On Krasnoselskii's Cone Fixed Point Theorem
Directory of Open Access Journals (Sweden)
Man Kam Kwong
2008-04-01
Full Text Available In recent years, the Krasnoselskii fixed point theorem for cone maps and its many generalizations have been successfully applied to establish the existence of multiple solutions in the study of boundary value problems of various types. In the first part of this paper, we revisit the Krasnoselskii theorem, in a more topological perspective, and show that it can be deduced in an elementary way from the classical Brouwer-Schauder theorem. This viewpoint also leads to a topology-theoretic generalization of the theorem. In the second part of the paper, we extend the cone theorem in a different direction using the notion of retraction and show that a stronger form of the often cited Leggett-Williams theorem is a special case of this extension.
Fixed point theorems in spaces and -trees
Directory of Open Access Journals (Sweden)
Kirk WA
2004-01-01
Full Text Available We show that if is a bounded open set in a complete space , and if is nonexpansive, then always has a fixed point if there exists such that for all . It is also shown that if is a geodesically bounded closed convex subset of a complete -tree with , and if is a continuous mapping for which for some and all , then has a fixed point. It is also noted that a geodesically bounded complete -tree has the fixed point property for continuous mappings. These latter results are used to obtain variants of the classical fixed edge theorem in graph theory.
Some Generalizations of Jungck's Fixed Point Theorem
Directory of Open Access Journals (Sweden)
J. R. Morales
2012-01-01
Full Text Available We are going to generalize the Jungck's fixed point theorem for commuting mappings by mean of the concepts of altering distance functions and compatible pair of mappings, as well as, by using contractive inequalities of integral type and contractive inequalities depending on another function.
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
Duan's fixed point theorem: Proof and generalization
Directory of Open Access Journals (Sweden)
Arkowitz Martin
2006-01-01
Full Text Available Let be an H-space of the homotopy type of a connected, finite CW-complex, any map and the th power map. Duan proved that has a fixed point if . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a -structure as defined by Hemmi-Morisugi-Ooshima. The conclusion is that and each has a fixed point.
Duan's fixed point theorem: proof and generalization
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Let X be an H-space of the homotopy type of a connected, finite CW-complex, f:X→X any map and p k :X→X the k th power map. Duan proved that p k f :X→X has a fixed point if k≥2 . We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a θ -structure μ θ :X→X as defined by Hemmi-Morisugi-Ooshima. The conclusion is that μ θ f and f μ θ each has a fixed point.
Duan's fixed point theorem: Proof and generalization
Directory of Open Access Journals (Sweden)
Martin Arkowitz
2006-02-01
Full Text Available Let X be an H-space of the homotopy type of a connected, finite CW-complex, f:XÃ¢Â†Â’X any map and pk:XÃ¢Â†Â’X the kth power map. Duan proved that pkf:XÃ¢Â†Â’X has a fixed point if kÃ¢Â‰Â¥2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map is played by a ÃŽÂ¸-structure ÃŽÂ¼ÃŽÂ¸:XÃ¢Â†Â’X as defined by Hemmi-Morisugi-Ooshima. The conclusion is that ÃŽÂ¼ÃŽÂ¸f and fÃŽÂ¼ÃŽÂ¸ each has a fixed point.
Fixed point theorems for generalized Lipschitzian semigroups
Directory of Open Access Journals (Sweden)
Jong Soo Jung
2001-01-01
semigroup of K into itself, that is, for s∈G, ‖Tsx−Tsy‖≤as‖x−y‖+bs(‖x−Tsx‖+‖y−Tsy‖+cs(‖x−Tsy‖+‖y−Tsx‖, for x,y∈K where as,bs,cs>0 such that there exists a t1∈G such that bs+cs<1 for all s≽t1. It is proved that if there exists a closed subset C of K such that ⋂sco¯{Ttx:t≽s}⊂C for all x∈K, then with [(α+βp(αp⋅2p−1−1/(cp−2p−1βp⋅Np]1/p<1 has a common fixed point, where α=lim sups(as+bs+cs/(1-bs-cs and β=lim sups(2bs+2cs/(1-bs-cs.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
Two fixed point theorems on quasi-metric spaces via mw- distances
Energy Technology Data Exchange (ETDEWEB)
Alegre, C.
2017-07-01
In this paper we prove a Banach-type fixed point theorem and a Kannan-type theorem in the setting of quasi-metric spaces using the notion of mw-distance. These theorems generalize some results that have recently appeared in the literature. (Author)
Directory of Open Access Journals (Sweden)
Badridatt Pant
2014-02-01
Full Text Available In this paper, we prove a common fixed point theorem for finite number of self mappings in Menger probabilistic quasi metric space. Our result improves and extends the results of Rezaiyan et al. [A common fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 37 (2008 1153-1157.], Miheţ [A note on a fixed point theorem in Menger probabilistic quasi-metric spaces, Chaos, Solitons and Fractals 40 (2009 2349-2352], Pant and Chauhan [Fixed points theorems in Menger probabilistic quasi metric spaces using weak compatibility, Internat. Math. Forum 5 (6 (2010 283-290] and Sastry et al. [A fixed point theorem in Menger PQM-spaces using weak compatibility, Internat. Math. Forum 5 (52 (2010 2563-2568
A fixed-point theorem for holomorphic maps
TIMONEY, RICHARD
1994-01-01
PUBLISHED We consider the action on the maximal ideal space M of the algebra H of bounded analytic functions, induced by an analytic self?map of a complex manifold, X. After some general preliminaries, we focus on the question of the existence of fixed points for this action, in the case when X is the open unit disk, D. We classify the fixed?point?free M?obius transformations, and we show that for an arbitrary analytic map from D into itself, the induced map has a fixed poin...
Common fixed point theorems for weakly compatible mappings in fuzzy metric spaces
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2013-05-01
Full Text Available The aim of this paper is to prove a common fixed point theorem for a pair of weakly compatible mappings in fuzzy metric space by using the (CLRg property. An example is also furnished which demonstrates the validity of our main result. As an application to our main result, we present a fixed point theorem for two finite families of self mappings in fuzzy metric space by using the notion of pairwise commuting. Our results improve the results of Sedghi, Shobe and Aliouche [A common fixed point theorem for weakly compatible mappings in fuzzy metric spaces, Gen. Math. 18(3 (2010, 3-12 MR2735558].
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.
Some common random fixed point theorems for contractive type conditions in cone random metric spaces
Directory of Open Access Journals (Sweden)
Saluja Gurucharan S.
2016-08-01
Full Text Available In this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.
Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces
Directory of Open Access Journals (Sweden)
Erdal Karapınar
2010-01-01
Full Text Available Some results of (Ćirić, 1974 on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.
Extension of Kirk-Saliga Fixed Point Theorem in a Metric Space with a Reflexive Digraph
Directory of Open Access Journals (Sweden)
Karim Chaira
2018-01-01
Full Text Available We extend the result of Kirk-Saliga and we generalize Alfuraidan and Khamsi theorem for reflexive graphs. As a consequence, we obtain the ordered version of Caristi’s fixed point theorem. Some concrete examples are given to support the obtained results.
A Borsuk-Ulam type generalization of the Leray-Schauder fixed point theorem
International Nuclear Information System (INIS)
Prykarpatsky, A.K.
2007-05-01
A generalization of the classical Leray-Schauder fixed point theorem, based on the infinite-dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. (author)
Some fixed point theorems on non-convex sets
Directory of Open Access Journals (Sweden)
Mohanasundaram Radhakrishnan
2017-10-01
Full Text Available In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\\to K$ is a nonexpansive map satisfying $\\frac{x+Tx}{2}\\in K$ for all $x\\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$
Fixed point theorems in complex valued metric spaces
Directory of Open Access Journals (Sweden)
Naval Singh
2016-07-01
Full Text Available The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces. Our results generalize and extend the results of Azam et al. (2011 [1], Sintunavarat and Kumam (2012 [2], Rouzkard and Imdad (2012 [3], Sitthikul and Saejung (2012 [4] and Dass and Gupta (1975 [5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also furnished.
Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Radenović Stojan
2010-01-01
Full Text Available We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2013-01-01
Full Text Available The objective of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in fuzzy metric spaces. Some illustrative examples are furnished which demonstrate the validity of the hypotheses and degree of utility of our results. We derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. As an application to our main result, we prove an integral-type fixed point theorem in fuzzy metric space. Our results improve and extend a host of previously known results including the ones contained in Imdad et al. (2012.
Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem
Babaei, E.; Evstigneev, I. V.; Pirogov, S. A.
2016-01-01
We provide conditions for the existence of measurable solutions to the equation $\\xi(T\\omega)=f(\\omega,\\xi(\\omega))$, where $T:\\Omega \\rightarrow\\Omega$ is an automorphism of the probability space $\\Omega$ and $f(\\omega,\\cdot)$ is a strictly non-expansive mapping. We use results of this kind to establish a stochastic nonlinear analogue of the Perron-Frobenius theorem on eigenvalues and eigenvectors of a positive matrix. We consider a random mapping $D(\\omega)$ of a random closed cone $K(\\omeg...
Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition
International Nuclear Information System (INIS)
Abu-Donia, H.M.
2007-01-01
Some common fixed point theorems for multi-valued mappings under φ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for φ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε ∞ -space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45
Common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition
Energy Technology Data Exchange (ETDEWEB)
Abu-Donia, H.M. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)
2007-10-15
Some common fixed point theorems for multi-valued mappings under {phi}-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for {phi}-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding {epsilon} {sup {infinity}}-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the {epsilon} {sup {infinity}}-space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45].
Fixed-point theorems for families of weakly non-expansive maps
Mai, Jie-Hua; Liu, Xin-He
2007-10-01
In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.
Fixed point theorems in locally convex spacesÃ¢Â€Â”the Schauder mapping method
Directory of Open Access Journals (Sweden)
S. Cobzaş
2006-03-01
Full Text Available In the appendix to the book by F. F. Bonsal, Lectures on Some Fixed Point Theorems of Functional Analysis (Tata Institute, Bombay, 1962 a proof by Singbal of the Schauder-Tychonoff fixed point theorem, based on a locally convex variant of Schauder mapping method, is included. The aim of this note is to show that this method can be adapted to yield a proof of Kakutani fixed point theorem in the locally convex case. For the sake of completeness we include also the proof of Schauder-Tychonoff theorem based on this method. As applications, one proves a theorem of von Neumann and a minimax result in game theory.
A Coupled Fixed Point Theorem in Fuzzy Metric Space Satisfying ϕ-Contractive Condition
Directory of Open Access Journals (Sweden)
B. D. Pant
2013-01-01
Full Text Available The intent of this paper is to prove a coupled fixed point theorem for two pairs of compatible and subsequentially continuous (alternately subcompatible and reciprocally continuous mappings, satisfying ϕ-contractive conditions in a fuzzy metric space. We also furnish some illustrative examples to support our results.
New versions of the Fan-Browder fixed point theorem and existence of economic equilibria
Directory of Open Access Journals (Sweden)
Park Sehie
2004-01-01
Full Text Available We introduce a generalized form of the Fan-Browder fixed point theorem and apply to game-theoretic and economic equilibrium existence problem under the more generous restrictions. Consequently, we state some of recent results of Urai (2000 in more general and efficient forms.
Directory of Open Access Journals (Sweden)
Xiangbing Zhou
2012-01-01
Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.
An application of Darbo\\'s fixed point theorem in the relative ...
African Journals Online (AJOL)
Sufficient conditions for the relative controllability of a class of nonlinear systems with distributed delays in the control are established. Our results are based on the measure of non-compactness of a set and the Darbo's fixed point theorem. Global Jouranl of Mathematical Sciences Vol. 6 (1) 2007: pp. 21-26 ...
Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces
International Nuclear Information System (INIS)
Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi
2009-01-01
In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
An application of a discrete fixed point theorem to the Cournot model
Sato, Junichi
2008-01-01
In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.
