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).
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.
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
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
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.
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.
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.
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…
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.
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.
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.
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!!!
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
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
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 .
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.
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.
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.
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.
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.
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.
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....
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....
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....
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
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.
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.
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.
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.
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 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-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.
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 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
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.
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).
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
2016-08-04
NOTES N/A 14. ABSTRACT The objective of this effort is to create a parametric Computer- Aided Design (CAD) accommodation model for the Fixed Heel...Heel Point (FHP), accommodation model, occupant work space, central 90% of the Soldier population, encumbrance, posture and position, computer aided ...Arbor, MI ABSTRACT The objective of this effort is to create a parametric Computer- Aided Design (CAD) accommodation model for the Fixed Heel
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.
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.
One loop beta functions and fixed points in higher derivative sigma models
Percacci, Roberto; Zanusso, Omar
2010-03-15
We calculate the one loop beta functions of nonlinear sigma models in four dimensions containing general two- and four-derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N{>=}4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2, 3. In the approximation considered, the four-derivative couplings are asymptotically free but the coupling in the two-derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymptotically safe.
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
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.
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.
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.
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 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
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 .
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.
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.
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
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.
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.
2011-01-01
REPORT Fixed-point Design of theLattice-reduction-aided Iterative Detection andDecoding Receiver for Coded MIMO Systems 14. ABSTRACT 16. SECURITY...298 (Rev 8/98) Prescribed by ANSI Std. Z39.18 - Fixed-point Design of theLattice-reduction-aided Iterative Detection andDecoding Receiver for Coded ...important, this report illustrates the performance of coded LR aided detectors. 1 Fixed-point Design of the Lattice-reduction-aided Iterative Detection and
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.
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
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.
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.
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.
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.
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.
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
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.
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,…
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.
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.
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.
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 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.
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.
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.
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.
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.
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.
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)
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.
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.
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.
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.
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)
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.
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.
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.
Formalin Fixed Paraffin Embedded Tissue as a Starting Point for PrPSc Detection by ELISA
Technology Transfer Automated Retrieval System (TEKTRAN)
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...
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.
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.
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.
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…
Starting points in plant-bacteria nitrogen-fixing symbioses: intercellular invasion of the roots.
Ibáñez, Fernando; Wall, Luis; Fabra, Adriana
2016-10-18
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.
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.
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
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)
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.
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)
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)
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.
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 [%].
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.
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
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…
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.
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.
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.
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.
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.
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)
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.
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)
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!!!
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
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.
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
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
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
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.
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.
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}.
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.
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.
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.
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…
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…
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].
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.
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).
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.
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.
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.
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)
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.
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)
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.
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…
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.
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.
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
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.
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
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)
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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…
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.…
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)
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.
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.
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.
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
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
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.
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…
2016-04-01
AND ROTORCRAFT FROM DISCRETE-POINT LINEAR MODELS Eric L. Tobias and Mark B. Tischler Aviation Development Directorate Aviation and Missile...Wing Aircraft and Rotorcraft from Discrete-Point Linear Models Eric L. Tobias San Jose State University U.S. Army Aviation Development Directorate...AMRDEC) Moffett Field, CA Mark B. Tischler U.S. Army Aviation Development Directorate (AMRDEC) Moffett Field, CA April 2016 Abstract A comprehensive model
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.
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.
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
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.
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.
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.
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.
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.
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.
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.)
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,…
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.
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…
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…
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…
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.
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.
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.
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.
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.
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
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.
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.
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).
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.
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.
On Fixed Points of Strictly Causal Functions
2013-04-08
present in all but the most trivial systems. But it makes systems self - referential , with one signal depending on another, and vice versa (see Figure 1...study the related convergence process . 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR) 18...and study the related convergence process . 1 Introduction This work is part of a larger effort aimed at the construction of well defined mathematical
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.
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.
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.
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.
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.
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.
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.
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.
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
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…
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
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.)
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…
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)
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.
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.
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).
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.
Quantum regression theorem and non-Markovianity of quantum dynamics
NASA Astrophysics Data System (ADS)
Guarnieri, Giacomo; Smirne, Andrea; Vacchini, Bassano
2014-08-01
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.
Comparison theorems for causal diamonds
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Gibbons, Gary; Solodukhin, Sergey N.
2015-09-01
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if d =4 or d >4 . This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all d . We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.
Structure theorem for Vaisman completely solvable solvmanifolds
NASA Astrophysics Data System (ADS)
Sawai, Hiroshi
2017-04-01
Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have the structure theorem for Vaisman completely solvable solvmanifolds.
ALGEBRAIC DEPENDENCE THEOREMS ON COMPLEX PSEUDOCONCAVE SPACES
The notion of pseudoconcave space is introduced and classical theorems on algebraic dependence of meromorphic functions are extended for this new class of spaces and for sections in a coherent sheaf. (Author)
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
A Physical Proof of the Pythagorean Theorem
NASA Astrophysics Data System (ADS)
Treeby, David
2017-02-01
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 such proof. Though far from the most elegant approach, we believe it to be novel.
Littlewood-Paley Theorem for Schrodinger Operators
2006-07-26
26 JUL 2006 2. REPORT TYPE 3. DATES COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE Littlewood -Paley theorem for Schrodinger operators...associated with H are well defined. We further give a Littlewood -Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes...unclassified c THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 LITTLEWOOD -PALEY THEOREM FOR SCHRÖDINGER
1989-06-09
47405 Prof. Arandiga F. Universidad de Valencia Prof. Khamsi Amine Departamento de Analisis Matematico Department of Mathematics Doctor Moliner, 50...Economics Departamento de Analisis Matematico Johns Hopkins University Dr. Moliner 50 Baltinore Md 21218 46100 Bujassot Prof. Kirk W. A. Prof. Llaudes...Francesco Arandiga Department of Mathematics Universidad de Valencia University of Iowa Departamento de Analisis Matematico Iowa City 52242 Dr. Moliner
Hu, Cheng; Yu, Juan; Chen, Zhanheng; Jiang, Haijun; Huang, Tingwen
2017-05-01
In this paper, the fixed-time stability of dynamical systems and the fixed-time synchronization of coupled discontinuous neural networks are investigated under the framework of Filippov solution. Firstly, by means of reduction to absurdity, a theorem of fixed-time stability is established and a high-precision estimation of the settling-time is given. It is shown by theoretic proof that the estimation bound of the settling time given in this paper is less conservative and more accurate compared with the classical results. Besides, as an important application, the fixed-time synchronization of coupled neural networks with discontinuous activation functions is proposed. By designing a discontinuous control law and using the theory of differential inclusions, some new criteria are derived to ensure the fixed-time synchronization of the addressed coupled networks. Finally, two numerical examples are provided to show the effectiveness and validity of the theoretical results.
Properties of Fixed-Fixed Models and Alternatives in Presence-Absence Data Analysis
Kallio, Aleksi
2016-01-01
Assessing the significance of patterns in presence-absence data is an important question in ecological data analysis, e.g., when studying nestedness. Significance testing can be performed with the commonly used fixed-fixed models, which preserve the row and column sums while permuting the data. The manuscript considers the properties of fixed-fixed models and points out how their strict constraints can lead to limited randomizability. The manuscript considers the question of relaxing row and column sun constraints of the fixed-fixed models. The Rasch models are presented as an alternative with relaxed constraints and sound statistical properties. Models are compared on presence-absence data and surprisingly the fixed-fixed models are observed to produce unreasonably optimistic measures of statistical significance, giving interesting insight into practical effects of limited randomizability. PMID:27812126
Properties of Fixed-Fixed Models and Alternatives in Presence-Absence Data Analysis.
