generalizations of Bell's theorem
NASA Astrophysics Data System (ADS)
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
The 1965 Penrose singularity theorem
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.; Garfinkle, David
2015-06-01
We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
ERIC Educational Resources Information Center
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
Equivalence theorem in effective theories
NASA Astrophysics Data System (ADS)
Chicherin, D.; Gorbenko, V.; Vereshagin, V.
2011-11-01
The famous equivalence theorem is reexamined in order to make it applicable to the case of effective theories. We slightly modify the formulation of this theorem and prove it based on the notion of the generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancellation of different groups of contributions.
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Using Bayes' theorem for free energy calculations
NASA Astrophysics Data System (ADS)
Rogers, David M.
Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.
Lanford's Theorem and the Emergence of Irreversibility
NASA Astrophysics Data System (ADS)
Uffink, Jos; Valente, Giovanni
2015-04-01
It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford (Dynamical systems, theory and applications, 1975, Asterisque 40:117-137, 1976, Physica 106A:70-76, 1981) shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford's theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford's theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all.
Nagai, Satoshi; Hida, Kohsuke; Urushizaki, Shingo; Onitsuka, Goh; Yasuike, Motoshige; Nakamura, Yoji; Fujiwara, Atushi; Tajimi, Seisuke; Kimoto, Katsunori; Kobayashi, Takanori; Gojobori, Takashi; Ototake, Mitsuru
2016-02-01
In this study, we investigated the influence of diurnal sampling bias on the community structure of plankton by comparing the biodiversity among seawater samples (n=9) obtained every 3h for 24h by using massively parallel sequencing (MPS)-based plankton monitoring at a fixed point conducted at Himedo seaport in Yatsushiro Sea, Japan. The number of raw operational taxonomy units (OTUs) and OTUs after re-sampling was 507-658 (558 ± 104, mean ± standard deviation) and 448-544 (467 ± 81), respectively, indicating high plankton biodiversity at the sampling location. The relative abundance of the top 20 OTUs in the samples from Himedo seaport was 48.8-67.7% (58.0 ± 5.8%), and the highest-ranked OTU was Pseudo-nitzschia species (Bacillariophyta) with a relative abundance of 17.3-39.2%, followed by Oithona sp. 1 and Oithona sp. 2 (Arthropoda). During seawater sampling, the semidiurnal tidal current having an amplitude of 0.3ms(-1) was dominant, and the westward residual current driven by the northeasterly wind was continuously observed during the 24-h monitoring. Therefore, the relative abundance of plankton species apparently fluctuated among the samples, but no significant difference was noted according to G-test (p>0.05). Significant differences were observed between the samples obtained from a different locality (Kusuura in Yatsushiro Sea) and at different dates, suggesting that the influence of diurnal sampling bias on plankton diversity, determined using the MPS-based survey, was not significant and acceptable.
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
Deviations from Wick's theorem in the canonical ensemble
NASA Astrophysics Data System (ADS)
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
A Theorem and its Application to Finite Tampers
DOE R&D Accomplishments Database
Feynman, R. P.
1946-08-15
A theorem is derived which is useful in the analysis of neutron problems in which all neutrons have the same velocity. It is applied to determine extrapolated end-points, the asymptotic amplitude from a point source, and the neutron density at the surface of a medium. Formulas fro the effect of finite tampers are derived by its aid, and their accuracy discussed.
Hohenberg-Kohn theorems in electrostatic and uniform magnetostatic fields
Pan, Xiao-Yin; Sahni, Viraht
2015-11-07
The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle in terms of these densities is also developed. These theorems are further generalized to electrons with spin by imposing the added constraint of fixed canonical orbital and spin angular momenta. The proofs differ from the original HK proof and explicitly account for the many-to-one relationship between the potentials and the nondegenerate ground state wave function. A Percus-Levy-Lieb constrained-search proof expanding the domain of validity to N-representable functions, and to degenerate states, again for fixed electron number and angular momentum, is also provided.