Employing Common Limit Range Property to Prove Unified Metrical Common Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Mohammad Imdad
2013-01-01
Full Text Available The purpose of this paper is to emphasize the role of “common limit range property” to ascertain the existence of common fixed point in metric spaces satisfying an implicit function essentially due to the paper of Ali and Imdad (2008. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Ali and Imdad (2008. We also furnish some illustrative examples to support our main results.
International Nuclear Information System (INIS)
Vidossich, G.
1979-01-01
The paper presents a proof of two fixed-point theorems, which unify previous results on periodic solutions of second-order ordinary differential equations, in the sense that the existence part of these solutions become a corollay of the fixed-point theorems. (author)
Searching for fixed point combinators by using automated theorem proving: A preliminary report
International Nuclear Information System (INIS)
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, Θ must satisfy the equation Θx = x(Θx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs
Searching for fixed point combinators by using automated theorem proving: A preliminary report
Energy Technology Data Exchange (ETDEWEB)
Wos, L.; McCune, W.
1988-09-01
In this report, we establish that the use of an automated theorem- proving program to study deep questions from mathematics and logic is indeed an excellent move. Among such problems, we focus mainly on that concerning the construction of fixed point combinators---a problem considered by logicians to be significant and difficult to solve, and often computationally intensive and arduous. To be a fixed point combinator, THETA must satisfy the equation THETAx = x(THETAx) for all combinators x. The specific questions on which we focus most heavily ask, for each chosen set of combinators, whether a fixed point combinator can be constructed from the members of that set. For answering questions of this type, we present a new, sound, and efficient method, called the kernel method, which can be applied quite easily by hand and very easily by an automated theorem-proving program. For the application of the kernel method by a theorem-proving program, we illustrate the vital role that is played by both paramodulation and demodulation---two of the powerful features frequently offered by an automated theorem-proving program for treating equality as if it is ''understood.'' We also state a conjecture that, if proved, establishes the completeness of the kernel method. From what we can ascertain, this method---which relies on the introduced concepts of kernel and superkernel---offers the first systematic approach for searching for fixed point combinators. We successfully apply the new kernel method to various sets of combinators and, for the set consisting of the combinators B and W, construct an infinite set of fixed point combinators such that no two of the combinators are equal even in the presence of extensionality---a law that asserts that two combinators are equal if they behave the same. 18 refs.
Directory of Open Access Journals (Sweden)
Hao Tao
2012-01-01
analysis of real estate asset securitization by using the generalized fixed point theorem for weakly contractive mappings in partially ordered sets. Based on the analysis for the existence and uniqueness of the solution and scientific numerical calculation of the solution, in further study, some optimization schemes for traditional risk control process will be obtained, and then the main results of this paper can be applied to the forefront of research of real estate asset securitization.
Directory of Open Access Journals (Sweden)
Kang Shin
2011-01-01
Full Text Available Abstract In this paper, the existence, uniqueness and iterative approximations of fixed points for contractive mappings of integral type in complete metric spaces are established. As applications, the existence, uniqueness and iterative approximations of solutions for a class of functional equations arising in dynamic programming are discussed. The results presented in this paper extend and improve essentially the results of Branciari (A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531-536, 2002, Kannan (Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76, 1968 and several known results. Four concrete examples involving the contractive mappings of integral type with uncountably many points are constructed. 2010 Mathematics Subject Classfication: 54H25, 47H10, 49L20, 49L99, 90C39
Directory of Open Access Journals (Sweden)
Magnolia Tilca
2014-10-01
Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2014-01-01
implicit relation, we prove a new coincidence and common fixed point theorem for a hybrid pair of occasionally coincidentally idempotent mappings in a metric space employing the common limit range property. Our main result improves and generalizes a host of previously known results. We also utilize suitable illustrative examples to substantiate the realized improvements in our results.
International Nuclear Information System (INIS)
Sharma, Sushil; Deshpande, Bhavana
2009-01-01
The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces. Our results extend, generalize and intuitionistic fuzzify several known results in fuzzy metric spaces. We give an example and also give formulas for total number of commutativity conditions for finite number of mappings.
L-fuzzy/span> fixed points theorems for L-fuzzy/span> mappings via βℱL-admissible pair.
Rashid, Maliha; Azam, Akbar; Mehmood, Nayyar
2014-01-01
We define the concept of βℱL-admissible for a pair of L-fuzzy/span> mappings and establish the existence of common L-fuzzy/span> fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result.
Some Common Fixed Point Theorems for F-Contraction Type Mappings in 0-Complete Partial Metric Spaces
Directory of Open Access Journals (Sweden)
Satish Shukla
2013-01-01
Full Text Available We prove some common fixed point theorems for F-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.
Solutions to second order non-homogeneous multi-point BVPs using a fixed-point theorem
Directory of Open Access Journals (Sweden)
Yuji Liu
2008-07-01
Full Text Available In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs of second order differential equations with the one-dimensional p-Laplacian. These problems have a common equation (in different function domains and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several known ones and are illustrated by examples. It is also shown that the approach for getting three positive solutions by using multi-fixed-point theorems can be extended to nonhomogeneous BVPs. The emphasis is on the nonhomogeneous boundary conditions and the nonlinear term involving first order derivative of the unknown. Some open problems are also proposed.
Directory of Open Access Journals (Sweden)
Bessem Samet
2011-09-01
Full Text Available Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.
Latif, Abdul; Mongkolkeha, Chirasak; Sintunavarat, Wutiphol
2014-01-01
We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
International Nuclear Information System (INIS)
Jesic, Sinisa N.; Babacev, Natasa A.
2008-01-01
The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given
Directory of Open Access Journals (Sweden)
Abdul Latif
2014-01-01
Full Text Available We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011 to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.
Directory of Open Access Journals (Sweden)
Sunny Chauhan
2013-11-01
Full Text Available In this paper, we utilize the notion of common limit range property in Non-Archimedean Menger PM-spaces and prove some fixed point theorems for two pairs of weakly compatible mappings. Some illustrative examples are furnished to support our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings. Our results improve and extend several known results existing in the literature.
Directory of Open Access Journals (Sweden)
Tong-Huei Chang
2009-01-01
Full Text Available We use a concept of abstract convexity to define the almost S-KKM𝒞 property, al-S-KKM𝒞(X,Y family, and almost Φ-spaces. We get some new approximate fixed point theorems and fixed point theorems in almost Φ-spaces. Our results extend some results of other authors.
On the Computational Content of the Krasnoselski and Ishikawa Fixed Point Theorems
DEFF Research Database (Denmark)
Kohlenbach, Ulrich
2001-01-01
This paper is part of a case study in proof mining applied to non-effective proofs in nonlinear functional analysis. More specifically, we are concerned with the fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study Krasnoselski and more general so-called K......This paper is part of a case study in proof mining applied to non-effective proofs in nonlinear functional analysis. More specifically, we are concerned with the fixed point theory of nonexpansive selfmappings f of convex sets C in normed spaces. We study Krasnoselski and more general so...... and Shafrir (1992) to unbounded sets C. Our explicit bounds also imply new qualitative results concerning the independence of the rate of asymptotic regularity from various data....
Fixed Point Theorems for T-Ciric Quasi-contractive Operator in CAT(0 Spaces
Directory of Open Access Journals (Sweden)
G. S. Saluja
2013-08-01
Full Text Available The purpose of this paper to study a three-step iterative algorithm for T-Ciric quasi-contractive (TCQC operator in the framework of CAT(0 spaces and establish strong convergence theorems for above said scheme and operator. Our results improve and extend the recent corresponding results from the existing literature (see, e.g., [28, 29, 30] and some others.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 5; Issue 5. Fixed Points - From Russia with Love - A Primer of Fixed Point Theory. A K Vijaykumar. Book Review Volume 5 Issue 5 May 2000 pp 101-102. Fulltext. Click here to view fulltext PDF. Permanent link:
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.
Directory of Open Access Journals (Sweden)
Sanjo Zlobec
2017-04-01
Full Text Available A set of sufficient conditions which guarantee the existence of a point x⋆ such that f(x⋆ = x⋆ is called a "fixed point theorem". Many such theorems are named after well-known mathematicians and economists. Fixed point theorems are among most useful ones in applied mathematics, especially in economics and game theory. Particularly important theorem in these areas is Kakutani's fixed point theorem which ensures existence of fixed point for point-to-set mappings, e.g., [2, 3, 4]. John Nash developed and applied Kakutani's ideas to prove the existence of (what became known as "Nash equilibrium" for finite games with mixed strategies for any number of players. This work earned him a Nobel Prize in Economics that he shared with two mathematicians. Nash's life was dramatized in the movie "Beautiful Mind" in 2001. In this paper, we approach the system f(x = x differently. Instead of studying existence of its solutions our objective is to determine conditions which are both necessary and sufficient that an arbitrary point x⋆ is a fixed point, i.e., that it satisfies f(x⋆ = x⋆. The existence of solutions for continuous function f of the single variable is easy to establish using the Intermediate Value Theorem of Calculus. However, characterizing fixed points x⋆, i.e., providing answers to the question of finding both necessary and sufficient conditions for an arbitrary given x⋆ to satisfy f(x⋆ = x⋆, is not simple even for functions of the single variable. It is possible that constructive answers do not exist. Our objective is to find them. Our work may require some less familiar tools. One of these might be the "quadratic envelope characterization of zero-derivative point" recalled in the next section. The results are taken from the author's current research project "Studying the Essence of Fixed Points". They are believed to be original. The author has received several feedbacks on the preliminary report and on parts of the project
Common fixed points for weakly compatible maps
Indian Academy of Sciences (India)
Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45
In 1976, Jungck [4] proved a common fixed point theorem for commuting maps generalizing the Banach's fixed point theorem, which states that, 'let (X, d) be a complete metric space. If T satisfies d(Tx,Ty) ≤ kd(x,y) for each x,y ∈ X where 0 ≤ k < 1, then T has a unique fixed point in X'. This theorem has many applications, ...
Directory of Open Access Journals (Sweden)
V. S. Serov
2010-01-01
Full Text Available A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.
Shapiro, Joel H
2016-01-01
This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests ...
Fixed points and self-reference
Directory of Open Access Journals (Sweden)
Raymond M. Smullyan
1984-01-01
Full Text Available It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist.
Fixed points of quantum operations
International Nuclear Information System (INIS)
Arias, A.; Gheondea, A.; Gudder, S.
2002-01-01
Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation, and quantum information theory. If an operator A is invariant under a quantum operation φ, we call A a φ-fixed point. Physically, the φ-fixed points are the operators that are not disturbed by the action of φ. Our main purpose is to answer the following question. If A is a φ-fixed point, is A compatible with the operation elements of φ? We shall show in general that the answer is no and we shall give some sufficient conditions under which the answer is yes. Our results will follow from some general theorems concerning completely positive maps and injectivity of operator systems and von Neumann algebras
Brouwer's ε-fixed point from Sperner's lemma
Dalen, D. van
It is by now common knowledge that Brouwer gave mathematics in 1911 a miraculous tool, the fixed point theorem, and that later in life, he disavowed it. It usually came as a shock when he replied to the question “is the fixed point theorem correct ?” with a point blank “no”. This rhetoric exchange
Fixed points of occasionally weakly biased mappings
Y. Mahendra Singh, M. R. Singh
2012-01-01
Common fixed point results due to Pant et al. [Pant et al., Weak reciprocal continuity and fixed point theorems, Ann Univ Ferrara, 57(1), 181-190 (2011)] are extended to a class of non commuting operators called occasionally weakly biased pair[ N. Hussain, M. A. Khamsi A. Latif, Commonfixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Analysis, 74, 2133-2140 (2011)]. We also provideillustrative examples to justify the improvements. Abstract....
International Nuclear Information System (INIS)
Howard, Lee M.