Kallio, Aleksi
2016-01-01
Assessing the significance of patterns in presence-absence data is an important question in ecological data analysis, e.g., when studying nestedness. Significance testing can be performed with the commonly used fixed-fixed models, which preserve the row and column sums while permuting the data. The manuscript considers the properties of fixed-fixed models and points out how their strict constraints can lead to limited randomizability. The manuscript considers the question of relaxing row and column sun constraints of the fixed-fixed models. The Rasch models are presented as an alternative with relaxed constraints and sound statistical properties. Models are compared on presence-absence data and surprisingly the fixed-fixed models are observed to produce unreasonably optimistic measures of statistical significance, giving interesting insight into practical effects of limited randomizability.
NASA Astrophysics Data System (ADS)
Wiggins, S.; Mancho, A. M.
2014-02-01
In this paper we consider fluid transport in two-dimensional flows from the dynamical systems point of view, with the focus on elliptic behaviour and aperiodic and finite time dependence. We give an overview of previous work on general nonautonomous and finite time vector fields with the purpose of bringing to the attention of those working on fluid transport from the dynamical systems point of view a body of work that is extremely relevant, but appears not to be so well known. We then focus on the Kolmogorov-Arnold-Moser (KAM) theorem and the Nekhoroshev theorem. While there is no finite time or aperiodically time-dependent version of the KAM theorem, the Nekhoroshev theorem, by its very nature, is a finite time result, but for a "very long" (i.e. exponentially long with respect to the size of the perturbation) time interval and provides a rigorous quantification of "nearly invariant tori" over this very long timescale. We discuss an aperiodically time-dependent version of the Nekhoroshev theorem due to Giorgilli and Zehnder (1992) (recently refined by Bounemoura, 2013 and Fortunati and Wiggins, 2013) which is directly relevant to fluid transport problems. We give a detailed discussion of issues associated with the applicability of the KAM and Nekhoroshev theorems in specific flows. Finally, we consider a specific example of an aperiodically time-dependent flow where we show that the results of the Nekhoroshev theorem hold.
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Adding Some Perspective to de Moivre's Theorem: Visualising the "n"-th Roots of Unity
ERIC Educational Resources Information Center
Bardell, Nicholas S.
2015-01-01
Traditionally, "z" is assumed to be a complex number and the roots are usually determined by using de Moivre's theorem adapted for fractional indices. The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius. The "n"-th roots of unity always include the real number 1, and…
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
Republication of: A theorem on Petrov types
NASA Astrophysics Data System (ADS)
Goldberg, J. N.; Sachs, R. K.
2009-02-01
This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.
A Paley-Wiener theorem for generalized entire functions on infinite-dimensional spaces
NASA Astrophysics Data System (ADS)
Khrennikov, A. Yu; Petersson, H.
2001-04-01
We study entire functions on infinite-dimensional spaces. The basis is the study of spaces of Gateaux holomorphic functions that are bounded on certain subsets (bounded entire functions). The main goal is to characterize the Fourier image of the corresponding spaces of generalized entire functions (ultra-distributions) by an infinite-dimensional Paley-Wiener theorem. We introduce entire functions of exponential type and prove a generalization of the classical Paley-Wiener theorem. The crucial point of our theory is the dimension-invariant estimate given by Lemma 4.12.
The optical theorem for local source excitation of a particle near a plane interface
NASA Astrophysics Data System (ADS)
Eremin, Yuri; Wriedt, Thomas
2015-11-01
Based on classic Maxwell's theory and the Gauss Theorem we extended the Optical Theorem to the case of a penetrable particle excited by a local source deposited near a plane interface. We demonstrate that the derived Extinction Cross-Section involves the total point source radiating cross-section and some definite integrals responsible for the scattering by the interface. The derived extinction cross-section can be employed to estimate the quantum yield and the optical antenna efficiency without computation of the absorption cross-section.
ERIC Educational Resources Information Center
Lopez-Real, Francis
2008-01-01
The Varignon parallelogram has always provided a simple geometric investigation for students that gives rise to a surprising result. It is possible to extend the Varignon investigation by looking at special quadrilaterals or by considering different dissection points along the sides. In the second of his two-part series, the author offers some…
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
NASA Astrophysics Data System (ADS)
Ford, I. J.
1997-11-01
The nucleation theorems relate the temperature and supersaturation dependence of the rate of nucleation of droplets from a metastable vapor phase to properties of the critical molecular cluster, the size that is approximately equally likely to grow or decay. They are derived here using a combination of statistical mechanics and cluster population dynamics, using an arbitrary model cluster definition. The theorems are employed to test the validity of the classical theory of homogeneous nucleation and its ``internally consistent'' form. It is found that the properties of the critical cluster for these models are incorrect, and it emerges that this occurs because the classical theory employs the free energy of a fixed droplet, rather than one free to take any position in space. Thus a term representing positional, or mixing, entropy is missing from the cluster free energy. A revised model is proposed, based on the capillarity approximation but with such a term included, and it is shown that it is fully consistent with the nucleation theorems. The model increases classical rates by factors of approximately 104-106. Other nucleation models should be tested for internal consistency using the same methods. Finally, the nucleation theorems are used to extract the excess internal energies of molecular clusters from experimental data for several substances.
Note on the theorems of Bjerknes and Crocco
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1946-01-01
The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
Type Theory, Computation and Interactive Theorem Proving
2015-09-01
Springer, Heidelberg, 61-76, 2014. [9] Jeremy Avigad and John Harrison , “Formally verified mathematics,” Communications of the ACM, 57(4):66-75, 2014. [10...inequalities," in Gerwin Klein and Ruben Gamboa, eds., Interactive Theorem Proving 2014, Springer, Heidelberg, 61-76, 2014. 9) Jeremy Avigad and John Harrison
Generalized Friedland's theorem for C0-semigroups
NASA Astrophysics Data System (ADS)
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An extension theorem for conformal gauge singularities
NASA Astrophysics Data System (ADS)
Lübbe, Christian; Tod, Paul
2009-11-01
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
The soft photon theorem for bremsstrahlung
Heller, L.
1990-01-01
We review this theorem and discuss the possible importance of the second term in the expansion of the cross section in powers of the photon momentum, especially for radiation from particle coming from the decay of resonances. 10 refs., 4 figs.
A non-differentiable Noether's theorem
NASA Astrophysics Data System (ADS)
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
"Dealing" with the Central Limit Theorem
ERIC Educational Resources Information Center
Matz, David C.; Hause, Emily L.
2008-01-01
We describe an easy-to-employ, hands-on demonstration using playing cards to illustrate the central limit theorem. This activity allows students to see how a collection of sample means drawn from a nonnormally distributed population will be normally distributed. Students who took part in the demonstration reported it to be helpful in understanding…
The time-rescaling theorem and its application to neural spike train data analysis.
Brown, Emery N; Barbieri, Riccardo; Ventura, Valérie; Kass, Robert E; Frank, Loren M
2002-02-01
Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
ERIC Educational Resources Information Center
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
Extending the Principal Axis Theorem to Fields Other than R.
ERIC Educational Resources Information Center
Friedberg, Stephen H.
1990-01-01
That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Aging and nonergodicity beyond the Khinchin theorem
Burov, S.; Metzler, R.; Barkai, E.
2010-01-01
The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics. PMID:20624984
Generalized Sampling Theorem for Bandpass Signals
NASA Astrophysics Data System (ADS)
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Fluctuation theorem for constrained equilibrium systems.
Gilbert, Thomas; Dorfman, J Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Fluctuation theorem for constrained equilibrium systems
NASA Astrophysics Data System (ADS)
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
About the Stokes decomposition theorem of waves
NASA Astrophysics Data System (ADS)
Lacaze, B.