Fluctuation theorem: A critical review
NASA Astrophysics Data System (ADS)
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
NASA Astrophysics Data System (ADS)
Sapritsky, V.; Ogarev, S.; Khlevnoy, B.
Several fixed-point cells (with 2 and 4 mm apertures for spectral-radiance application, and with 8 and 10 mm apertures (for the spectral irradiance measurements) have been designed and investigated at VNIIOFI consisted of a high- purity graphite crucibles containing Re-C ingots with nominal total impurity levels of 5,5N at the eutectic composition(s). It was investigated that fix-point reproducibility (freezing plateau level for all measured cells) was up to 0.01...0.02% between series of measurements / crucibles, and 0.002...0.004% within a sample measurement session, i.e. better than 100 mK. Measurements of high-temperature fixed points blackbodies based on Ir-C and Re-C eutectics were carried out to investigate their applicability as radiation sources for precision photometry and radiometry, in particular for astronomy and space applications, like long-term measurements of solar variability, etc. The measurement results encourage that the utilization of a new series of a high-temperature fix-point sources hand in hand with cryo-radiometer detector could cardinally change the situation in reproduction of spectral radiance, irradiance and temperature international scales. Several more high-temperature eutectics (e.g. TiC-C metal- carbon eutectics with T = 3057 C) are being investigated further for use as high- temperature fixed-point radiance and irradiance sources in o der to increase ther accuracy of radiometric and radiance-temperature scales above the conventionally assigned values of temperatures of ITS-90.
Metric rigidity theorems on Hermitian locally symmetric spaces
Mok, Ngaiming
1986-01-01
Let X = Ω/Γ be a compact quotient of an irreducible bounded symmetric domain Ω of rank ≥2 by a discrete group ω of automorphisms without fixed points. It is well known that the Kähler-Einstein metric g on X carries seminegative curvature (in the sense of Griffiths). I show that any Hermitian metric h on X carrying seminegative curvature must be a constant multiple of g. This can be applied to prove rigidity theorems of holomorphic maps from X into Hermitian manifolds (Y, k) carrying seminegative curvature. These results are also generalized to the case of quotients of finite volume. On the other hand, let (Xc, gc) be an irreducible compact Hermitian symmetric manifold of rank ≥2. Then gc is Kähler and carries semipositive holomorphic bisectional curvature. I prove that any Kähler h on Xc carrying semipositive holomorphic bisectional curvature must be equal to gc up to a constant multiple and up to a biholomorphic transformation of Xc. PMID:16593680
The Digital Morphological Sampling Theorem
NASA Astrophysics Data System (ADS)
Haralick, Robert M.; Zhuang, Xinhua; Lin, Charlotte; Lee, James
1988-02-01
There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
MEASURABLE UTILITY AND THE MEASURABLE CHOICE THEOREM.
Three theorems are proved that are useful in mathematical treatments of economic models with a continuum of economic agents . The first, called the...measurable. Both these theorems generalize known theorems on these subjects. The third theorem treats a situation in which the set of economic agents forms
More on soft theorems: Trees, loops, and strings
NASA Astrophysics Data System (ADS)
Bianchi, Massimo; He, Song; Huang, Yu-tin; Wen, Congkao
2015-09-01
We study soft theorems in a broader context, their universality in effective field theories and string theory, as well as continue the analysis of their fate at loop level. In effective field theories with F3 and R3 interactions, the soft theorems are not modified. However, for gravity theories with R2ϕ interactions, the sub-subleading order soft graviton theorem, which is beyond what is implied by the extended Bondi, van der Burg, Metzner, and Sachs symmetry, requires modifications at tree level for nonsupersymmetric theories and at loop level for N ≤4 supergravity due to anomalies. For open and closed superstrings at finite α', via explicit calculation for lower-point examples as well as world sheet operator product expansion analysis for arbitrary multiplicity, we show that scattering amplitudes satisfy the same soft theorem as their field-theory counterpart. This is no longer true for closed bosonic or heterotic strings due to the presence of R2ϕ interactions. We also consider loop corrections to gauge theories in the planar limit, where we show that tree-level soft gluon theorems are respected at the integrand level for 1 ≤N ≤4 SYM. Finally, we discuss the fate of soft theorems for finite loop amplitudes in pure Yang-Mills theory and gravity.