2014-01-01
Sharkovskii proved that, for continuous maps on intervals, the existence of 3-cycle implies the existence of all others. Li and Yorke proved that 3-cycle implies chaos. To establish a domain of uncountable cycles in the logistic map and to understand chaos in it, the fixed points of 3-cycle are obtained analytically by solving a sextic equation. At one parametric value, a fixed-point spectrum, resulted from the Sharkovskii limit, helps to realize chaos in the sense of Li and Yorke. (general)
Fixed points for weak contractions in metric type spaces
Gaba, Yaé Ulrich
2014-01-01
In this article, we prove some fixed point theorems in metric type spaces. This article is just a generalization some results previously proved in \\cite{niyi-gaba}. In particular, we give some coupled common fixed points theorems under weak contractions. These results extend well known similar results existing in the literature.
Characterizations of fixed points of quantum operations
International Nuclear Information System (INIS)
Li Yuan
2011-01-01
Let φ A be a general quantum operation. An operator B is said to be a fixed point of φ A , if φ A (B)=B. In this note, we shall show conditions under which B, a fixed point φ A , implies that B is compatible with the operation element of φ A . In particular, we offer an extension of the generalized Lueders theorem.
J.W. de Bakker (Jaco)
1975-01-01
textabstractParameter mechanisms for recursive procedures are investigated. Contrary to the view of Manna et al., it is argued that both call-by-value and call-by-name mechanisms yield the least fixed points of the functionals determined by the bodies of the procedures concerned. These functionals
Directory of Open Access Journals (Sweden)
Manish Jain
2013-01-01
Full Text Available We establish the existence and uniqueness of coupled common fixed point for symmetric (φ,ψ-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011, Nashine (2012, and Mohiuddine and Alotaibi (2012, thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.
The universal cardinal ordering of fixed points
International Nuclear Information System (INIS)
San Martin, Jesus; Moscoso, Ma Jose; Gonzalez Gomez, A.
2009-01-01
We present the theorem which determines, by a permutation, the cardinal ordering of fixed points for any orbit of a period doubling cascade. The inverse permutation generates the orbit and the symbolic sequence of the orbit is obtained as a corollary. Interestingly enough, it is important to point that this theorem needs no previous information about any other orbit; also the cardinal ordering is achieved automatically with no need to compare numerical values associated with every point of the orbit (as would be the case if kneading theory were used).
Common Fixed Points for Weakly Compatible Maps
Indian Academy of Sciences (India)
The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalized the results of Jungck [3], Fisher [1], Kang and Kim [8], Jachymski [2], and Rhoades [9].
Fixed Point Approach to Bagley Torvik Problem
Directory of Open Access Journals (Sweden)
Lale CONA
2017-10-01
Full Text Available In the present paper, a sufficient condition for existence and uniqueness of Bagley Torvik problem is obtained. The theorem on existence and uniqueness is established. This approach permits us to use fixed point iteration method to solve problem for differential equation involving derivatives of nonlinear order.
Hybrid fixed point in CAT(0 spaces
Directory of Open Access Journals (Sweden)
Hemant Kumar Pathak
2018-02-01
Full Text Available In this paper, we introduce an ultrapower approach to prove fixed point theorems for $H^{+}$-nonexpansive multi-valued mappings in the setting of CAT(0 spaces and prove several hybrid fixed point results in CAT(0 spaces for families of single-valued nonexpansive or quasinonexpansive mappings and multi-valued upper semicontinuous, almost lower semicontinuous or $H^{+}$-nonexpansive mappings which are weakly commuting. We also establish a result about structure of the set of fixed points of $H^{+}$-quasinonexpansive mapping on a CAT(0 space.
Fixed Points of Expansive Type Mappings in 2-Banach Spaces
Directory of Open Access Journals (Sweden)
Prabha Chouhan
2013-08-01
Full Text Available In present paper, we define expansive mappings in 2-Banach space and prove some common unique fixed point theorems which are the extension of results of Wang et al. [12] and Rhoades [9] in 2-Banach space.
Tripled Fixed Point in Ordered Multiplicative Metric Spaces
Directory of Open Access Journals (Sweden)
Laishram Shanjit
2017-06-01
Full Text Available In this paper, we present some triple fixed point theorems in partially ordered multiplicative metric spaces depended on another function. Our results generalise the results of [6] and [5].
Fixed point theory in metric type spaces
Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco
2015-01-01
Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...
Fixed points of quantum gravity
Litim, D F
2003-01-01
Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.
Fixed Points in Grassmannians with Applications to Economic Equilibrium
DEFF Research Database (Denmark)
Keiding, Hans
2017-01-01
In some applications of equilibrium theory, the fixed point involves not only a state and a value of a parameter in the dual of the state space, but also a particular subspace of the state space. Since the set of all subspaces of a finite-dimensional Euclidean space has a structure which does...... not allow immediate application of fixed point theorems, the problem must be reformulated using a suitable parametrization of subspaces. One such parametrization, the Plücker coordinates, is used here to prove a general equilibrium existence theorem. Applications to economic problems involving hierarchies...... of consumers or incomplete markets with real assets are outlined....
Measures of Noncircularity and Fixed Points of Contractive Multifunctions
Directory of Open Access Journals (Sweden)
Marrero Isabel
2010-01-01
Full Text Available In analogy to the Eisenfeld-Lakshmikantham measure of nonconvexity and the Hausdorff measure of noncompactness, we introduce two mutually equivalent measures of noncircularity for Banach spaces satisfying a Cantor type property, and apply them to establish a fixed point theorem of Darbo type for multifunctions. Namely, we prove that every multifunction with closed values, defined on a closed set and contractive with respect to any one of these measures, has the origin as a fixed point.
Padgett, Wayne T
2009-01-01
This book is intended to fill the gap between the ""ideal precision"" digital signal processing (DSP) that is widely taught, and the limited precision implementation skills that are commonly required in fixed-point processors and field programmable gate arrays (FPGAs). These skills are often neglected at the university level, particularly for undergraduates. We have attempted to create a resource both for a DSP elective course and for the practicing engineer with a need to understand fixed-point implementation. Although we assume a background in DSP, Chapter 2 contains a review of basic theory
Fixed points in a group of isometries
Voorneveld, M.
2000-01-01
The Bruhat-Tits xed point theorem states that a group of isometries on a complete metric space with negative curvature possesses a xed point if it has a bounded orbit. This theorem is extended by a relaxation of the negative curvature condition in terms of the w-distance functions introduced by Kada
Flat Coalgebraic Fixed Point Logics
Schröder, Lutz; Venema, Yde
Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the μ-calculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the μ-calculus. The family of such flat fixed point logics includes, e.g., CTL, the *-nesting-free fragment of PDL, and the logic of common knowledge. Here, we extend this notion to the generic semantic framework of coalgebraic logic, thus covering a wide range of logics beyond the standard μ-calculus including, e.g., flat fragments of the graded μ-calculus and the alternating-time μ-calculus (such as ATL), as well as probabilistic and monotone fixed point logics. Our main results are completeness of the Kozen-Park axiomatization and a timed-out tableaux method that matches ExpTime upper bounds inherited from the coalgebraic μ-calculus but avoids using automata.
Common fixed points of single-valued and multivalued maps
Directory of Open Access Journals (Sweden)
Yicheng Liu
2005-01-01
Full Text Available We define a new property which contains the property (EA for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.
Fixed Points on the Real numbers without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita
2002-01-01
In this paper we present a study of definability properties of fixed points of effective operators on the real numbers without the equality test. In particular we prove that Gandy theorem holds for the reals without the equality test. This provides a useful tool for dealing with recursive...
Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions
Hussain, N.
2008-02-01
The common fixed point theorems, similar to those of Ciric [Lj.B. Ciric, On a common fixed point theorem of a Gregus type, Publ. Inst. Math. (Beograd) (N.S.) 49 (1991) 174-178; Lj.B. Ciric, On Diviccaro, Fisher and Sessa open questions, Arch. Math. (Brno) 29 (1993) 145-152; Lj.B. Ciric, On a generalization of Gregus fixed point theorem, Czechoslovak Math. J. 50 (2000) 449-458], Fisher and Sessa [B. Fisher, S. Sessa, On a fixed point theorem of Gregus, Internat. J. Math. Math. Sci. 9 (1986) 23-28], Jungck [G. Jungck, On a fixed point theorem of Fisher and Sessa, Internat. J. Math. Math. Sci. 13 (1990) 497-500] and Mukherjee and Verma [R.N. Mukherjee, V. Verma, A note on fixed point theorem of Gregus, Math. Japon. 33 (1988) 745-749], are proved for a Banach operator pair. As applications, common fixed point and approximation results for Banach operator pair satisfying Ciric type contractive conditions are obtained without the assumption of linearity or affinity of either T or I. Our results unify and generalize various known results to a more general class of noncommuting mappings.
A common fixed point for operators in probabilistic normed spaces
International Nuclear Information System (INIS)
Ghaemi, M.B.; Lafuerza-Guillen, Bernardo; Razani, A.
2009-01-01
Probabilistic Metric spaces was introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger [Alsina C, Schweizer B, Sklar A. On the definition of a probabilistic normed spaces. Aequationes Math 1993;46:91-8]. Here, we consider the equicontinuity of a class of linear operators in probabilistic normed spaces and finally, a common fixed point theorem is proved. Application to quantum Mechanic is considered.
Some Fixed Point Results for Caristi Type Mappings in Modular Metric Spaces with an Application
Directory of Open Access Journals (Sweden)
Duran Turkoglu
2016-08-01
Full Text Available In this paper we give Caristi type fixed point theorem in complete modular metric spaces. Moreover we give a theorem which can be derived from Caristi type. Also an application for the bounded solution of funcional equations is investigated.
Fixed Point Learning Based Intelligent Traffic Control System
Zongyao, Wang; Cong, Sui; Cheng, Shao
2017-10-01
Fixed point learning has become an important tool to analyse large scale distributed system such as urban traffic network. This paper presents a fixed point learning based intelligence traffic network control system. The system applies convergence property of fixed point theorem to optimize the traffic flow density. The intelligence traffic control system achieves maximum road resources usage by averaging traffic flow density among the traffic network. The intelligence traffic network control system is built based on decentralized structure and intelligence cooperation. No central control is needed to manage the system. The proposed system is simple, effective and feasible for practical use. The performance of the system is tested via theoretical proof and simulations. The results demonstrate that the system can effectively solve the traffic congestion problem and increase the vehicles average speed. It also proves that the system is flexible, reliable and feasible for practical use.
Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-05-01
Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banach spaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs
Infra-red fixed points in supersymmetry
Indian Academy of Sciences (India)
¾c /font>, and c stands for the color quadratic Casimir of the field. Fixed points arise when R* ¼ or when R*. /nobr>. ´S-½. µ ´r ·b¿µ. The stability of the solutions may be tested by linearizing the system about the fixed points. For the non-trivial fixed points we need to consider the eigenvalues of the stability matrix whose ...
Algorithms for solving common fixed point problems
Zaslavski, Alexander J
2018-01-01
This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems, the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning. Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter ...
Magnetic Fixed Points and Emergent Supersymmetry
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Pica, Claudio
2013-01-01
We establish in perturbation theory the existence of fixed points along the renormalization group flow for QCD with an adjoint Weyl fermion and scalar matter reminiscent of magnetic duals of QCD [1-3]. We classify the fixed points by analyzing their basin of attraction. We discover that among...
Metallic and antiferromagnetic fixed points from gravity
Paul, Chandrima
2018-06-01
We consider SU(2) × U(1) gauge theory coupled to matter field in adjoints and study RG group flow. We constructed Callan-Symanzik equation and subsequent β functions and study the fixed points. We find there are two fixed points, showing metallic and antiferromagnetic behavior. We have shown that metallic phase develops an instability if certain parametric conditions are satisfied.