2011-06-01
The Stokes decomposition theorem deals with the electrical field E→=X,Y of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a "strong definition" of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a "weak definition", solutions are given by elementary properties of bidimensional random variables.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Bidirectional Single-Electron Counting and the Fluctuation Theorem
NASA Astrophysics Data System (ADS)
Utsumi, Yasuhiro; Golubev, Dimitri; Marthaler, Michael; Saito, Keiji; Fujisawa, Toshimasa; Schoen, Gerd
2010-03-01
We investigate the direction-resolved full counting statistics of single-electron tunneling through a double quantum dot system and compare with predictions of the fluctuation theorem (FT) for Markovian stochastic processes. Experimental data obtained for GaAs/GaAlAs heterostructures appear to violate the FT. After analyzing various potential sources for the discrepancy we conclude that the nonequilibrium shot noise of the quantum point contact electrometer, which is used to study the transport, induces strong dot-level fluctuations which significantly influence the tunneling statistics. Taking these modifications into account we find consistency with the FT once we introduce the ``effective temperature.'' Y. Utsumi, D. S. Golubev, M. Marthaler, K. Saito, T. Fujisawa, Gerd Schoen, arXiv:0908.0229
[Objectivity of BSE symptoms using Bayes theorem].
Hässig, M; Urech Hässig, B; Knubben-Schweizer, G
2011-12-01
In clinical epidemiology the Bayes theorem finds ever more use to render clinical acting more objective. It is shown that unusual examinations of BSE (bovine spongiform encephalopathy) as noise producing with ladle covers may quite objectively be evaluated. With the help of the likelihood ratio computed thereby, also a ranking of importance (clinical utility) of symptoms can be provided. The single most important symptom for BSE is photosensibility.
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
Spontaneously broken spacetime symmetries and Goldstone's theorem.
Low, Ian; Manohar, Aneesh V
2002-03-11
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincaré and conformal invariance.
Infinite flag varieties and conjugacy theorems
Peterson, Dale H.; Kac, Victor G.
1983-01-01
We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Asynchronous networks: modularization of dynamics theorem
NASA Astrophysics Data System (ADS)
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
Mechanistic slumber vs. statistical insomnia: the early history of Boltzmann's H-theorem (1868-1877)
NASA Astrophysics Data System (ADS)
Badino, M.
2011-11-01
An intricate, long, and occasionally heated debate surrounds Boltzmann's H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt's 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In the first part, I discuss the development of Boltzmann's research from 1868 to the formulation of the H-theorem. This reconstruction shows that Boltzmann adopted a pluralistic strategy based on the interplay between a kinetic and a combinatorial approach. Moreover, it shows that the extensive use of asymptotic conditions allowed Boltzmann to bracket the problem of exceptions. In the second part I suggest that both Loschmidt's challenge and Boltzmann's response to it did not concern the H-theorem. The close relation between the theorem and the reversibility argument is a consequence of later investigations on the subject.
Applications of the Theorem of Pythagoras in R[superscript 3
ERIC Educational Resources Information Center
Srinivasan, V. K.
2010-01-01
Three distinct points A = (a, 0, 0) B = (0, b, 0) and (c, 0, 0) with abc not equal to 0 are taken, respectively on the "x", "y" and the "z"-axes of a rectangular coordinate system in R[superscript 3]. Using the converse of the theorem of Pythagoras, it is shown that the triangle [delta]ABC can never be a right-angled triangle. The result seems to…
Z{sub 2} index theorem for Majorana zero modes in a class D topological superconductor
Fukui, Takahiro; Fujiwara, Takanori
2010-11-01
We propose a Z{sub 2} index theorem for a generic topological superconductor in class D with a point defect. Introducing a particle-hole symmetry breaking term depending on a parameter and regarding it as a coordinate of an extra dimension, we define the index of the zero modes and corresponding topological invariant for such an extended Hamiltonian. It is shown that these are related with the number of the zero modes of the original Hamiltonian modulo 2.
The van Cittert-Zernike theorem for electromagnetic fields.
Ostrovsky, Andrey S; Martínez-Niconoff, Gabriel; Martínez-Vara, Patricia; Olvera-Santamaría, Miguel A
2009-02-02
The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2002-02-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
NASA Technical Reports Server (NTRS)
Lynnes, Chris
2014-01-01
Three current search engines are queried for ozone data at the GES DISC. The results range from sub-optimal to counter-intuitive. We propose a method to fix dataset search by implementing a robust relevancy ranking scheme. The relevancy ranking scheme is based on several heuristics culled from more than 20 years of helping users select datasets.
Future Fixed Target Facilities
Melnitchouk, Wolodymyr
2009-01-01
We review plans for future fixed target lepton- and hadron-scattering facilities, including the 12 GeV upgraded CEBAF accelerator at Jefferson Lab, neutrino beam facilities at Fermilab, and the antiproton PANDA facility at FAIR. We also briefly review recent theoretical developments which will aid in the interpretation of the data expected from these facilities.
Neal, Daniel R.
2000-01-01
A rigid mount and method of mounting for a wavefront sensor. A wavefront dissector, such as a lenslet array, is rigidly mounted at a fixed distance relative to an imager, such as a CCD camera, without need for a relay imaging lens therebetween.
A qualitative approach to Bayes' theorem.
Medow, Mitchell A; Lucey, Catherine R
2011-12-01
While decisions made according to Bayes' theorem are the academic normative standard, the theorem is rarely used explicitly in clinical practice. Yet the principles can be followed without intimidating mathematics. To do so, one can first categorise the prior-probability of the disease being tested for as very unlikely (less likely than 10%), unlikely (10-33%), uncertain (34-66%), likely (67-90%) or very likely (more likely than 90%). Usually, for disorders that are very unlikely or very likely, no further testing is needed. If the prior probability is unlikely, uncertain or likely, a test and a Bayesian-inspired update process incorporating the result can help. A positive result of a good test increases the probability of the disorder by one likelihood category (eg, from uncertain to likely) and a negative test decreases the probability by one category. If testing is needed to escape the extremes of likelihood (eg, a very unlikely but particularly dangerous condition or in the circumstance of population screening, or a very likely condition with a particularly noxious treatment), two tests may be needed to achieve. Negative results of tests with sensitivity ≥99% are sufficient to rule-out a diagnosis; positive results of tests with specificity ≥99% are sufficient to rule-in a diagnosis. This method overcomes some common heuristic errors: ignoring the base rate, probability adjustment errors and order effects. The simplicity of the method, while still adhering to the basic principles of Bayes' theorem, has the potential to increase its application in clinical practice.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Stochastic thermodynamics, fluctuation theorems and molecular machines
NASA Astrophysics Data System (ADS)
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Fluctuation theorem in dynamical systems with quenched disorder
NASA Astrophysics Data System (ADS)
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
NASA Astrophysics Data System (ADS)
Benincasa, Dionigi M. T.
2011-07-01
We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.
Fixed Target Collisions at STAR
NASA Astrophysics Data System (ADS)
Meehan, Kathryn C.