Noether’s theorem for dissipative quantum dynamical semi-groups
Gough, John E.; Ratiu, Tudor S.; Smolyanov, Oleg G.
2015-02-15
Noether’s theorem on constants of the motion of dynamical systems has recently been extended to classical dissipative systems (Markovian semi-groups) by Baez and Fong [J. Math. Phys. 54, 013301 (2013)]. We show how to extend these results to the fully quantum setting of quantum Markov dynamics. For finite-dimensional Hilbert spaces, we construct a mapping from observables to completely positive maps that leads to the natural analogue of their criterion of commutativity with the infinitesimal generator of the Markov dynamics. Using standard results on the relaxation of states to equilibrium under quantum dynamical semi-groups, we are able to characterise the constants of the motion under quantum Markov evolutions in the infinite-dimensional setting under the usual assumption of existence of a stationary strictly positive density matrix. In particular, the Noether constants are identified with the fixed point of the Heisenberg picture semi-group.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
On the decoupling theorem for vacuum metastability
NASA Astrophysics Data System (ADS)
Patel, Hiren H.; Radovčić, Branimir
2017-10-01
In this paper, we numerically study the impact heavy field degrees of freedom have on vacuum metastability in a toy model, with the aim of better understanding how the decoupling theorem extends to semiclassical processes. We observe that decoupling applies to partial amplitudes associated with fixed final state field configurations emerging from the tunneling processes, characterized by a scale such as the inverse radius of a spherically symmetric bubble, and not directly on the total lifetime (as determined by the ;bounce;). More specifically, tunneling amplitudes for bubbles with inverse radii smaller than the scale of the heavier fields are largely insensitive to their presence, while those for bubbles with inverse radii larger than that scale may be significantly modified.
Rotating and rolling rigid bodies and the "hairy ball" theorem
NASA Astrophysics Data System (ADS)
Bormashenko, Edward; Kazachkov, Alexander
2017-06-01
Rotating and rolling rigid bodies exemplify a fascinating theorem of topology, jokingly called the "hairy ball" theorem, which demands that any continuous tangent vector field on the sphere has at least one point where the field is zero. We demonstrate via a gedanken experiment how drilling through a rotating ball, thereby converting it into a torus, leads to the elimination of zero-velocity points on the ball surface. Using the same reasoning, zero-velocity points can be removed from the surface of a drilled spinning top. We discuss the location of zero-velocity points on the surfaces of rigid bodies rolling with no slip and with slip. Observations made from different reference frames identify various zero-velocity points. Illustrative experiments visualizing zero-velocity points are presented.
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
NASA Astrophysics Data System (ADS)
Gong, Zongping; Quan, H. T.
2015-07-01
By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase-space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs and might be valuable for studying thermodynamic processes with information exchange.
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
Soft theorems in superstring theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2017-06-01
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum field theories coupled to gravity with generic interactions. We discuss the technical issue involved in extending this analysis to loop amplitudes of superstring theory including Ramond sector external states, and its possible resolution.
A categorical account of the Hofmann-Mislove theorem
NASA Astrophysics Data System (ADS)
Townsend, Christopher F.
2005-11-01
A categorical account is given of the Hofmann-Mislove theorem, describing the Scott open filters on a frame. The account is stable under an order duality and so is shown to also cover Bunge and Funk's constructive description of the points of the lower power locale.
Hamiltonian Noether theorem for gauge systems and two time physics
NASA Astrophysics Data System (ADS)
Villanueva, V. M.; Nieto, J. A.; Ruiz, L.; Silvas, J.
2005-08-01
The Noether theorem for Hamiltonian constrained systems is revisited. In particular, our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints. We apply our results to the relativistic point particle, to the Friedberg et al model and, with special emphasis, to two time physics.