Guided Discovery of the Nine-Point Circle Theorem and Its Proof
Buchbinder, Orly
2018-01-01
The nine-point circle theorem is one of the most beautiful and surprising theorems in Euclidean geometry. It establishes an existence of a circle passing through nine points, all of which are related to a single triangle. This paper describes a set of instructional activities that can help students discover the nine-point circle theorem through…
An introduction to nonlinear analysis and fixed point theory
Pathak, Hemant Kumar
2018-01-01
This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines. Nonlinear analysis is characterised by its applications in numerous interdisciplinary fields, ranging from engineering to space science, hydromechanics to astrophysics, chemistry to biology, theoretical mechanics to biomechanics and economics to stochastic game theory. Organised into ten chapters, the book shows the elegance of the subject and its deep-rooted concepts and techniques, which provide the tools for developing more realistic and accurate models for ...
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!!!
About Applications of the Fixed Point Theory
Directory of Open Access Journals (Sweden)
Bucur Amelia
2017-06-01
Full Text Available The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.
Fixed-Point Configurable Hardware Components
Directory of Open Access Journals (Sweden)
Rocher Romuald
2006-01-01
Full Text Available To reduce the gap between the VLSI technology capability and the designer productivity, design reuse based on IP (intellectual properties is commonly used. In terms of arithmetic accuracy, the generated architecture can generally only be configured through the input and output word lengths. In this paper, a new kind of method to optimize fixed-point arithmetic IP has been proposed. The architecture cost is minimized under accuracy constraints defined by the user. Our approach allows exploring the fixed-point search space and the algorithm-level search space to select the optimized structure and fixed-point specification. To significantly reduce the optimization and design times, analytical models are used for the fixed-point optimization process.
Anderson Acceleration for Fixed-Point Iterations
Energy Technology Data Exchange (ETDEWEB)
Walker, Homer F. [Worcester Polytechnic Institute, MA (United States)
2015-08-31
The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.
Topological fixed point theory of multivalued mappings
Górniewicz, Lech
1999-01-01
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...
Topological fixed point theory for singlevalued and multivalued mappings and applications
Ben Amar, Afif
2016-01-01
This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of ax...
Directory of Open Access Journals (Sweden)
Samet Bessem
2011-01-01
Full Text Available Abstract In this article, we establish coincidence point and common fixed point theorems for mappings satisfying a contractive inequality which involves two generalized altering distance functions in ordered complete metric spaces. As application, we study the existence of a common solution to a system of integral equations. 2000 Mathematics subject classification. Primary 47H10, Secondary 54H25
1989-06-09
could be used to establish a conjectured minimax for a search game of Baston and Bostock [2]. An application of Theorem 1 is to the problem of getting...Alpern S., Search for point in interval, with high-low feedback, Math. Proc., Cambridge Phil. Soc. 98, (1985), 569-578. [2] Baston V. J. and Bostock F. A
Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions
Directory of Open Access Journals (Sweden)
Jin Liang
2008-06-01
Full Text Available This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term, we obtain sufficient and necessary conditions, as well as sufficient conditions, for the existence of a fixed point. As one will see, we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems.
The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices
Directory of Open Access Journals (Sweden)
Eleftherios Matsikoudis
2013-08-01
Full Text Available We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed-complete generalized ultrametric semilattices, and introduce a corresponding induction principle. We cite examples of application in the semantics of logic programming and timed computation, where, until now, the only tool available has been the non-constructive fixed-point theorem of Priess-Crampe and Ribenboim for strictly contracting functions on spherically complete generalized ultrametric semilattices.
Quantum entanglement and fixed-point bifurcations
International Nuclear Information System (INIS)
Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.
2005-01-01
How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation
The computation of fixed points and applications
Todd, Michael J
1976-01-01
Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore ...
Fixed points for alpha-psi contractive mappings with an application to quadratic integral equations
Directory of Open Access Journals (Sweden)
Bessem Samet
2014-06-01
Full Text Available Recently, Samet et al [24] introduced the concept of alpha-psi contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ciric, Nieto, Lopez, and many others. We prove that alpha-psi contractions unify large classes of contractive type operators, whose fixed points can be obtained by means of the Picard iteration. Finally, we utilize our results to discuss the existence and uniqueness of solutions to a class of quadratic integral equations.
Fixed point algebras for easy quantum groups
DEFF Research Database (Denmark)
Gabriel, Olivier; Weber, Moritz
2016-01-01
Compact matrix quantum groups act naturally on Cuntz algebras. The first author isolated certain conditions under which the fixed point algebras under this action are Kirchberg algebras. Hence they are completely determined by their K-groups. Building on prior work by the second author,we prove...... that free easy quantum groups satisfy these conditions and we compute the K-groups of their fixed point algebras in a general form. We then turn to examples such as the quantum permutation group S+ n,the free orthogonal quantum group O+ n and the quantum reflection groups Hs+ n. Our fixed point......-algebra construction provides concrete examples of free actions of free orthogonal easy quantum groups,which are related to Hopf-Galois extensions....
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1993-05-01
It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs
Directory of Open Access Journals (Sweden)
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
ASIC For Complex Fixed-Point Arithmetic
Petilli, Stephen G.; Grimm, Michael J.; Olson, Erlend M.
1995-01-01
Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.
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.
Directory of Open Access Journals (Sweden)
Klin-eam Chakkrid
2009-01-01
Full Text Available Abstract A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover, we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space.
Fixed point of the parabolic renormalization operator
Lanford III, Oscar E
2014-01-01
This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...
Branes, superpotentials and superconformal fixed points
International Nuclear Information System (INIS)
Aharony, O.
1997-01-01
We analyze various brane configurations corresponding to field theories in three, four and five dimensions. We find brane configurations which correspond to three-dimensional N=2 and four-dimensional N=1 supersymmetric QCD theories with quartic superpotentials, in which what appear to be ''hidden parameters'' play an important role. We discuss the construction of five-dimensional N=1 supersymmetric gauge theories and superconformal fixed points using branes, which leads to new five-dimensional N=1 superconformal field theories. The same five-dimensional theories are also used, in a surprising way, to describe new superconformal fixed points of three-dimensional N=2 supersymmetric theories, which have both ''electric'' and ''magnetic'' Coulomb branches. (orig.)
Directory of Open Access Journals (Sweden)
N. Shahzad
2013-01-01
Full Text Available In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.
Evolution families of conformal mappings with fixed points and the Löwner-Kufarev equation
International Nuclear Information System (INIS)
Goryainov, V V
2015-01-01
The paper is concerned with evolution families of conformal mappings of the unit disc to itself that fix an interior point and a boundary point. Conditions are obtained for the evolution families to be differentiable, and an existence and uniqueness theorem for an evolution equation is proved. A convergence theorem is established which describes the topology of locally uniform convergence of evolution families in terms of infinitesimal generating functions. The main result in this paper is the embedding theorem which shows that any conformal mapping of the unit disc to itself with two fixed points can be embedded into a differentiable evolution family of such mappings. This result extends the range of the parametric method in the theory of univalent functions. In this way the problem of the mutual change of the derivative at an interior point and the angular derivative at a fixed point on the boundary is solved for a class of mappings of the unit disc to itself. In particular, the rotation theorem is established for this class of mappings. Bibliography: 27 titles
New fixed and periodic point results on cone metric spaces
Directory of Open Access Journals (Sweden)
Ghasem Soleimani Rad
2014-05-01
Full Text Available In this paper, several xed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.
Equivalence of functional limit theorems for stationary point processes and their Palm distributions
Nieuwenhuis, G.
1989-01-01
Let P be the distribution of a stationary point process on the real line and let P0 be its Palm distribution. In this paper we consider two types of functional limit theorems, those in terms of the number of points of the point process in (0, t] and those in terms of the location of the nth point
M. Aamri; A. Bassou; S. Bennani; D. El Moutawakil
2007-01-01
The main purpose of this paper is to give some common fixed point theorems of mappings and set-valued mappings of a symmetric space with some applications to probabilistic spaces. In order to get these results, we define the concept of E-weak compatibility between set-valued and single-valued mappings of a symmetric space.
Nonthermal fixed points and the functional renormalization group
International Nuclear Information System (INIS)
Berges, Juergen; Hoffmeister, Gabriele
2009-01-01
Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium
Fixed points of quantum gravity in extra dimensions
International Nuclear Information System (INIS)
Fischer, Peter; Litim, Daniel F.
2006-01-01
We study quantum gravity in more than four dimensions with renormalisation group methods. We find a non-trivial ultraviolet fixed point in the Einstein-Hilbert action. The fixed point connects with the perturbative infrared domain through finite renormalisation group trajectories. We show that our results for fixed points and related scaling exponents are stable. If this picture persists at higher order, quantum gravity in the metric field is asymptotically safe. We discuss signatures of the gravitational fixed point in models with low scale quantum gravity and compact extra dimensions
Impulsive differential inclusions a fixed point approach
Ouahab, Abdelghani; Henderson, Johnny
2013-01-01
Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, etc. The questions of existence and stability of solutions for different classes of initial values problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems and relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simple
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
Directory of Open Access Journals (Sweden)
A. Neamaty
2015-03-01
Full Text Available In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
A. Neamaty; Sh. Akbarpoor; A. Dabbaghian
2015-01-01
In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Floating-to-Fixed-Point Conversion for Digital Signal Processors
Directory of Open Access Journals (Sweden)
Menard Daniel
2006-01-01
Full Text Available Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.
Floating-to-Fixed-Point Conversion for Digital Signal Processors
Menard, Daniel; Chillet, Daniel; Sentieys, Olivier
2006-12-01
Digital signal processing applications are specified with floating-point data types but they are usually implemented in embedded systems with fixed-point arithmetic to minimise cost and power consumption. Thus, methodologies which establish automatically the fixed-point specification are required to reduce the application time-to-market. In this paper, a new methodology for the floating-to-fixed point conversion is proposed for software implementations. The aim of our approach is to determine the fixed-point specification which minimises the code execution time for a given accuracy constraint. Compared to previous methodologies, our approach takes into account the DSP architecture to optimise the fixed-point formats and the floating-to-fixed-point conversion process is coupled with the code generation process. The fixed-point data types and the position of the scaling operations are optimised to reduce the code execution time. To evaluate the fixed-point computation accuracy, an analytical approach is used to reduce the optimisation time compared to the existing methods based on simulation. The methodology stages are described and several experiment results are presented to underline the efficiency of this approach.
Fixed-point data-collection method of video signal
International Nuclear Information System (INIS)
Tang Yu; Yin Zejie; Qian Weiming; Wu Xiaoyi
1997-01-01
The author describes a Fixed-point data-collection method of video signal. The method provides an idea of fixed-point data-collection, and has been successfully applied in the research of real-time radiography on dose field, a project supported by National Science Fund
ORIGINAL Some Generalized Fixed Point Results on Compact ...
African Journals Online (AJOL)
Abstract. The goal of this research is to study some generalized fixed point results in compact metric space. It mainly focuses on the existence and unique fixed point of a selfmap on a compact metric space and its generalizations. In this study iterative techniques due to. Edelstein, Bhardwaj et al. and Sastry et al. are used to ...
A hierarchical model exhibiting the Kosterlitz-Thouless fixed point
International Nuclear Information System (INIS)
Marchetti, D.H.U.; Perez, J.F.
1985-01-01
A hierarchical model for 2-d Coulomb gases displaying a line stable of fixed points describing the Kosterlitz-Thouless phase transition is constructed. For Coulomb gases corresponding to Z sub(N)- models these fixed points are stable for an intermediate temperature interval. (Author) [pt
Fixed Points on Abstract Structures without the Equality Test
DEFF Research Database (Denmark)
Korovina, Margarita
2002-01-01
The aim of this talk is to present a study of definability properties of fixed points of effective operators on abstract structures without the equality test. The question of definability of fixed points of -operators on abstract structures with equality was first studied by Gandy, Barwise, Mosch...