2016-12-01
The RHIC Beam Energy Scan (BES) program was proposed to look for the turn-off of signatures of the quark gluon plasma (QGP), search for a possible QCD critical point, and study the nature of the phase transition between hadronic and partonic matter. Previous results have been used to claim that the onset of deconfinement occurs at a center-of-mass energy of 7 GeV. Data from lower energies are needed to test if this onset occurs. The goal of the STAR Fixed-Target Program is to extend the collision energy range in BES II to energies that are likely below the onset of deconfinement. Currently, STAR has inserted a gold target into the beam pipe and conducted test runs at center-of-mass energies of 3.9 and 4.5 GeV. Tests have been done with both Au and Al beams. First physics results from a Coulomb potential analysis of Au + Au fixed-target collisions are presented and are found to be consistent with results from previous experiments. Furthermore, the Coulomb potential, which is sensitive to the Z of the projectile and degree of baryonic stopping, will be compared to published results from the AGS.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
De Finetti Theorem on the CAR Algebra
NASA Astrophysics Data System (ADS)
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
Kaufmann, Ralph M.; Khlebnikov, Sergei; Wehefritz-Kaufmann, Birgit
2012-11-15
Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians. The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of A{sub n} type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an A{sub k} singularity. We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties. - Highlights: Black-Right-Pointing-Pointer New method for analytically finding Dirac points. Black-Right-Pointing-Pointer Novel relation of level crossings to singularity theory. Black-Right-Pointing-Pointer More precise version of the von-Neumann-Wigner theorem for arbitrary smooth families of Hamiltonians of fixed size. Black-Right-Pointing-Pointer Analytical proof of the existence of Dirac points for the Gyroid wire network.
Nie, Xiaobing; Zheng, Wei Xing; Cao, Jinde
2016-12-01
In this paper, the coexistence and dynamical behaviors of multiple equilibrium points are discussed for a class of memristive neural networks (MNNs) with unbounded time-varying delays and nonmonotonic piecewise linear activation functions. By means of the fixed point theorem, nonsmooth analysis theory and rigorous mathematical analysis, it is proven that under some conditions, such n-neuron MNNs can have 5(n) equilibrium points located in ℜ(n), and 3(n) of them are locally μ-stable. As a direct application, some criteria are also obtained on the multiple exponential stability, multiple power stability, multiple log-stability and multiple log-log-stability. All these results reveal that the addressed neural networks with activation functions introduced in this paper can generate greater storage capacity than the ones with Mexican-hat-type activation function. Numerical simulations are presented to substantiate the theoretical results.
Beklaryan, Leva A
2011-03-31
A boundary value problem and an initial-boundary value problems are considered for a linear functional differential equation of point type. A suitable scale of functional spaces is introduced and existence theorems for solutions are stated in terms of this scale, in a form analogous to Noether's theorem. A key fact is established for the initial boundary value problem: the space of classical solutions of the adjoint equation must be extended to include impulsive solutions. A test for the pointwise completeness of solutions is obtained. The results presented are based on a formalism developed by the author for this type of equation. Bibliography: 7 titles.
Tipton, H.R.
1984-07-31
A fixed solar energy collector system has facing panels of different size forming a Vee-shaped trough open at its base and supporting a plurality of highly reflective convex reflectors strategically disposed upon said panels in reflective relationship to a plurality of Fresnel lenses positioned at the base of the trough. A suitable reflector, disposed beneath the Fresnel lenses, directs the reflected energy to a heat-needy target.
Fermat's point from five perspectives
NASA Astrophysics Data System (ADS)
Park, Jungeun; Flores, Alfinio
2015-04-01
The Fermat point of a triangle is the point such that minimizes the sum of the distances from that point to the three vertices. Five approaches to study the Fermat point of a triangle are presented in this article. First, students use a mechanical device using masses, strings and pulleys to study the Fermat point as the one that minimizes the potential energy of the system. Second, students use soap films between parallel planes connecting three pegs. The tension on the film will be minimal when the sum of distances is minimal. Third, students use an empirical approach, measuring distances in an interactive GeoGebra page. Fourth, students use Euclidean geometry arguments for two proofs based on the Torricelli configuration, and one using Viviani's Theorem. And fifth, the kinematic method is used to gain additional insight on the size of the angles between the segments joining the Fermat point with the vertices.
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
Unique Factorization and the Fundamental Theorem of Arithmetic
ERIC Educational Resources Information Center
Sprows, David
2017-01-01
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
Solving boundary-value electrostatics problems using Green's reciprocity theorem
NASA Astrophysics Data System (ADS)
Hu, Ben Yu-Kuang
2001-12-01
Formal solutions to electrostatics boundary-value problems are derived using Green's reciprocity theorem. This method provides a more transparent interpretation of the solutions than the standard Green's function derivation. An energy-based argument for the reciprocity theorem is also presented.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
On the Weighted Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Polezzi, M.
2006-01-01
The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…
Interactive Theorem Finding through Continuous Variation of Geometric Configurations.
ERIC Educational Resources Information Center
Schumann, Heinz
1991-01-01
Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
The First Fundamental Theorem of Invariant Theory for the Orthosymplectic Supergroup
NASA Astrophysics Data System (ADS)
Lehrer, G. I.; Zhang, R. B.
2017-01-01
We give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of Atiyah, Bott and Patodi to the supergroup context. We use methods from super-algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space. In this way, super Schur-Weyl-Brauer duality is established between the orthosymplectic supergroup of superdimension ( m|2 n) and the Brauer algebra with parameter m - 2 n. The result may be interpreted either in terms of the group scheme OSp( V) over C, where V is a finite dimensional super space, or as a statement about the orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra {Λ}. We take the latter point of view here, and also state a corresponding theorem for the orthosymplectic Lie superalgebra, which involves an extra invariant generator, the super-Pfaffian.
Mesa, Socorro; Hauser, Felix; Friberg, Markus; Malaguti, Emmanuelle; Fischer, Hans-Martin; Hennecke, Hauke
2008-01-01
Symbiotic N2 fixation in Bradyrhizobium japonicum is controlled by a complex transcription factor network. Part of it is a hierarchically arranged cascade in which the two-component regulatory system FixLJ, in response to a moderate decrease in oxygen concentration, activates the fixK2 gene. The FixK2 protein then activates not only a number of genes essential for microoxic respiration in symbiosis (fixNOQP and fixGHIS) but also further regulatory genes (rpoN1, nnrR, and fixK1). The results of transcriptome analyses described here have led to a comprehensive and expanded definition of the FixJ, FixK2, and FixK1 regulons, which, respectively, consist of 26, 204, and 29 genes specifically regulated in microoxically grown cells. Most of these genes are subject to positive control. Particular attention was addressed to the FixK2-dependent genes, which included a bioinformatics search for putative FixK2 binding sites on DNA (FixK2 boxes). Using an in vitro transcription assay with RNA polymerase holoenzyme and purified FixK2 as the activator, we validated as direct targets eight new genes. Interestingly, the adjacent but divergently oriented fixK1 and cycS genes shared the same FixK2 box for the activation of transcription in both directions. This recognition site may also be a direct target for the FixK1 protein, because activation of the cycS promoter required an intact fixK1 gene and either microoxic or anoxic, denitrifying conditions. We present evidence that cycS codes for a c-type cytochrome which is important, but not essential, for nitrate respiration. Two other, unexpected results emerged from this study: (i) specifically FixK1 seemed to exert a negative control on genes that are normally activated by the N2 fixation-specific transcription factor NifA, and (ii) a larger number of genes are expressed in a FixK2-dependent manner in endosymbiotic bacteroids than in culture-grown cells, pointing to a possible symbiosis-specific control. PMID:18689489
Fixed target facility at the SSC
Loken, S.C.; Morfin, J.G.
1985-01-01
The question of whether a facility for fixed target physics should be provided at the SSC must be answered before the final technical design of the SSC can be completed, particularly if the eventual form of extraction would influence the magnet design. To this end, an enthusiastic group of experimentalists, theoreticians and accelerator specialists have studied this point. The accelerator physics issues were addressed by a group led by E. Colton whose report is contained in these proceedings. The physics addressable by fixed target was considered by many of the Physics area working groups and in particular by the Structure Function Group. This report is the summary of the working group which considered various SSC fixed target experiments and determined which types of beams and detectors would be required. 13 references, 5 figures.