Quantum cryptography without Bell's theorem
NASA Astrophysics Data System (ADS)
Bennett, Charles H.; Brassard, Gilles; Mermin, N. David
1992-02-01
Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.
Generalized Bezout's Theorem and its applications in coding theory
NASA Technical Reports Server (NTRS)
Berg, Gene A.; Feng, Gui-Liang; Rao, T. R. N.
1996-01-01
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
Pion Electroproduction and Siegert's Theorem
NASA Astrophysics Data System (ADS)
Tiator, Lothar
2016-11-01
Nucleon to Resonance transition form factors are discussed within the MAID model for pion electroproduction on the nucleon. For low Q^2 the consequences of Siegert's theorem are presented and medium to large violations of the Long Wavelength Limit at the pseudo-threshold are observed for the phenomenological parametrizations of the longitudinal transition form factors of different nucleon resonances.
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
NASA Astrophysics Data System (ADS)
Chambers, Chris M.; Moss, Ian G.
1994-08-01
A generalization of Price's theorem is given for application to inflationary cosmologies. Namely, we show that on a Schwarzschild-de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Arriving at the Pythagorean Theorem.
ERIC Educational Resources Information Center
Jaramillo, James; Brown, Jonathan Caius
This lesson plan uses group activity and manipulative materials to teach English-speaking students (ages 15-16) of diverse ethnic backgrounds an operatonal understanding of the Pythagorean Theorem. It is based on theories of constructivism and holism and includes teacher instructions, discussion questions, a retrospective vision, and an ancillary…
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
A note on generalized Weyl's theorem
NASA Astrophysics Data System (ADS)
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Khalfin's Theorem and Neutral Mesons Subsystem
NASA Astrophysics Data System (ADS)
Urbanowski, Krzysztof
2009-01-01
The consequences of Khalfin's Theorem are discussed. we find, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Within a given model we examine numerically the Khalfin's Theorem and show in a graphic form how the Khalfin's Theorem works.
Cubature/ Unscented/ Sigma Point Kalman Filtering with Angular Measurement Models
2015-07-06
based on the Fundamental Theorem of Gaussian Integration, which states that the definite integral of any polynomial up to a given degree times a weighting ... function w having certain properties can be determined exactly by a weighted summation of the polynomial evaluated at certain fixed points based on...the weighting function . As an equation, for a scalar integral, this means that Z b a w(x)g(x) dx = nX i=0 ωig(ξi), (1) where a and b are the bounds of
Equipartition theorem and the dynamics of liquids
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S; Morris, James R
2008-01-01
In liquids, phonons have a very short lifetime and the total potential energy does not depend linearly on temperature. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic-oscillator model and that the equipartition theorem for the potential energy is not upheld. In this paper we show that the description of the local atomic dynamics in terms of the atomic-level stresses provides such a description, satisfying the equipartition theorem. To prove this point we carried out molecular-dynamics simulations with several pairwise potentials, including the Lennard-Jones potential, the modified Johnson potential, and the repulsive part of the Johnson potential, at various particle number densities. In all cases studied the total self-energy of the atomic-level stresses followed the (3/2)kBT law. From these results we suggest that the concept of local atomic stresses can provide description of thermodynamic properties of glasses and liquids on the basis of harmonic atomistic excitations. An example of application of this approach to the description of the glass transition temperature in metallic glasses is discussed.