Wall shear stress fixed points in blood flow
Arzani, Amirhossein; Shadden, Shawn
2017-11-01
Patient-specific computational fluid dynamics produces large datasets, and wall shear stress (WSS) is one of the most important parameters due to its close connection with the biological processes at the wall. While some studies have investigated WSS vectorial features, the WSS fixed points have not received much attention. In this talk, we will discuss the importance of WSS fixed points from three viewpoints. First, we will review how WSS fixed points relate to the flow physics away from the wall. Second, we will discuss how certain types of WSS fixed points lead to high biochemical surface concentration in cardiovascular mass transport problems. Finally, we will introduce a new measure to track the exposure of endothelial cells to WSS fixed points.
A new compact fixed-point blackbody furnace
International Nuclear Information System (INIS)
Hiraka, K.; Oikawa, H.; Shimizu, T.; Kadoya, S.; Kobayashi, T.; Yamada, Y.; Ishii, J.
2013-01-01
More and more NMIs are realizing their primary scale themselves with fixed-point blackbodies as their reference standard. However, commercially available fixed-point blackbody furnaces of sufficient quality are not always easy to obtain. CHINO Corp. and NMIJ, AIST jointly developed a new compact fixed-point blackbody furnace. The new furnace has such features as 1) improved temperature uniformity when compared to previous products, enabling better plateau quality, 2) adoption of the hybrid fixed-point cell structure with internal insulation to improve robustness and thereby to extend lifetime, 3) easily ejectable and replaceable heater unit and fixed-point cell design, leading to reduced maintenance cost, 4) interchangeability among multiple fixed points from In to Cu points. The replaceable cell feature facilitates long term maintenance of the scale through management of a group of fixed-point cells of the same type. The compact furnace is easily transportable and therefore can also function as a traveling standard for disseminating the radiation temperature scale, and for maintaining the scale at the secondary level and industrial calibration laboratories. It is expected that the furnace will play a key role of the traveling standard in the anticipated APMP supplementary comparison of the radiation thermometry scale
Random fixed point equations and inverse problems using "collage method" for contraction mappings
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2007-10-01
In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations T(w,x(w))=x(w) where is a given operator, [Omega] is a probability space and X is a Polish metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations, and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.
A New Iterative Method for Equilibrium Problems and Fixed Point Problems
Directory of Open Access Journals (Sweden)
Abdul Latif
2013-01-01
Full Text Available Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012, Cianciaruso et al. (2010, and many others.
Large deviation tail estimates and related limit laws for stochastic fixed point equations
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
We study the forward and backward recursions generated by a stochastic fixed point equation (SFPE) of the form $V \\stackrel{d}{=} A\\max\\{V, D\\}+B$, where $(A, B, D) \\in (0, \\infty)\\times {\\mathbb R}^2$, for both the stationary and explosive cases. In the stationary case (when ${\\bf E} [\\log \\: A......] explosive case (when ${\\bf E} [\\log \\: A] > 0)$, we establish a central limit theorem for the forward recursion generated by the SFPE, namely the process $V_n= A_n \\max\\{V_{n-1...
Accuracy Constraint Determination in Fixed-Point System Design
Directory of Open Access Journals (Sweden)
Serizel R
2008-01-01
Full Text Available Most of digital signal processing applications are specified and designed with floatingpoint arithmetic but are finally implemented using fixed-point architectures. Thus, the design flow requires a floating-point to fixed-point conversion stage which optimizes the implementation cost under execution time and accuracy constraints. This accuracy constraint is linked to the application performances and the determination of this constraint is one of the key issues of the conversion process. In this paper, a method is proposed to determine the accuracy constraint from the application performance. The fixed-point system is modeled with an infinite precision version of the system and a single noise source located at the system output. Then, an iterative approach for optimizing the fixed-point specification under the application performance constraint is defined and detailed. Finally the efficiency of our approach is demonstrated by experiments on an MP3 encoder.
Wall shear stress fixed points in cardiovascular fluid mechanics.
Arzani, Amirhossein; Shadden, Shawn C
2018-05-17
Complex blood flow in large arteries creates rich wall shear stress (WSS) vectorial features. WSS acts as a link between blood flow dynamics and the biology of various cardiovascular diseases. WSS has been of great interest in a wide range of studies and has been the most popular measure to correlate blood flow to cardiovascular disease. Recent studies have emphasized different vectorial features of WSS. However, fixed points in the WSS vector field have not received much attention. A WSS fixed point is a point on the vessel wall where the WSS vector vanishes. In this article, WSS fixed points are classified and the aspects by which they could influence cardiovascular disease are reviewed. First, the connection between WSS fixed points and the flow topology away from the vessel wall is discussed. Second, the potential role of time-averaged WSS fixed points in biochemical mass transport is demonstrated using the recent concept of Lagrangian WSS structures. Finally, simple measures are proposed to quantify the exposure of the endothelial cells to WSS fixed points. Examples from various arterial flow applications are demonstrated. Copyright © 2018 Elsevier Ltd. All rights reserved.
Eigenvectors and fixed point of non-linear operators
Directory of Open Access Journals (Sweden)
Giulio Trombetta
2007-12-01
Full Text Available Let X be a real inﬁnite-dimensional Banach space and ψ a measure of noncompactness on X. Let Ω be a bounded open subset of X and A : Ω → X a ψ-condensing operator, which has no ﬁxed points on ∂Ω.Then the ﬁxed point index, ind(A,Ω, of A on Ω is deﬁned (see, for example, ([1] and [18]. In particular, if A is a compact operator ind(A,Ω agrees with the classical Leray-Schauder degree of I −A on Ω relative to the point 0, deg(I −A,Ω,0. The main aim of this note is to investigate boundary conditions, under which the ﬁxed point index of strict- ψ-contractive or ψ-condensing operators A : Ω → X is equal to zero. Correspondingly, results on eigenvectors and nonzero ﬁxed points of k-ψ-contractive and ψ-condensing operators are obtained. In particular we generalize the Birkhoff-Kellog theorem [4] and Guo’s domain compression and expansion theorem [17]. The note is based mainly on the results contained in [7] and [8].
Coexistence of an unstirred chemostat model with B-D functional response by fixed point index theory
Directory of Open Access Journals (Sweden)
Xiao-zhou Feng
2016-11-01
Full Text Available Abstract This paper deals with an unstirred chemostat model with the Beddington-DeAngelis functional response. First, some prior estimates for positive solutions are proved by the maximum principle and the method of upper and lower solutions. Second, the calculation on the fixed point index of chemostat model is obtained by degree theory and the homotopy invariance theorem. Finally, some sufficient condition on the existence of positive steady-state solutions is established by fixed point index theory and bifurcation theory.
Directory of Open Access Journals (Sweden)
Wei-Qi Deng
2013-01-01
Full Text Available Based on an original idea, namely, a specific way of choosing the indexes of the involved mappings, we propose a new hybrid shrinking iteration scheme for approximating some common fixed points of a countable family of asymptotically strictly quasi-ϕ-pseudocontractions and obtain a strong convergence theorem in the framework of Banach space. Our result extends other authors, related results existing in the current literature. As application, an iterative solution to a system of equilibrium problems is provided.
Fixed Points in Discrete Models for Regulatory Genetic Networks
Directory of Open Access Journals (Sweden)
Orozco Edusmildo
2007-01-01
Full Text Available It is desirable to have efficient mathematical methods to extract information about regulatory iterations between genes from repeated measurements of gene transcript concentrations. One piece of information is of interest when the dynamics reaches a steady state. In this paper we develop tools that enable the detection of steady states that are modeled by fixed points in discrete finite dynamical systems. We discuss two algebraic models, a univariate model and a multivariate model. We show that these two models are equivalent and that one can be converted to the other by means of a discrete Fourier transform. We give a new, more general definition of a linear finite dynamical system and we give a necessary and sufficient condition for such a system to be a fixed point system, that is, all cycles are of length one. We show how this result for generalized linear systems can be used to determine when certain nonlinear systems (monomial dynamical systems over finite fields are fixed point systems. We also show how it is possible to determine in polynomial time when an ordinary linear system (defined over a finite field is a fixed point system. We conclude with a necessary condition for a univariate finite dynamical system to be a fixed point system.
Matrix product density operators: Renormalization fixed points and boundary theories
Energy Technology Data Exchange (ETDEWEB)
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)
2017-03-15
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
IR fixed points in SU(3 gauge theories
Directory of Open Access Journals (Sweden)
K.-I. Ishikawa
2015-09-01
Full Text Available We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the SU(3 gauge theories with Nf fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cutoff, which we cannot remove in the conformal field theories in sharp contrast to the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for Nf=16,12,8 and Nf=7 and indeed identify the location of the IR fixed points in all cases.
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.
An existence theorem for a type of functional differential equation with infinite delay
Izsak, F.
We prove an existence theorem for a functional differential equation with infinite delay using the Schauder fixpoint theorem. We extend a result in [19] applying the fixed point procedure in an appropriate function space.
Stability of common fixed points in uniform spaces
Directory of Open Access Journals (Sweden)
Singh Shyam
2011-01-01
Full Text Available Abstract Stability results for a pair of sequences of mappings and their common fixed points in a Hausdorff uniform space using certain new notions of convergence are proved. The results obtained herein extend and unify several known results. AMS(MOS Subject classification 2010: 47H10; 54H25.
STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION VIA FIXED POINT
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a nonlinear neutral differential equation is considered.By a fixed point theory,we give some conditions to ensure that the zero solution to the equation is asymptotically stable.Some existing results are improved and generalized.
Probabilistic G-Metric space and some fixed point results
Directory of Open Access Journals (Sweden)
A. R. Janfada
2013-01-01
Full Text Available In this note we introduce the notions of generalized probabilistic metric spaces and generalized Menger probabilistic metric spaces. After making our elementary observations and proving some basic properties of these spaces, we are going to prove some fixed point result in these spaces.
On stability of fixed points and chaos in fractional systems
Edelman, Mark
2018-02-01
In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0 logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.
Radiative symmetry breaking from interacting UV fixed points
DEFF Research Database (Denmark)
Abel, Steven; Sannino, Francesco
2017-01-01
It is shown that the addition of positive mass-squared terms to asymptotically safe gauge-Yukawa theories with perturbative UV fixed points leads to calculable radiative symmetry breaking in the IR. This phenomenon, and the multiplicative running of the operators that lies behind it, is akin...
Renormalization group fixed points of foliated gravity-matter systems
Energy Technology Data Exchange (ETDEWEB)
Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)
2017-05-17
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.
On stability of fixed points and chaos in fractional systems.
Edelman, Mark
2018-02-01
In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0chaos is impossible in the corresponding continuous fractional systems.
Directory of Open Access Journals (Sweden)
Ishak Altun
2016-01-01
Full Text Available We provide sufficient conditions for the existence of a unique common fixed point for a pair of mappings T,S:X→X, where X is a nonempty set endowed with a certain metric. Moreover, a numerical algorithm is presented in order to approximate such solution. Our approach is different to the usual used methods in the literature.
A new 6d fixed point from holography
Energy Technology Data Exchange (ETDEWEB)
Apruzzi, Fabio [Department of Physics, University of North Carolina,Chapel Hill, NC 27599 (United States); CUNY Graduate Center, Initiative for the Theoretical Sciences,New York, NY 10016 (United States); Department of Physics, Columbia University,New York, NY 10027 (United States); Dibitetto, Giuseppe; Tizzano, Luigi [Department of Physics and Astronomy, Uppsala university,Box 516, SE-75120 Uppsala (Sweden)
2016-11-22
We propose a stringy construction giving rise to a class of interacting and non-supersymmetric CFT’s in six dimensions. Such theories may be obtained as an IR conformal fixed point of an RG flow ending up in a (1,0) theory in the UV. We provide the due holographic evidence in the context of massive type IIA on AdS{sub 7}×M{sub 3}, where M{sub 3} is topologically an S{sup 3}. In particular, in this paper we present a 10d flow solution which may be interpreted as a non-BPS bound state of NS5, D6 and (D6)-bar branes. Moreover, by adopting its 7d effective description, we are able to holographically compute the free energy and the operator spectrum in the novel IR conformal fixed point.