Splitting theorem for Z2n -supermanifolds
NASA Astrophysics Data System (ADS)
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert
2016-12-01
Smooth Z2n -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the 'scalar product' of the involved Z2n -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. The classical Batchelor-Gawȩdzki theorem says that any smooth supermanifold is diffeomorphic to the 'superization' ΠE of a vector bundle E. It is also known that this result fails in the complex analytic category. Hence, it is natural to ask whether an analogous statement goes through in the category of Z2n -supermanifolds with its local model made of formal power series. We give a positive answer to this question.
Differential diagnosis in immunohistochemistry with Bayes theorem.
Vollmer, Robin T
2009-05-01
When immunohistochemical stains that are specific for specific tumor diagnoses do not yield diagnostic results, we often turn to less specific immunohistochemical stains and consider the resulting lists of possible tumor types. Typically, such lists are ordered according to tumor sensitivities for the stains. In probability terminology, sensitivity is the conditional probability of a positive stain given a specific tumor. Yet, the most useful probability to know is the probability of a specific tumor diagnosis, given a set of staining results. Bayes theorem provides this probability. To illustrate its use for differential diagnosis, I apply it here to the situation of carcinomas of uncertain primary site and use the information provided by stains for cytokeratin 7 and cytokeratin 20.
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
Complex virial theorem and complex scaling
Junker, B.R.
1983-06-01
We present the simple generalization to complex energies of the normal global real scaling used for bound-state calculations to produce a variational energy which satisfies the virial theorem. We show that in two limiting cases, one or the other of which is almost always p satisfied in all calculations, the virially stabilized complex energy is sensitive to only the real part or the imaginary part of the complex virial expression. We then compute the virial expression for a number of wave functions for the 1s2s/sup 2/ /sup 2/S He/sup -/, 1s2s2p /sup 2/P/sup o/ He/sup -/, and 1s/sup 2/2s/sup 2/kp /sup 2/P/sup o/ Be/sup -/ resonances and the corresponding virially stabilized resonance energies. In all calculations one of the limiting cases was applicable.
Fixed solar energy concentrator
Houghton, A.J.; Knasel, T.M.
1981-01-20
An apparatus for the concentration of solar energy upon a fixed array of solar cells is disclosed. A transparent material is overlayed upon the cell array, and a diffuse reflective coating is applied to the surface area of the transparent medium in between cells. Radiant light, which reflects through the transparent layer and does not fall directly incident to a cell surface is reflected by the coating layer in an approximate cosine pattern. Thereafter, such light undergoes internal reflection and rediffusion until subsequently it either strikes a solar cell surface or is lost through the upper surface of the transparent material.
41. Detail showing meeting of two fixed land span segments, ...
41. Detail showing meeting of two fixed land span segments, bridge land span at left, viaduct at right. VIEW NORTH - Broadway Bridge, Spanning Foundry Street, MBTA Yard, Fort Point Channel, & Lehigh Street, Boston, Suffolk County, MA
BLOCK-FLOATING-POINT REALIZATION OF DIGITAL FILTERS
A realization for digital filters using block- floating - point arithmetic is proposed. A statistical model for roundoff noise is presented and used to compare block- floating - point with fixed-point and floating - point realizations.
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
Using a Card Trick to Illustrate Fixed Points and Stability
ERIC Educational Resources Information Center
Champanerkar, Jyoti; Jani, Mahendra
2015-01-01
Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…
Stability analysis of fixed points via chaos control.
Locher, M.; Johnson, G. A.; Hunt, E. R.
1997-12-01
This paper reviews recent advances in the application of chaos control techniques to the stability analysis of two-dimensional dynamical systems. We demonstrate how the system's response to one or multiple feedback controllers can be utilized to calculate the characteristic multipliers associated with an unstable periodic orbit. The experimental results, obtained for a single and two coupled diode resonators, agree well with the presented theory. (c) 1997 American Institute of Physics.
From Fixed Points to Chaos: Three Models of Delayed Discrimination
Barak, Omri; Sussillo, David; Romo, Ranulfo; Tsodyks, Misha; Abbott, L.F.
2013-01-01
Working memory is a crucial component of most cognitive tasks. Its neuronal mechanisms are still unclear despite intensive experimental and theoretical explorations. Most theoretical models of working memory assume both time-invariant neural representations and precise connectivity schemes based on the tuning properties of network neurons. A different, more recent class of models assumes randomly connected neurons that have no tuning to any particular task, and bases task performance purely on adjustment of network readout. Intermediate between these schemes are networks that start out random but are trained by a learning scheme. Experimental studies of a delayed vibrotactile discrimination task indicate that some of the neurons in prefrontal cortex are persistently tuned to the frequency of a remembered stimulus, but the majority exhibit more complex relationships to the stimulus that vary considerably across time. We compare three models, ranging from a highly organized linear attractor model to a randomly connected network with chaotic activity, with data recorded during this task. The random network does a surprisingly good job of both performing the task and matching certain aspects of the data. The intermediate model, in which an initially random network is partially trained to perform the working memory task by tuning its recurrent and readout connections, provides a better description, although none of the models matches all features of the data. Our results suggest that prefrontal networks may begin in a random state relative to the task and initially rely on modified readout for task performance. With further training, however, more tuned neurons with less time-varying responses should emerge as the networks become more structured. PMID:23438479
The Fixed-Point Theory of Strictly Causal Functions
2013-06-09
mechanism, present in all but the most trivial systems. But it makes systems self - referential , with one signal depending on another, and vice versa (see...principle, and study the related convergence process . 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Same as Report (SAR...principle, and study the related convergence process . 1 Introduction This work is part of a larger effort aimed at the construction of well defined
Infrared Behavior and Fixed Points in Landau-Gauge QCD
NASA Astrophysics Data System (ADS)
Pawlowski, Jan M.; Litim, Daniel F.; Nedelko, Sergei; von Smekal, Lorenz
2004-10-01
We investigate the infrared behavior of gluon and ghost propagators in Landau-gauge QCD by means of an exact renormalization group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimization procedure is devised to remove residual regulator dependences. In Landau-gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.
Global stabilization using LSS-Theorem: Applications to Robotics and Aerospace Vehicles
NASA Astrophysics Data System (ADS)
Selman, AbdulRazzak
Underactuated mechanical systems are gaining interest as they can sometimes provide the desired motion or functionality at reduced cost due to their using fewer expensive actuators. The term "underactuated" refers to the fact that such mechanical systems have fewer actuators than degrees of freedom, which makes them very difficult to control. Moreover, underactuated robots have nonlinear dynamics which must be tackled with nonlinear control techniques. Furthermore, control theory for underactuated mechanical systems has been an active area of research for the past 15-20 years. Most of the research has focused on local and global asymptotic stabilization by feedback. Underactuated systems can either possess nonminimum phase or minimum phase characteristics. For minimum phase underactuated systems, the stabilization problem is rather simple and many existing control design methodologies have been proved powerful in providing a solution to this problem. For nonminimum phase underactuated systems, asymptotic stabilization problem has been, and still is, an attractive subject to the researchers in the field of nonlinear control system and theory. In particular, global asymptotic stabilization (GAS) at a desired equilibrium point of such systems by means of a single smooth static or dynamic state feedback law is still largely an open problem in the literature. In this thesis, the problem of GAS via a smooth static state feedback law is addressed for a class of an underactuated nonlinear system that is affine (possibly non affine) in the control, partially feedback linearizable, nonminimum phase and (possibly) has a non-integrable acceleration constraint. The core result of the thesis is formulated through a theorem that the author refers to through this thesis as the Legend of Salah Salman (LSS) Theorem. LSS theorem states the existence of a smooth static state feedback law that globally asymptotically stabilizes the origin of the nonlinear underactuated system that is
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Lumley, J. L.; Abid, R.