The de Finetti theorem for test spaces
NASA Astrophysics Data System (ADS)
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
Equivalence theorem of uncertainty relations
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Qiao, Cong-Feng
2017-01-01
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e. the variance-based ones and the entropic forms, showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. This means that an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature, and variance-based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
The Floquet Adiabatic Theorem revisited
NASA Astrophysics Data System (ADS)
Weinberg, Phillip; Bukov, Marin; D'Alessio, Luca; Kolodrubetz, Michael; Davidson, Shainen; Polkovnikov, Anatoli
2015-03-01
The existance of the adiabatic theorem for Floquet systems has been the subject of an active debate with different articles reaching opposite conclusions over the years. In this talk we clarify the situation by deriving a systematic expansion in the time-derivatives of a slow parameter for the occupation probabilities of the Floque states. Our analysis shows that the in a certain limit the transition between Floquet eigenstates are suppressed and it is possible to define an adiabatic theorem for Floquet systems. Crucially we observe however that the conditions for adiabaticity in ordinary and Floquet systems are different and that this difference can become important when the amplitude of the periodic driving is large. We illustrate our results with specific examples of a periodically driven harmonic oscillator and cold atoms in optical lattices which are relevant in current experiments.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
Theorem Proving in Intel Hardware Design
NASA Technical Reports Server (NTRS)
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
Quantum violation of fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Shimizu, Akira; Fujikura, Kyota
2017-02-01
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
NASA Astrophysics Data System (ADS)
Lavin, Alicia; Cano, Daniel; González-Pola, Cesar; Tel, Elena; Rodriguez, Carmen; Ruiz, Manuel; Somavilla, Raquel
2015-04-01
, but Dissolved Oxygen sensor is also problematic. Periods of realistic smooth variations present strong offset that is corrected based on the Winkler analysis of water samples. The incorporation of these observatories on larger scale research programs, as done in 2003 in the framework of the VACLAN and COVACLAN projects, is important in order to provide them with a larger spatial dimension and maximize its utility for process-oriented studies. In 2003, the Santander section was extended 90 miles offshore in the framework of a large-scale hydrographic and circulation monitoring program. Partnerships in a large EU project as FixO3 has provided tools for coordination, homogenization and data validation as well as improve the use of chemical-biological data.
The Reciprocal of the Fundamental Theorem of Riemannian Geometry
NASA Astrophysics Data System (ADS)
Calderon, Hector
2008-05-01
The fundamental theorem of Riemannian geometry is inverted for analytic Christoffel symbols. The inversion formula, henceforth dubbed Ricardo's formula, is obtained without ancillary assumptions and it is well suited to compute the uncertainty in the metric that arises from the uncertainty in the measurement of positions. The solution is given up to a constant conformal factor, in part, because there are no experiments that can fix such factor without probing the whole universe. Ricardo's formula excludes some pathological examples and works for manifolds of any dimension and metrics of any signature.
Londeree, William; Davis, Konrad; Helman, Donald; Abadie, Jude
2014-09-01
Forward deployed military medical units can provide sophisticated medical care with limited resources. Point-of-Care Testing (POCT) may facilitate care and expedite diagnosis. This study assessed the accuracy of results for POCT for non-serum samples (pleural, peritoneal, and cerebrospinal fluid) using iSTAT and Piccolo hand-held devices compared with results obtained using a hospital chemistry analyzer. Pleural, peritoneal, and cerebrospinal fluids obtained during routine care were simultaneously analyzed on a Vitros 5600 automated clinical chemistry hospital analyzer, iSTAT, and Piccolo POCT devices. POCT results were highly correlated with the Vitros 5600 for pleural fluid LDH, glucose, and triglycerides (TG); for peritoneal fluid bilirubin, TG, glucose, albumin, and protein; and glucose for cerebrospinal fluid. POCT results for non-serum samples from pleural, peritoneal, and cerebrospinal fluid correlate with standard hospital chemistry analysis. The results of this study demonstrate potential for possible new diagnostic roles for POCT in resource-limited environments.
Optical theorem for multipole sources in wave diffraction theory
NASA Astrophysics Data System (ADS)
Eremin, Yu. A.; Sveshnikov, A. G.
2016-05-01
The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
Scattering theorems for dyadic chiral fields
NASA Astrophysics Data System (ADS)
Athanasiadis, Christodoulos; Gotopoulos, Stavros
2004-06-01
A time-harmonic plane dyadic electromagnetic field is scattered by a chiral body in a chiral environment. The body is either a perfect conductor or a dielectric. The incident field is a linear combination of left-circularly polarized and right-circularly polarized dyadic electromagnetic fields, each of which has a different wave number. We prove reciprocity and scattering theorems in dyadic form, which incorporate as special cases the corresponding known theorems for vector electromagnetic waves. Specializing to the same direction of incidence and observation in the general scattering theorems we obtain forward scattering theorems.