Fixed Points of Multivalued Contractive Mappings in Partial Metric Spaces
Directory of Open Access Journals (Sweden)
Abdul Rahim Khan
2014-01-01
Full Text Available The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established.
Fixed point structure of quenched, planar quantum electrodynamics
International Nuclear Information System (INIS)
Love, S.T.
1986-07-01
Gauge theories exhibiting a hierarchy of fermion mass scales may contain a pseudo-Nambu-Boldstone boson of spontaneously broken scale invariance. The relation between scale and chiral symmetry breaking is studied analytically in quenched, planar quantum electrodynamics in four dimensions. The model possesses a novel nonperturbative ultraviolet fixed point governing its strong coupling phase which requires the mixing of four fermion operators. 12 refs
Almost Fixed-Point-Free Automorphisms of Prime Power Order
Directory of Open Access Journals (Sweden)
B.A.F. Wehrfritz
2016-06-01
Full Text Available We study the effect under various rank restrictions of a group having an automorphism of prime power order whose fixed-point set is also finite of prime power order for the same prime. Generally our conclusions are that the group has a soluble normal subgroup of bounded derived length. Not surprisingly the bound gets larger as the rank restrictions get weaker.
New results for the Liebau phenomenon via fixed point index
Czech Academy of Sciences Publication Activity Database
Cid, J.A.; Infante, G.; Tvrdý, Milan; Zima, M.
2017-01-01
Roč. 35, June (2017), s. 457-469 ISSN 1468-1218 R&D Projects: GA ČR(CZ) GA14-06958S Institutional support: RVO:67985840 Keywords : cone * fixed point index * Green's function Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.659, year: 2016 http://www.sciencedirect.com/science/article/pii/S1468121816301511
Approximate solutions of common fixed-point problems
Zaslavski, Alexander J
2016-01-01
This book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal...
Directory of Open Access Journals (Sweden)
Wiyada Kumam
2016-05-01
Full Text Available In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field.
Iterative approximation of fixed points of nonexpansive mappings
International Nuclear Information System (INIS)
Chidume, C.E.; Chidume, C.O.
2007-07-01
Let K be a nonempty closed convex subset of a real Banach space E which has a uniformly Gateaux differentiable norm and T : K → K be a nonexpansive mapping with F(T) := { x element of K : Tx = x} ≠ 0 . For a fixed δ element of (0, 1), define S : K → K by Sx := (1- δ)x+ δ Tx , for all x element of K. Assume that { z t } converges strongly to a fixed point z of T as t → 0, where z t is the unique element of K which satisfies z t = tu + (1 - t)Tz t for arbitrary u element of K. Let {α n } be a real sequence in (0, 1) which satisfies the following conditions: C1 : lim α n = 0; C2 : Σαn = ∞. For arbitrary x 0 element of K, let the sequence { x n } be defined iteratively by x n+1 = α n u + (1 - α n )Sx n . Then, {x n } converges strongly to a fixed point of T. (author)
Directory of Open Access Journals (Sweden)
Wilson Rodríguez Calderón
2015-04-01
Full Text Available When we need to determine the solution of a nonlinear equation there are two options: closed-methods which use intervals that contain the root and during the iterative process reduce the size of natural way, and, open-methods that represent an attractive option as they do not require an initial interval enclosure. In general, we know open-methods are more efficient computationally though they do not always converge. In this paper we are presenting a divergence case analysis when we use the method of fixed point iteration to find the normal height in a rectangular channel using the Manning equation. To solve this problem, we propose applying two strategies (developed by authors that allow to modifying the iteration function making additional formulations of the traditional method and its convergence theorem. Although Manning equation is solved with other methods like Newton when we use the iteration method of fixed-point an interesting divergence situation is presented which can be solved with a convergence higher than quadratic over the initial iterations. The proposed strategies have been tested in two cases; a study of divergence of square root of real numbers was made previously by authors for testing. Results in both cases have been successful. We present comparisons because are important for seeing the advantage of proposed strategies versus the most representative open-methods.
Stability by fixed point theory for functional differential equations
Burton, T A
2006-01-01
This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicia
Border collisions inside the stability domain of a fixed point
DEFF Research Database (Denmark)
Avrutin, Viktor; Zhusubaliyev, Zhanybai T.; Mosekilde, Erik
2016-01-01
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......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...
Improved fixed point iterative method for blade element momentum computations
DEFF Research Database (Denmark)
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
The blade element momentum (BEM) theory is widely used in aerodynamic performance calculations and optimization applications for wind turbines. The fixed point iterative method is the most commonly utilized technique to solve the BEM equations. However, this method sometimes does not converge...... are addressed through both theoretical analysis and numerical tests. A term from the BEM equations equals to zero at a critical inflow angle is the source of the convergence problems. When the initial inflow angle is set larger than the critical inflow angle and the relaxation methodology is adopted...
Third generation masses from a two Higgs model fixed point
International Nuclear Information System (INIS)
Froggatt, C.D.; Knowles, I.G.; Moorhouse, R.G.
1990-01-01
The large mass ratio between the top and bottom quarks may be attributed to a hierarchy in the vacuum expectation values of scalar doublets. We consider an effective renormalisation group fixed point determination of the quartic scalar and third generation Yukawa couplings in such a two doublet model. This predicts a mass m t =220 GeV and a mass ratio m b /m τ =2.6. In its simplest form the model also predicts the scalar masses, including a light scalar with a mass of order the b quark mass. Experimental implications are discussed. (orig.)
International Nuclear Information System (INIS)
Schrempp, B.
1994-10-01
The two loop 'top-down' renormalization group flow for the top, bottom and tau Yukawa couplings, from μ=M GUT ≅O(10 16 GeV) to μ≅m t , is explored in the framework of supersymmetric grand unification; reproduction of the physical bottom and tau masses is required. Instead of following the recent trend of implementing exact Yukawa coupling unification i) a search for infrared (IR) fixed lines and fixed points in the m t pole -tan β plane is performed and ii) the extent to which these imply approximate Yukawa unification is determined. In the m t pole -tan β plane two IR fixed lines, intersecting in an IR fixed point, are located. The more attractive fixed line has a branch of almost constant top mass, m t pole ≅168≅180 GeV (close to the experimental value), for the large interval 2.5 GUT approximately. The less attractive fixed line as well as the fixed point at m t pole ≅170 GeV, tan β≅55 implement approximate top-bottom Yukawa unification at all scales μ. The renormalization group flow is attracted towards the IR fixed point by way of the more attractive IR fixed line. The fixed point and lines are distinct from the much quoted effective IR fixed point m t pole ≅O(200 GeV) sin β. (orig.)
Non-monotonic Pre-fixed Points and Learning
Directory of Open Access Journals (Sweden)
Stefano Berardi
2013-08-01
Full Text Available We consider the problem of finding pre-fixed points of interactive realizers over arbitrary knowledge spaces, obtaining a relative recursive procedure. Knowledge spaces and interactive realizers are an abstract setting to represent learning processes, that can interpret non-constructive proofs. Atomic pieces of information of a knowledge space are stratified into levels, and evaluated into truth values depending on knowledge states. Realizers are then used to define operators that extend a given state by adding and possibly removing atoms: in a learning process states of knowledge change nonmonotonically. Existence of a pre-fixed point of a realizer is equivalent to the termination of the learning process with some state of knowledge which is free of patent contradictions and such that there is nothing to add. In this paper we generalize our previous results in the case of level 2 knowledge spaces and deterministic operators to the case of omega-level knowledge spaces and of non-deterministic operators.
Fixed-point image orthorectification algorithms for reduced computational cost
French, Joseph Clinton
Imaging systems have been applied to many new applications in recent years. With the advent of low-cost, low-power focal planes and more powerful, lower cost computers, remote sensing applications have become more wide spread. Many of these applications require some form of geolocation, especially when relative distances are desired. However, when greater global positional accuracy is needed, orthorectification becomes necessary. Orthorectification is the process of projecting an image onto a Digital Elevation Map (DEM), which removes terrain distortions and corrects the perspective distortion by changing the viewing angle to be perpendicular to the projection plane. Orthorectification is used in disaster tracking, landscape management, wildlife monitoring and many other applications. However, orthorectification is a computationally expensive process due to floating point operations and divisions in the algorithm. To reduce the computational cost of on-board processing, two novel algorithm modifications are proposed. One modification is projection utilizing fixed-point arithmetic. Fixed point arithmetic removes the floating point operations and reduces the processing time by operating only on integers. The second modification is replacement of the division inherent in projection with a multiplication of the inverse. The inverse must operate iteratively. Therefore, the inverse is replaced with a linear approximation. As a result of these modifications, the processing time of projection is reduced by a factor of 1.3x with an average pixel position error of 0.2% of a pixel size for 128-bit integer processing and over 4x with an average pixel position error of less than 13% of a pixel size for a 64-bit integer processing. A secondary inverse function approximation is also developed that replaces the linear approximation with a quadratic. The quadratic approximation produces a more accurate approximation of the inverse, allowing for an integer multiplication calculation
Directory of Open Access Journals (Sweden)
Adrian Petruşel
2015-01-01
Full Text Available We will discuss discrete dynamics generated by single-valued and multivalued operators in spaces endowed with a generalized metric structure. More precisely, the behavior of the sequence (fn(xn∈N of successive approximations in complete generalized gauge spaces is discussed. In the same setting, the case of multivalued operators is also considered. The coupled fixed points for mappings t1:X1×X2→X1 and t2:X1×X2→X2 are discussed and an application to a system of nonlinear integral equations is given.
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We introduce and analyze one iterative algorithm by hybrid shrinking projection method for finding a solution of the minimization problem for a convex and continuously Fréchet differentiable functional, with constraints of several problems: finitely many generalized mixed equilibrium problems, finitely many variational inequalities, the general system of variational inequalities and the fixed point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another iterative algorithm by hybrid shrinking projection method for finding a fixed point of infinitely many nonexpansive mappings with the same constraints, and derive its strong convergence under mild assumptions.
Fixed Points and Fuzzy Stability of Functional Equations Related to Inner Product
Directory of Open Access Journals (Sweden)
Hassan Azadi Kenary
2012-04-01
Full Text Available In , Th.M. Rassias introduced the following equality sum_{i,j=1}^m |x_i - x_j |^2 = 2m sum_{i=1}^m|x_i|^2, qquad sum_{i=1}^m x_i =0 for a fixed integer $m ge 3$. Let $V, W$ be real vector spaces. It is shown that if a mapping $f : V ightarrow W$ satisfies sum_{i,j=1}^m f(x_i - x_j = 2m sum_{i=1}^m f(x_i for all $x_1, ldots, x_{m} in V$ with $sum_{i=1}^m x_i =0$, then the mapping $f : V ightarrow W$ is realized as the sum of an additive mapping and a quadratic mapping. From the above equality we can define the functional equation f(x-y +f(2x+y + f(x+2y= 3f(x+ 3f(y + 3f(x+y , which is called a {it quadratic functional equation}. Every solution of the quadratic functional equation is said to be a {it quadratic mapping}. Using fixed point theorem we prove the Hyers-Ulam stability of the functional equation ( in fuzzy Banach spaces.