1994-01-01
A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.
Hall, David R.; Bartholomew, David B.; Moon, Justin; Koehler, Roger O.
2009-09-08
An apparatus for fixing computational latency within a deterministic region on a network comprises a network interface modem, a high priority module and at least one deterministic peripheral device. The network interface modem is in communication with the network. The high priority module is in communication with the network interface modem. The at least one deterministic peripheral device is connected to the high priority module. The high priority module comprises a packet assembler/disassembler, and hardware for performing at least one operation. Also disclosed is an apparatus for executing at least one instruction on a downhole device within a deterministic region, the apparatus comprising a control device, a downhole network, and a downhole device. The control device is near the surface of a downhole tool string. The downhole network is integrated into the tool string. The downhole device is in communication with the downhole network.
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
Fixed Wages, Layoffs, Unemployment Compensation, and Welfare.
1976-10-01
feasibility and optimality of alternative employment contracts. For the case where layoffs are prohibited, they demonstrate that both the fixed wage--constant...society’s point of view. In the case with layoffs , they show that the competitive mechanism leads to a less than optimal number of layoffs , and...demonstrate that unemployment insurance with less than complete experience rating lowers the cost of layoffs to the firm and encourages labor mobility. In the
NASA Astrophysics Data System (ADS)
Cornaglia, Bruno; Young, Gavin; Marchetta, Antonio
2015-12-01
Fixed broadband network deployments are moving inexorably to the use of Next Generation Access (NGA) technologies and architectures. These NGA deployments involve building fiber infrastructure increasingly closer to the customer in order to increase the proportion of fiber on the customer's access connection (Fibre-To-The-Home/Building/Door/Cabinet… i.e. FTTx). This increases the speed of services that can be sold and will be increasingly required to meet the demands of new generations of video services as we evolve from HDTV to "Ultra-HD TV" with 4k and 8k lines of video resolution. However, building fiber access networks is a costly endeavor. It requires significant capital in order to cover any significant geographic coverage. Hence many companies are forming partnerships and joint-ventures in order to share the NGA network construction costs. One form of such a partnership involves two companies agreeing to each build to cover a certain geographic area and then "cross-selling" NGA products to each other in order to access customers within their partner's footprint (NGA coverage area). This is tantamount to a bi-lateral wholesale partnership. The concept of Fixed Access Network Sharing (FANS) is to address the possibility of sharing infrastructure with a high degree of flexibility for all network operators involved. By providing greater configuration control over the NGA network infrastructure, the service provider has a greater ability to define the network and hence to define their product capabilities at the active layer. This gives the service provider partners greater product development autonomy plus the ability to differentiate from each other at the active network layer.
47 CFR 22.591 - Channels for point-to-point operation.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 2 2013-10-01 2013-10-01 false Channels for point-to-point operation. 22.591... PUBLIC MOBILE SERVICES Paging and Radiotelephone Service Point-To-Point Operation § 22.591 Channels for point-to-point operation. The following channels are allocated for assignment to fixed transmitters...
47 CFR 22.591 - Channels for point-to-point operation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 2 2011-10-01 2011-10-01 false Channels for point-to-point operation. 22.591... PUBLIC MOBILE SERVICES Paging and Radiotelephone Service Point-To-Point Operation § 22.591 Channels for point-to-point operation. The following channels are allocated for assignment to fixed transmitters...
47 CFR 22.591 - Channels for point-to-point operation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Channels for point-to-point operation. 22.591... PUBLIC MOBILE SERVICES Paging and Radiotelephone Service Point-To-Point Operation § 22.591 Channels for point-to-point operation. The following channels are allocated for assignment to fixed transmitters...
47 CFR 22.591 - Channels for point-to-point operation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 2 2012-10-01 2012-10-01 false Channels for point-to-point operation. 22.591... PUBLIC MOBILE SERVICES Paging and Radiotelephone Service Point-To-Point Operation § 22.591 Channels for point-to-point operation. The following channels are allocated for assignment to fixed transmitters...
47 CFR 22.591 - Channels for point-to-point operation.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 2 2014-10-01 2014-10-01 false Channels for point-to-point operation. 22.591... PUBLIC MOBILE SERVICES Paging and Radiotelephone Service Point-To-Point Operation § 22.591 Channels for point-to-point operation. The following channels are allocated for assignment to fixed transmitters...
NASA Astrophysics Data System (ADS)
Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga
2016-02-01
We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.
Non-linear energy conservation theorem in the framework of special relativity
NASA Astrophysics Data System (ADS)
Pérez Teruel, Ginés R.
2015-07-01
In this work we revisit the study of the gravitational interaction in the context of the special theory of relativity. It is found that, as long as the equivalence principle is respected, a relativistic nonlinear energy conservation theorem arises in a natural way. We interpret that this nonlinear conservation law stresses the nonlinear character of the gravitational interaction. The theorem reproduces the energy conservation theorem of Newtonian mechanics in the corresponding low energy limit, but also allows to derive some standard results of post-Newtonian gravity, such as the formula of the gravitational redshift. Guided by this conservation law, we develop a Lagrangian formalism for a particle in a gravitational field. We realize that the Lagrangian can be written in an explicit covariant fashion, and turns out to be the geodesic Lagrangian of a curved Lorentzian manifold. Therefore, any attempt to describe gravity within the special theory, leads outside their own domains towards a curved space-time. Thus, the pedagogical content of the paper may be useful as a starting point to discuss the problem of gravitation in the context of the special theory, as a preliminary step before introducing general relativity.
Nyquist-Shannon sampling theorem applied to refinements of the atomic pair distribution function
NASA Astrophysics Data System (ADS)
Farrow, Christopher L.; Shaw, Margaret; Kim, Hyunjeong; Juhás, Pavol; Billinge, Simon J. L.
2011-10-01
We have systematically studied the optimal real-space sampling of atomic pair distribution (PDF) data by comparing refinement results from oversampled and resampled data. Based on nickel and a complex perovskite system, we show that not only is the optimal sampling bounded by the Nyquist interval described by the Nyquist-Shannon (NS) sampling theorem as expected, but near this sampling interval, the data points in the PDF are minimally correlated, which results in more reliable uncertainty estimates in the modeling. Surprisingly, we find that PDF refinements quickly become unstable for data on coarser grids. Although the Nyquist-Shannon sampling theorem is well known, it has not been applied to PDF refinements, despite the growing popularity of the PDF method and its adoption in a growing number of communities. Here, we give explicit expressions for the application of NS sampling theorem to the PDF case, and establish through modeling that it is working in practice, which lays the groundwork for this to become more widely adopted. This has implications for the speed and complexity of possible refinements that can be carried out many times faster than currently with no loss of information, and it establishes a theoretically sound limit on the amount of information contained in the PDF that will prevent over-parametrization during modeling.