On Liouville's theorem in fluid mechanics
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Bouchet, F.; Thalabard, S.; Zaboronski, O. V.
2011-11-01
Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g. Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
NASA Astrophysics Data System (ADS)
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
A generalization of the Funk-Hecke theorem to the case of hyperbolic spaces
NASA Astrophysics Data System (ADS)
Shtepina, T. V.
2004-10-01
The well-known Funk-Hecke theorem states that for integral operators whose kernels depend only on the distance between points in spherical geometry and where the integral is taken over the surface of a hypersphere, every surface spherical harmonic is an eigenvector. In this paper we extend this theorem to the case of non-compact Lobachevsky spaces. We compute the corresponding eigenvalue in some physically important cases.
INTERPOLATION THEOREMS FOR THE SPACES L_{p,q}
NASA Astrophysics Data System (ADS)
Ovchinnikov, V. I.
1989-02-01
A sharp or optimal interpolation theorem is proved for the Lorentz spaces L_{p,q}, generalizing the Marcinkiewicz theorem and refining the Riesz-Thorin theorem and the Stein-Weiss theorem. This theorem extends to the spaces \\overline{X}_{\\theta,p} of the real method constructed from any Banach pair; thus it extends also to Besov spaces.Bibliography: 12 titles.
Uniqueness theorems in bioluminescence tomography.
Wang, Ge; Li, Yi; Jiang, Ming
2004-08-01
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case the BLT solution is not unique by constructing the set of all the solutions to this inverse problem. Then, we show the uniqueness of the solution in the case of impulse sources. Finally, we present our main theorem that solid/hollow ball sources can be uniquely determined up to nonradiating sources. For better readability, the exact conditions for and rigorous proofs of the theorems are given in the Appendices. Further research directions are also discussed.
NASA Astrophysics Data System (ADS)
Pavese, Franco
2011-10-01
The expression of uncertainty in the field of metrology is based, since 1993, on the Guide to the Expression of Uncertainty in Measurement. According to this, 'it is assumed that the results of a measurement have been corrected for all recognized significant systematic effects'. Since the International Temperature Scale of 1990 considers the substances used for the realization of the 'fixed points' to be ideally pure, to fully implement the intent of the GUM corrections should be applied for any chemical impurities that affect the value of the measurand. The present paper aims at reviewing an aspect that must be tackled to arrive to reliable and scientifically sound corrections: the use of an appropriate statistical method. In addition to the SIE, OME and hybrid methods recommended by the CCT, two new approaches are proposed in this paper, called one-sided OME and Average Overall Estimate (AOE). They are illustrated and their merits compared with the previous one, by applying them for the correction of the measured values of the triple-point temperature of the four gaseous substances (hydrogen, neon, oxygen and argon) used for the realization of the ITS-90 reference points in the range 13.8 K to 273.16 K. Some suggestions are drawn from the resulting evidence.
Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines
Smith, E. |
1998-09-01
Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright} {ital 1998} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
McRae, S. M.; Vrscay, E. R.
1992-09-01
The classical hypervirial and Hellmann-Feynman theorems are used to formulate a "perturbation theory without Fourier series" that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical Hamiltonians. Here, the method is applied to one-dimensional anharmonic oscillators and radial Kepler problems. In all cases, the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit. This "action fixing" is inherent in the classical Hellmann-Feynman theorem applied to periodic orbits.
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
A Physical Proof of the Pythagorean Theorem
ERIC Educational Resources Information Center
Treeby, David
2017-01-01
What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one…
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
Euler and the Fundamental Theorem of Algebra.
ERIC Educational Resources Information Center
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
A note on Morley's triangle theorem
NASA Astrophysics Data System (ADS)
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-06-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an n-gon are n-sected.
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
The Pythagorean Theorem: I. The finite case
Kadison, Richard V.