International Nuclear Information System (INIS)
Gutlé, Claudine
2017-01-01
Incomplete spaces are investigated for solving the Schrödinger equation under the Born–Oppenheimer approximation. It is shown that the Hellmann–Feynman theorem cannot be used for computing the electronic force exerted on a nucleus, when a variational wavefunction with floating centers is used, if multicenter polynomial components are added in order to describe the polarization effects through the chemical bond. This is because the minimum of the potential energy surface is not a stationary point in the direction of the float parameter. Such a failure can be fixed by considering a molecular model with finite size nuclei, as defined herein. The classical electronic force is computed for that model, as compared with the standard point charge approximation, and it is applied to the H 2 + molecular ion. As a result, the former model is found more accurate by several orders of magnitude. (author)
Approximation of fixed points of strongly pseudo-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1991-10-01
Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Let T:K→K be a continuous strongly pseudocontractive mapping of K into itself. Let {c n } n=1 ∞ be a real sequence satisfying: (i) 0 n n=1 ∞ c n =∞; and (iii) Σ n=1 ∞ c n b(c n ) n } n=1 ∞ generated by x 1 is an element of K. x n+1 =(1-c n )x n +c n Tx n , n≥1, converges strongly to the unique fixed point of T. A related result deals with the Ishikawa iteration scheme when T is Lipschitzian and strongly pseudocontractive. (author). 28 refs
Multi-Valued Modal Fixed Point Logics for Model Checking
Nishizawa, Koki
In this paper, I will show how multi-valued logics are used for model checking. Model checking is an automatic technique to analyze correctness of hardware and software systems. A model checker is based on a temporal logic or a modal fixed point logic. That is to say, a system to be checked is formalized as a Kripke model, a property to be satisfied by the system is formalized as a temporal formula or a modal formula, and the model checker checks that the Kripke model satisfies the formula. Although most existing model checkers are based on 2-valued logics, recently new attempts have been made to extend the underlying logics of model checkers to multi-valued logics. I will summarize these new results.
Fixed point and anomaly mediation in partial {\\boldsymbol{N}}=2 supersymmetric standard models
Yin, Wen
2018-01-01
Motivated by the simple toroidal compactification of extra-dimensional SUSY theories, we investigate a partial N = 2 supersymmetric (SUSY) extension of the standard model which has an N = 2 SUSY sector and an N = 1 SUSY sector. We point out that below the scale of the partial breaking of N = 2 to N = 1, the ratio of Yukawa to gauge couplings embedded in the original N = 2 gauge interaction in the N = 2 sector becomes greater due to a fixed point. Since at the partial breaking scale the sfermion masses in the N = 2 sector are suppressed due to the N = 2 non-renormalization theorem, the anomaly mediation effect becomes important. If dominant, the anomaly-induced masses for the sfermions in the N = 2 sector are almost UV-insensitive due to the fixed point. Interestingly, these masses are always positive, i.e. there is no tachyonic slepton problem. From an example model, we show interesting phenomena differing from ordinary MSSM. In particular, the dark matter particle can be a sbino, i.e. the scalar component of the N = 2 vector multiplet of {{U}}{(1)}Y. To obtain the correct dark matter abundance, the mass of the sbino, as well as the MSSM sparticles in the N = 2 sector which have a typical mass pattern of anomaly mediation, is required to be small. Therefore, this scenario can be tested and confirmed in the LHC and may be further confirmed by the measurement of the N = 2 Yukawa couplings in future colliders. This model can explain dark matter, the muon g-2 anomaly, and gauge coupling unification, and relaxes some ordinary problems within the MSSM. It is also compatible with thermal leptogenesis.
An extension of Brosowski-Meinardus theorem on invariant approximation
International Nuclear Information System (INIS)
Liaqat Ali Khan; Abdul Rahim Khan.
1991-07-01
We obtain a generalization of a fixed point theorem of Dotson for non-expansive mappings on star-shaped sets and then use it to prove a unified Brosowski-Meinardus theorem on invariant approximation in the setting of p-normed linear spaces. (author). 13 refs
Fundamental flavours, fields and fixed points: a brief account
Energy Technology Data Exchange (ETDEWEB)
Kundu, Arnab [Theory Division, Saha Institute of Nuclear Physics,1/AF Bidhannagar, Kolkata 700064 (India); Homi Bhaba National Institute, Training School Complex,Anushakti Nagar, Mumbai 400085 (India); Kundu, Nilay [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP),Kyoto University,Kyoto 606-8502 (Japan)
2017-03-13
In this article we report on a preliminary study, via Holography, of infrared fixed points in a putative strongly coupled SU(N{sub c}) gauge theory, with N{sub f} fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently effective or a bottom up approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS{sub m}×ℝ{sup n}-type, which has appeared in the literature before; and AdS{sub m}×EAdS{sub n}-type, where m and n are suitable integers. Both these classes of solutions are non-perturbative in back-reaction. The AdS{sub m}×EAdS{sub n}-type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS{sub 5} ultraviolet to both an AdS{sub 2} and an AdS{sub 3} IR.
Fixed points of IA-endomorphisms of a free metabelian Lie algebra
Indian Academy of Sciences (India)
Let be a free metabelian Lie algebra of finite rank at least 2. We show the existence of non-trivial fixed points of an -endomorphism of and give an algorithm detecting them. In particular, we prove that the fixed point subalgebra Fix of an -endomorphism of is not finitely generated.
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
Convergence theorems for quasi-contractive mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
It is proved that each of two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of a quasi-contractive map in real Banach spacers with property (U, α, m+1, m). These Banach spaces include the L p (or l p ) spaces, p ≥ 2. Our theorems generalize important known results. (author). 29 refs
Common fixed points for generalized contractive mappings in cone metric spaces
Directory of Open Access Journals (Sweden)
Hassen Aydi
2012-06-01
Full Text Available The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.
Gaussian point count statistics for families of curves over a fixed finite field
Kurlberg, Par; Wigman, Igor
2010-01-01
We produce a collection of families of curves, whose point count statistics over F_p becomes Gaussian for p fixed. In particular, the average number of F_p points on curves in these families tends to infinity.
Another look at the second incompleteness theorem
Visser, Albert
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is fixed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the
The D4-D8 Brane System and Five Dimensional Fixed Points
Brandhuber, A; Oz, Y
1999-01-01
We construct dual Type I' string descriptions to five dimensional supersymmetric fixed points with $E_{N_f+1}$ global symmetry. The background is obtained as the near horizon geometry of the D4-D8 brane system in massive Type IIA supergravity. We use the dual description to deduce some properties of the fixed points.
Area law for fixed points of rapidly mixing dissipative quantum systems
Energy Technology Data Exchange (ETDEWEB)
Brandão, Fernando G. S. L. [Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052 (United States); Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom); Cubitt, Toby S. [Department of Computer Science, University College London, Gower Street, London WC1E 6BT (United Kingdom); DAMTP, University of Cambridge, Cambridge (United Kingdom); Lucia, Angelo, E-mail: anlucia@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Madrid (Spain); Michalakis, Spyridon [Institute for Quantum Information and Matter, Caltech, California 91125 (United States); Perez-Garcia, David [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Madrid (Spain); IMI, Universidad Complutense de Madrid, Madrid (Spain); ICMAT, C/Nicolás Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain)
2015-10-15
We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure or the system is frustration free.
Mangum, B W
1983-07-01
In an investigation of the melting and freezing behavior of succinonitrile, the triple-point temperature was determined to be 58.0805 degrees C, with an estimated uncertainty of +/- 0.0015 degrees C relative to the International Practical Temperature Scale of 1968 (IPTS-68). The triple-point temperature of this material is evaluated as a temperature-fixed point, and some clinical laboratory applications of this fixed point are proposed. In conjunction with the gallium and ice points, the availability of succinonitrile permits thermistor thermometers to be calibrated accurately and easily on the IPTS-68.
The fixed point structure of lattice field theories
International Nuclear Information System (INIS)
Baier, R.; Reusch, H.J.; Lang, C.B.
1989-01-01
Monte-Carlo renormalization group methods allow to analyze lattice regularized quantum field theories. The properties of the quantized field theory in the continuum may be recovered at a critical point of the lattice model. This requires a study of the phase diagram and the renormalization flow structure of the coupling constants. As an example the authors discuss the results of a recent MCRG investigation of the SU(2) adjoint Higgs model, where they find evidence for the existence of a tricritical point at finite values of the inverse gauge coupling β
Design and Implementation of Numerical Linear Algebra Algorithms on Fixed Point DSPs
Directory of Open Access Journals (Sweden)
Gene Frantz
2007-01-01
Full Text Available Numerical linear algebra algorithms use the inherent elegance of matrix formulations and are usually implemented using C/C++ floating point representation. The system implementation is faced with practical constraints because these algorithms usually need to run in real time on fixed point digital signal processors (DSPs to reduce total hardware costs. Converting the simulation model to fixed point arithmetic and then porting it to a target DSP device is a difficult and time-consuming process. In this paper, we analyze the conversion process. We transformed selected linear algebra algorithms from floating point to fixed point arithmetic, and compared real-time requirements and performance between the fixed point DSP and floating point DSP algorithm implementations. We also introduce an advanced code optimization and an implementation by DSP-specific, fixed point C code generation. By using the techniques described in the paper, speed can be increased by a factor of up to 10 compared to floating point emulation on fixed point hardware.
Approximating fixed points for nonself mappings in CAT(0) spaces
Razani Abdolrahman; Shabani Saeed
2011-01-01
Abstract Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T : K → X be a nonself mapping, satisfying Condition (E) with F(T): = {x ∈ K : Tx = x} ≠ ∅. Suppose {xn} is generated iteratively by x1 ∈ K, xn+1 = P ((1 - αn)xn ⊕ αnTP [(1 - βn)xn ⊕ βnTxn]),n ≥ 1, where {αn} and {βn} are real sequences in [ε, 1 - ε] for some ε W...
Directory of Open Access Journals (Sweden)
Liu Min
2010-01-01
Full Text Available In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem
Directory of Open Access Journals (Sweden)
Oleg Zubelevich
2003-05-01
Full Text Available We extend the classical majorant functions method to a PDE system which right hand side is a mapping of one functional space to another. This extension is based on some generalization of the Schauder fixed point theorem.
Lyapunov functions for the fixed points of the Lorenz model
International Nuclear Information System (INIS)
Bakasov, A.A.; Govorkov, B.B. Jr.
1992-11-01
We have shown how the explicit Lyapunov functions can be constructed in the framework of a regular procedure suggested and completed by Lyapunov a century ago (''method of critical cases''). The method completely covers all practically encountering subtle cases of stability study for ordinary differential equations when the linear stability analysis fails. These subtle cases, ''the critical cases'', according to Lyapunov, include both bifurcations of solutions and solutions of systems with symmetry. Being properly specialized and actually powerful in case of ODE's, this Lyapunov's method is formulated in simple language and should attract a wide interest of the physical audience. The method leads to inevitable construction of the explicit Lyapunov function, takes automatically into account the Fredholm alternative and avoids infinite step calculations. Easy and apparent physical interpretation of the Lyapunov function as a potential or as a time-dependent entropy provides one with more details about the local dynamics of the system at non-equilibrium phase transition points. Another advantage is that this Lyapunov's method consists of a set of very detailed explicit prescriptions which allow one to easy programmize the method for a symbolic processor. The application of the Lyapunov theory for critical cases has been done in this work to the real Lorenz equations and it is shown, in particular, that increasing σ at the Hopf bifurcation point suppresses the contribution of one of the variables to the destabilization of the system. The relation of the method to contemporary methods and its place among them have been clearly and extensively discussed. Due to Appendices, the paper is self-contained and does not require from a reader to approach results published only in Russian. (author). 38 refs
Boundary Fixed Points, Enhanced Gauge Symmetry and Singular Bundles on K3
Fuchs, J; Lerche, Wolfgang; Lütken, C A; Schweigert, C; Walcher, J
2001-01-01
We investigate certain fixed points in the boundary conformal field theory representation of type IIA D-branes on Gepner points of K3. They correspond geometrically to degenerate brane configurations, and physically lead to enhanced gauge symmetries on the world-volume. Non-abelian gauge groups arise if the stabilizer group of the fixed points is realized projectively, which is similar to D-branes on orbifolds with discrete torsion. Moreover, the fixed point boundary states can be resolved into several irreducible components. These correspond to bound states at threshold and can be viewed as (non-locally free) sub-sheaves of semi-stable sheaves. Thus, the BCFT fixed points appear to carry two-fold geometrical information: on the one hand they probe the boundary of the instanton moduli space on K3, on the other hand they probe discrete torsion in D-geometry.