Applying the multivariate time-rescaling theorem to neural population models
Gerhard, Felipe; Haslinger, Robert; Pipa, Gordon
2011-01-01
Statistical models of neural activity are integral to modern neuroscience. Recently, interest has grown in modeling the spiking activity of populations of simultaneously recorded neurons to study the effects of correlations and functional connectivity on neural information processing. However any statistical model must be validated by an appropriate goodness-of-fit test. Kolmogorov-Smirnov tests based upon the time-rescaling theorem have proven to be useful for evaluating point-process-based statistical models of single-neuron spike trains. Here we discuss the extension of the time-rescaling theorem to the multivariate (neural population) case. We show that even in the presence of strong correlations between spike trains, models which neglect couplings between neurons can be erroneously passed by the univariate time-rescaling test. We present the multivariate version of the time-rescaling theorem, and provide a practical step-by-step procedure for applying it towards testing the sufficiency of neural population models. Using several simple analytically tractable models and also more complex simulated and real data sets, we demonstrate that important features of the population activity can only be detected using the multivariate extension of the test. PMID:21395436
Colligative Properties of Solutions: I. Fixed Concentrations
NASA Astrophysics Data System (ADS)
Alexander, Kenneth S.; Biskup, Marek; Chayes, Lincoln
2005-05-01
Using the formalism of rigorous statistical mechanics, we study the phenomena of phase separation and freezing-point depression upon freezing of solutions. Specifically, we devise an Ising-based model of a solvent--solute system and show that, in the ensemble with a fixed amount of solute, a macroscopic phase separation occurs in an interval of values of the chemical potential of the solvent. The boundaries of the phase separation domain in the phase diagram are characterized and shown to asymptotically agree with the formulas used in heuristic analyses of freezing-point depression. The limit of infinitesimal concentrations is described in a subsequent paper.
The Pythagorean Theorem and the Solid State
NASA Astrophysics Data System (ADS)
Kelly, Brenda S.; Splittgerber, Allen G.
2005-05-01
Solid-state parameters such as radius ratios, packing efficiencies, and crystal densities may be calculated for various crystal structures from basic Euclidean geometry relating to the Pythagorean theorem of right triangles. Because simpler cases are often discussed in the standard inorganic chemistry texts, this article only presents calculations for closest-packed A-type lattices (one type of particle) and several compound AB lattices (A and B particles) including sodium chloride, cesium chloride, zinc blende (sphalerite), wurtzite, and fluorite. For A-type metallic crystals, the use of recommended values of atomic radii results in calculated densities within 1% of observed values. For AB lattices, assuming ionic crystals, the use of recommended values of ionic radii results in density determinations that are usually but not always close to observed values. When there is covalent character to the bonding, the use of covalent radii results in calculated densities that correlate well with observed values. If interionic or interatomic spacings are used, the calculated densities are always close to the observed values. As indicated by a survey of the standard inorganic texts, these calculations are generally not presented. However, as an illustration of the application of simple mathematical principles to the study of chemistry, discussion of the methods presented in this manuscript may be of value in classroom presentations pertaining to the solid state.
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
Nonequilibrium fluctuation theorems in the presence of local heating
NASA Astrophysics Data System (ADS)
Pradhan, Punyabrata; Kafri, Yariv; Levine, Dov
2008-04-01
We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of ⟨exp(-βW)⟩ to its theoretical mean value, where W is the work done on the test system and β is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.
Generalized Browder's and Weyl's theorems for Banach space operators
NASA Astrophysics Data System (ADS)
Curto, Raúl E.; Han, Young Min
2007-12-01
We find necessary and sufficient conditions for a Banach space operator T to satisfy the generalized Browder's theorem. We also prove that the spectral mapping theorem holds for the Drazin spectrum and for analytic functions on an open neighborhood of [sigma](T). As applications, we show that if T is algebraically M-hyponormal, or if T is algebraically paranormal, then the generalized Weyl's theorem holds for f(T), where f[set membership, variant]H((T)), the space of functions analytic on an open neighborhood of [sigma](T). We also show that if T is reduced by each of its eigenspaces, then the generalized Browder's theorem holds for f(T), for each f[set membership, variant]H([sigma](T)).
Gibbs Paradox Revisited from the Fluctuation Theorem with Absolute Irreversibility
NASA Astrophysics Data System (ADS)
Murashita, Yûto; Ueda, Masahito
2017-02-01
The inclusion of the factor ln (1 /N !) in the thermodynamic entropy proposed by Gibbs is shown to be equivalent to the validity of the fluctuation theorem with absolute irreversibility for gas mixing.
The Pythagorean Theorem: II. The infinite discrete case
Kadison, Richard V.
2002-01-01
The study of the Pythagorean Theorem and variants of it as the basic result of noncommutative, metric, Euclidean Geometry is continued. The emphasis in the present article is the case of infinite discrete dimensionality. PMID:16578869
Wigner-Araki-Yanase theorem beyond conservation laws
NASA Astrophysics Data System (ADS)
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
Comparison theorems for neutral stochastic functional differential equations
NASA Astrophysics Data System (ADS)
Bai, Xiaoming; Jiang, Jifa
2016-05-01
The comparison theorems under Wu and Freedman's order are proved for neutral stochastic functional differential equations with finite or infinite delay whose drift terms satisfy the quasimonotone condition and diffusion term is the same.
Forest Carbon Uptake and the Fundamental Theorem of Calculus
ERIC Educational Resources Information Center
Zobitz, John
2013-01-01
Using the fundamental theorem of calculus and numerical integration, we investigate carbon absorption of ecosystems with measurements from a global database. The results illustrate the dynamic nature of ecosystems and their ability to absorb atmospheric carbon.
Fluctuation theorem in driven nonthermal systems with quenched disorder
Reichhardt, Charles; Reichhardt, C J; Drocco, J A
2009-01-01
We demonstrate that the fluctuation theorem of Evans and Searles can be used to characterize the class of dynamics that arises in nonthermal systems of collectively interacting particles driven over random quenched disorder. By observing the frequency of entropy-destroying trajectories, we show that there are specific dynamical regimes near depinning in which this theorem holds. Hence the fluctuation theorem can be used to characterize a significantly wider class of non-equilibrium systems than previously considered. We discuss how the fluctuation theorem could be tested in specific systems where noisy dynamics appear at the transition from a pinned to a moving phase such as in vortices in type-II superconductors, magnetic domain walls, and dislocation dynamics.
A Computer Science Version of Goedel’s Theorem.
1983-08-01
The author presents a simplified proof of Godel’s theorem by appealing to well-known programming concepts. The significance of Goedel’s result to computer science , mathematics and logic is discussed. (Author)
Two time physics and Hamiltonian Noether theorem for gauge systems
Nieto, J. A.; Ruiz, L.; Silvas, J.; Villanueva, V. M.
2006-09-25
Motivated by two time physics theory we revisited the Noether theorem for Hamiltonian constrained systems. Our review presents a novel method to show that the gauge transformations are generated by the conserved quantities associated with the first class constraints.
Conformal frames and the validity of Birkhoff's theorem
NASA Astrophysics Data System (ADS)
Capozziello, S.; Sáez-Gómez, D.
2012-07-01
Birkhoff's theorem is one of the most important statements of Einstein's general relativity, which generally can not be extended to modified theories of gravity. Here we study the validity of the theorem in scalar-tensor theories using a perturbative approach, and compare the results in the so-called Einstein and Jordan frames. The implications of the results question the physical equivalence between both frames, at least in perturbations.
No-broadcasting theorem and its classical counterpart.
Kalev, Amir; Hen, Itay
2008-05-30
Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.
Levinson theorem for Aharonov-Bohm scattering in two dimensions
Sheka, Denis D.; Mertens, Franz G.
2006-11-15
We apply the recently generalized Levinson theorem for potentials with inverse-square singularities [Sheka et al., Phys. Rev. A 68, 012707 (2003)] to Aharonov-Bohm systems in two dimensions (2D). By this theorem, the number of bound states in a given mth partial wave is related to the phase shift and the magnetic flux. The results are applied to 2D soliton-magnon scattering.