2002-01-01
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both “discrete” and “continuous.” PMID:11929992
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
Virial theorem in quasi-coordinates and Lie algebroid formalism
NASA Astrophysics Data System (ADS)
Cariñena, José F.; Gheorghiu, Irina; Martínez, Eduardo; Santos, Patrícia
2014-04-01
In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Cariñena, F. Falceto and M. F. Rañada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Cariñena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031-10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.
Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper
NASA Technical Reports Server (NTRS)
Schumann, Johann; Koga, Dennis (Technical Monitor)
1999-01-01
In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).
On the Theorem of Correspondence.
Krøjgaard, Peter
2017-03-01
In a recent paper, Mammen (Integrative Psychological and Behavioral Science, 50, 196-233, 2016a) brought novel arguments into the discussion concerning the importance of being able to single out and track objects through space and time. Mammen offered a formal account of two basic, yet distinct, ways in which we as human beings encounter objects in the real world, that is, sense and choice categories. In this paper I discuss aspects of his theory and in particular the Theorem of Correspondence. I shall attempt to argue that Mammen's formal account is indeed a novel and powerful analytical generic tool allowing us to see the important relevance in different domains of being able to establish choice categories. Meanwhile, I will attempt to show that evidence from the so-called multiple object tracking studies -- even though these use highly artificial stimuli -- provide compelling evidence in support of Mammen's formal account.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems.
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Alarm points for fixed oxygen monitors
Miller, G.C.
1987-05-01
Oxygen concentration monitors were installed in a vault where numerous pipes carried inert cryogens and gases to the Mirror Fusion Test Facility (MFTF-B) experimental vessel at Lawrence Livermore National Laboratory (LLNL). The problems associated with oxygen-monitoring systems and the reasons why such monitors were installed were reviewed. As a result of this review, the MFTF-B monitors were set to sound an evacuation alarm when the oxygen concentration fell below 18%. We chose the 18% alarm criterion to minimize false alarms and to allow time for personnel to escape in an oxygen-deficient environment.
Complex networks renormalization: flows and fixed points.
Radicchi, Filippo; Ramasco, José J; Barrat, Alain; Fortunato, Santo
2008-10-03
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.
Posterior Probability and Fluctuation Theorem in Stochastic Processes
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Analogues of Chernoff's theorem and the Lie-Trotter theorem
Neklyudov, Alexander Yu
2009-10-31
This paper is concerned with the abstract Cauchy problem .x=Ax, x(0)=x{sub 0} element of D(A), where A is a densely defined linear operator on a Banach space X. It is proved that a solution x( {center_dot} ) of this problem can be represented as the weak limit lim {sub n{yields}}{sub {infinity}}{l_brace}F(t/n){sup n}x{sub 0}{r_brace}, where the function F:[0,{infinity}){yields}L(X) satisfies the equality F'(0)y=Ay, y element of D(A), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator C to be closable and for its closure to be the generator of a C{sub 0}-semigroup. Also, we obtain new criteria for the sum of two generators of C{sub 0}-semigroups to be the generator of a C{sub 0}-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.
Construction of solutions for some nonlinear two-point boundary value problems
NASA Technical Reports Server (NTRS)
Pennline, J. A.
1982-01-01
Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.
The Lax-Onsager regression `theorem' revisited
NASA Astrophysics Data System (ADS)
Lax, Melvin
2000-05-01
It is stated by Ford and O'Connell in this festschrift issue and elsewhere that "there is no quantum regression theorem" although Lax "obtained a formula for correlation in a driven quantum system that has come to be called the quantum regression theorem". This produces a puzzle: "How can it be that a non-existent theorem gives correct results?" Clarification will be provided in this paper by a description of the Lax procedure, with a quantitative estimate of the error for a damped harmonic oscillator based on expressions published in the 1960's.
Kato type operators and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos
2005-09-01
A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).
Cosmological singularity theorems and black holes
NASA Astrophysics Data System (ADS)
Vilenkin, Alexander; Wall, Aron C.
2014-03-01
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from nonsingular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities. If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces. Unlike the original Penrose theorem, our theorems provide some information about the location of singularities. We illustrate how they can be used to rule out some cosmological scenarios.