Crawford, John R; Garthwaite, Paul H; Betkowska, Karolina
2009-05-01
Most neuropsychologists are aware that, given the specificity and sensitivity of a test and an estimate of the base rate of a disorder, Bayes' theorem can be used to provide a post-test probability for the presence of the disorder given a positive test result (and a post-test probability for the absence of a disorder given a negative result). However, in the standard application of Bayes' theorem the three quantities (sensitivity, specificity, and the base rate) are all treated as fixed, known quantities. This is very unrealistic as there may be considerable uncertainty over these quantities and therefore even greater uncertainty over the post-test probability. Methods of obtaining interval estimates on the specificity and sensitivity of a test are set out. In addition, drawing and extending upon work by Mossman and Berger (2001), a Monte Carlo method is used to obtain interval estimates for post-test probabilities. All the methods have been implemented in a computer program, which is described and made available (www.abdn.ac.uk/~psy086/dept/BayesPTP.htm). When objective data on the base rate are lacking (or have limited relevance to the case at hand) the program elicits opinion for the pre-test probability.
Configurable hot spot fixing system
NASA Astrophysics Data System (ADS)
Kajiwara, Masanari; Kobayashi, Sachiko; Mashita, Hiromitsu; Aburada, Ryota; Furuta, Nozomu; Kotani, Toshiya
2014-03-01
Hot spot fixing (HSF) method has been used to fix many hot spots automatically. However, conventional HSF based on a biasing based modification is difficult to fix many hot spots under a low-k1 lithography condition. In this paper we proposed a new HSF, called configurable hotspot fixing system. The HSF has two major concepts. One is a new function to utilize vacant space around a hot spot by adding new patterns or extending line end edges around the hot spot. The other is to evaluate many candidates at a time generated by the new functions. We confirmed the proposed HSF improves 73% on the number of fixing hot spots and reduces total fixing time by 50% on a device layout equivalent to 28nm-node. The result shows the proposed HSF is effective for layouts under the low-k1 lithography condition.
The PBR theorem: Whose side is it on?
NASA Astrophysics Data System (ADS)
Ben-Menahem, Yemima
2017-02-01
This paper examines the implications of the PBR theorem for the debate on the reality of the quantum state. The theorem seeks to undermine epistemic interpretations of the quantum state and support realist interpretations thereof, but there remains ambiguity about the precise nature of epistemic interpretations, and thus ambiguity about the implications of the theorem. The aim of this paper is to examine a radical epistemic interpretation that is not undermined by the theorem and is, arguably, strengthened by it. It is this radical interpretation, rather than the one assumed by the PBR theorem, that many epistemic theorists subscribe to. In order to distinguish the radical epistemic interpretation from alternative interpretations of quantum states-in particular, to distinguish it from instrumentalism-a historical comparison of different approaches to the meaning of quantum probabilities is provided. The comparison highlights, in particular, Schrödinger's work on the nature of quantum probabilities as distinct from probabilities in statistical mechanics, and the implications of this distinction for an epistemic interpretation of probability in the two areas. Schrödinger's work also helps to identify the difficulties in the PBR definition of an epistemic interpretation and is shown to anticipate the radical alternative that is not undermined by the theorem.
ERIC Educational Resources Information Center
Dobbs, David E.
2005-01-01
The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…
Simple Robust Fixed Lag Smoothing
1988-12-02
SIMPLE ROBUST FIXED LAG SMOOTHING by ~N. D. Le R.D. Martin 4 TECHNICAL RlEPORT No. 149 December 1988 Department of Statistics, GN-22 Accesion For...frLsD1ist Special A- Z Simple Robust Fixed Lag Smoothing With Application To Radar Glint Noise * N. D. Le R. D. Martin Department of Statistics, GN...smoothers. The emphasis here is on fixed-lag smoothing , as opposed to the use of existing robust fixed interval smoothers (e.g., as in Martin, 1979
Dose fractionation theorem in 3-D reconstruction (tomography)
Glaeser, R.M.
1997-02-01
It is commonly assumed that the large number of projections for single-axis tomography precludes its application to most beam-labile specimens. However, Hegerl and Hoppe have pointed out that the total dose required to achieve statistical significance for each voxel of a computed 3-D reconstruction is the same as that required to obtain a single 2-D image of that isolated voxel, at the same level of statistical significance. Thus a statistically significant 3-D image can be computed from statistically insignificant projections, as along as the total dosage that is distributed among these projections is high enough that it would have resulted in a statistically significant projection, if applied to only one image. We have tested this critical theorem by simulating the tomographic reconstruction of a realistic 3-D model created from an electron micrograph. The simulations verify the basic conclusions of high absorption, signal-dependent noise, varying specimen contrast and missing angular range. Furthermore, the simulations demonstrate that individual projections in the series of fractionated-dose images can be aligned by cross-correlation because they contain significant information derived from the summation of features from different depths in the structure. This latter information is generally not useful for structural interpretation prior to 3-D reconstruction, owing to the complexity of most specimens investigated by single-axis tomography. These results, in combination with dose estimates for imaging single voxels and measurements of radiation damage in the electron microscope, demonstrate that it is feasible to use single-axis tomography with soft X-ray microscopy of frozen-hydrated specimens.
Central limit theorem: the cornerstone of modern statistics
2017-01-01
According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding. PMID:28367284
Formalization of the Integral Calculus in the PVS Theorem Prover
NASA Technical Reports Server (NTRS)
Butler, Ricky W.
2004-01-01
The PVS Theorem prover is a widely used formal verification tool used for the analysis of safety-critical systems. The PVS prover, though fully equipped to support deduction in a very general logic framework, namely higher-order logic, it must nevertheless, be augmented with the definitions and associated theorems for every branch of mathematics and Computer Science that is used in a verification. This is a formidable task, ultimately requiring the contributions of researchers and developers all over the world. This paper reports on the formalization of the integral calculus in the PVS theorem prover. All of the basic definitions and theorems covered in a first course on integral calculus have been completed.The theory and proofs were based on Rosenlicht's classic text on real analysis and follow the traditional epsilon-delta method. The goal of this work was to provide a practical set of PVS theories that could be used for verification of hybrid systems that arise in air traffic management systems and other aerospace applications. All of the basic linearity, integrability, boundedness, and continuity properties of the integral calculus were proved. The work culminated in the proof of the Fundamental Theorem Of Calculus. There is a brief discussion about why mechanically checked proofs are so much longer than standard mathematics textbook proofs.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
Weighted Sobolev theorem in Lebesgue spaces with variable exponent
NASA Astrophysics Data System (ADS)
Samko, N. G.; Samko, S. G.; Vakulov, B. G.
2007-11-01
For the Riesz potential operator I[alpha] there are proved weighted estimates within the framework of weighted Lebesgue spaces Lp([dot operator])([Omega],w) with variable exponent. In case [Omega] is a bounded domain, the order [alpha]=[alpha](x) is allowed to be variable as well. The weight functions are radial type functions "fixed" to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential operators on the unit sphere .
Fixed drug eruption to sitagliptin.
Gupta, Mrinal; Gupta, Anish
2015-01-01
Fixed drug eruption is a common adverse effect seen with various drugs notably antibiotics, antiepileptics and non-steroidal anti-inflammatory drugs. Herein we report a case of Sitagliptin induced fixed drug eruption in a 46 year old female who developed circumscribed, erythematous macules all over the body within one week of initiation of Sitagliptin. The lesions resolved with residual hyperpigmentation on cessation of the drug. The diagnosis was confirmed by an oral provocation test which led to a reactivation of the lesions. To the best of our knowledge, this is the first case of fixed drug eruption to Sitagliptin reported in the literature.