Common Fixed Points of Generalized Cocyclic Mappings in Complex Valued Metric Spaces
Directory of Open Access Journals (Sweden)
Mujahid Abbas
2015-01-01
Full Text Available We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces
Directory of Open Access Journals (Sweden)
Mujahid Abbas
2015-01-01
Full Text Available The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.
Revisiting the dilatation operator of the Wilson-Fisher fixed point
Energy Technology Data Exchange (ETDEWEB)
Liendo, Pedro [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2017-01-15
We revisit the order ε dilatation operator of the Wilson-Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-ε scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.
Swinford, Echo
2006-01-01
If you're vexed and perplexed by PowerPoint, pick up a copy of Fixing PowerPoint Annoyances. This funny, and often opinionated, guide is chock full of tools and techniques for eliminating all the problems that drive audiences and presenters crazy. There's nothing more discouraging than an unresponsive audience--or worse, one that snickers at your slides. And there's nothing more maddening than technical glitches that turn your carefully planned slide show into a car wreck. Envious when you see other presenters effectively use nifty features that you've never been able to get to work right?
Fixed Point Methods in the Stability of the Cauchy Functional Equations
Directory of Open Access Journals (Sweden)
Z. Dehvari
2013-03-01
Full Text Available By using the fixed point methods, we prove some generalized Hyers-Ulam stability of homomorphisms for Cauchy and CauchyJensen functional equations on the product algebras and on the triple systems.
Fixed Point in Topological Vector Space-Valued Cone Metric Spaces
Directory of Open Access Journals (Sweden)
Muhammad Arshad
2010-01-01
Full Text Available We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.
Three Boundary Conditions for Computing the Fixed-Point Property in Binary Mixture Data.
Directory of Open Access Journals (Sweden)
Leendert van Maanen
Full Text Available 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.
Finding Non-Zero Stable Fixed Points of the Weighted Kuramoto model is NP-hard
Taylor, Richard
2015-01-01
The Kuramoto model when considered over the full space of phase angles [$0,2\\pi$) can have multiple stable fixed points which form basins of attraction in the solution space. In this paper we illustrate the fundamentally complex relationship between the network topology and the solution space by showing that determining the possibility of multiple stable fixed points from the network topology is NP-hard for the weighted Kuramoto Model. In the case of the unweighted model this problem is shown...
Error tolerance in an NMR implementation of Grover's fixed-point quantum search algorithm
International Nuclear Information System (INIS)
Xiao Li; Jones, Jonathan A.
2005-01-01
We describe an implementation of Grover's fixed-point quantum search algorithm on a nuclear magnetic resonance quantum computer, searching for either one or two matching items in an unsorted database of four items. In this algorithm the target state (an equally weighted superposition of the matching states) is a fixed point of the recursive search operator, so that the algorithm always moves towards the desired state. The effects of systematic errors in the implementation are briefly explored
Infrared fixed point of SU(2) gauge theory with six flavors
Leino, Viljami; Rummukainen, Kari; Suorsa, Joni; Tuominen, Kimmo; Tähtinen, Sara
2018-06-01
We compute the running of the coupling in SU(2) gauge theory with six fermions in the fundamental representation of the gauge group. We find strong evidence that this theory has an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point. This theory therefore likely lies close to the boundary of the conformal window and will display novel infrared dynamics if coupled with the electroweak sector of the Standard Model.
International Nuclear Information System (INIS)
Neves, A.G.M.
1988-01-01
The renormalization transformation e sup(-S 1) sup((B)) const. ζ e sup(-S o (A) - V(A)) δ (B-C sub(1) A) δ sub(Ax) (A)DA for the U(1) lattice gauge theory, where S sub(o) (A) is the gaussian fixed point of the transformation, V(A) is a gauge invariant perturbation, C sub(1) is the averaging operator and δ sub(Ax) (A) fixes the local axial gauge is studied via an equivalent renormalization transformation on the 2-forms F = dA. The transformation is linearized in the neighborhood of the fixed point and then diagonalized. (author)
n-Tupled Coincidence Point Theorems in Partially Ordered Metric Spaces for Compatible Mappings
Directory of Open Access Journals (Sweden)
Sumitra Dalal
2014-01-01
Full Text Available The intent of this paper is to introduce the notion of compatible mappings for n-tupled coincidence points due to (Imdad et al. (2013. Related examples are also given to support our main results. Our results are the generalizations of the results of (Gnana Bhaskar and Lakshmikantham (2006, Lakshmikantham and Ćirić (2009, Choudhury and Kundu (2010, and Choudhary et al. (2013.
Gauge-fixing parameter dependence of two-point gauge-variant correlation functions
International Nuclear Information System (INIS)
Zhai, C.
1996-01-01
The gauge-fixing parameter ξ dependence of two-point gauge-variant correlation functions is studied for QED and QCD. We show that, in three Euclidean dimensions, or for four-dimensional thermal gauge theories, the usual procedure of getting a general covariant gauge-fixing term by averaging over a class of covariant gauge-fixing conditions leads to a nontrivial gauge-fixing parameter dependence in gauge-variant two-point correlation functions (e.g., fermion propagators). This nontrivial gauge-fixing parameter dependence modifies the large-distance behavior of the two-point correlation functions by introducing additional exponentially decaying factors. These factors are the origin of the gauge dependence encountered in some perturbative evaluations of the damping rates and the static chromoelectric screening length in a general covariant gauge. To avoid this modification of the long-distance behavior introduced by performing the average over a class of covariant gauge-fixing conditions, one can either choose a vanishing gauge-fixing parameter or apply an unphysical infrared cutoff. copyright 1996 The American Physical Society
Application of fixed point theory to chaotic attractors of forced oscillators
International Nuclear Information System (INIS)
Stewart, H.B.
1990-11-01
A review of the structure of chaotic attractors of periodically forced second order nonlinear oscillators suggests that the theory of fixed points of transformations gives information about the fundamental topological structure of attractors. First a simple extension of the Levinson index formula is proved. Then numerical evidence is used to formulate plausible conjectures about absorbing regions containing chaotic attractors in forced oscillators. Applying the Levinson formula suggests a fundamental relation between the number of fixed points or periodic points in a section of the chaotic attractor on the one hand, and a topological invariant of an absorbing region on the other hand. (author)
Convergence theorems for certain classes of nonlinear mappings
International Nuclear Information System (INIS)
Chidume, C.E.
1992-01-01
Recently, Xinlong Weng announced a convergence theorem for the iterative approximation of fixed points of local strictly pseudo-contractive mappings in uniformly smooth Banach spaces, (Proc. Amer. Math. Soc. Vol.113, No.3 (1991) 727-731). An example is presented which shows that this theorem of Weng is false. Then, a convergence theorem is proved, in certain real Banach spaces, for approximation a solution of the inclusion f is an element of x + Tx, where T is a set-valued monotone operator. An explicit error estimate is also presented. (author). 26 refs
Nezir, Veysel; Mustafa, Nizami
2017-04-01
In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.
Infrared fixed point solution for the top quark mass and unification of couplings in the MSSM
International Nuclear Information System (INIS)
Bardeen, W.A.; Carena, M.; Pokorski, S.; Wagner, C.E.M.
1993-08-01
We analyze the implications of the infrared quasi fixed point solution for the top quark mass in the Minimal Supersymmetric Standard Model. This solution could explain in a natural way the relatively large value of the top quark mass and, if confirmed experimentally, may be suggestive of the onset of nonperturbative physics at very high energy scales. In the framework of grand unification, the expected bottom quark -- tau lepton Yukawa coupling unification is very sensitive to the fixed point structure of the top quark mass. For the presently allowed values of the electroweak parameters and the bottom quark mass, the Yukawa coupling unification implies that the top quark mass must be within ten percent of its fixed point values
International Nuclear Information System (INIS)
Anselmi, Damiano
2004-01-01
I discuss several issues about the irreversibility of the RG flow and the trace anomalies c, a and a'. First I argue that in quantum field theory: (i) the scheme-invariant area Δ a' of the graph of the effective beta function between the fixed points defines the length of the RG flow; (ii) the minimum of Δ a' in the space of flows connecting the same UV and IR fixed points defines the (oriented) distance between the fixed points and (iii) in even dimensions, the distance between the fixed points is equal to Δ a = a UV - a IR . In even dimensions, these statements imply the inequalities 0 ≤ Δ a ≤ Δ a' and therefore the irreversibility of the RG flow. Another consequence is the inequality a ≤ c for free scalars and fermions (but not vectors), which can be checked explicitly. Secondly, I elaborate a more general axiomatic set-up where irreversibility is defined as the statement that there exist no pairs of non-trivial flows connecting interchanged UV and IR fixed points. The axioms, based on the notions of length of the flow, oriented distance between the fixed points and certain 'oriented-triangle inequalities', imply the irreversibility of the RG flow without a global a function. I conjecture that the RG flow is also irreversible in odd dimensions (without a global a function). In support of this, I check the axioms of irreversibility in a class of d = 3 theories where the RG flow is integrable at each order of the large N expansion
One loop beta functions and fixed points in higher derivative sigma models
International Nuclear Information System (INIS)
Percacci, Roberto; Zanusso, Omar
2010-01-01
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.
Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology.
Mori, Fumito; Mochizuki, Atsushi
2017-07-14
Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.
Parallel Fixed Point Implementation of a Radial Basis Function Network in an FPGA
Directory of Open Access Journals (Sweden)
Alisson C. D. de Souza
2014-09-01
Full Text Available This paper proposes a parallel fixed point radial basis function (RBF artificial neural network (ANN, implemented in a field programmable gate array (FPGA trained online with a least mean square (LMS algorithm. The processing time and occupied area were analyzed for various fixed point formats. The problems of precision of the ANN response for nonlinear classification using the XOR gate and interpolation using the sine function were also analyzed in a hardware implementation. The entire project was developed using the System Generator platform (Xilinx, with a Virtex-6 xc6vcx240t-1ff1156 as the target FPGA.
Combined GPS/GLONASS Precise Point Positioning with Fixed GPS Ambiguities
Pan, Lin; Cai, Changsheng; Santerre, Rock; Zhu, Jianjun
2014-01-01
Precise point positioning (PPP) technology is mostly implemented with an ambiguity-float solution. Its performance may be further improved by performing ambiguity-fixed resolution. Currently, the PPP integer ambiguity resolutions (IARs) are mainly based on GPS-only measurements. The integration of GPS and GLONASS can speed up the convergence and increase the accuracy of float ambiguity estimates, which contributes to enhancing the success rate and reliability of fixing ambiguities. This paper presents an approach of combined GPS/GLONASS PPP with fixed GPS ambiguities (GGPPP-FGA) in which GPS ambiguities are fixed into integers, while all GLONASS ambiguities are kept as float values. An improved minimum constellation method (MCM) is proposed to enhance the efficiency of GPS ambiguity fixing. Datasets from 20 globally distributed stations on two consecutive days are employed to investigate the performance of the GGPPP-FGA, including the positioning accuracy, convergence time and the time to first fix (TTFF). All datasets are processed for a time span of three hours in three scenarios, i.e., the GPS ambiguity-float solution, the GPS ambiguity-fixed resolution and the GGPPP-FGA resolution. The results indicate that the performance of the GPS ambiguity-fixed resolutions is significantly better than that of the GPS ambiguity-float solutions. In addition, the GGPPP-FGA improves the positioning accuracy by 38%, 25% and 44% and reduces the convergence time by 36%, 36% and 29% in the east, north and up coordinate components over the GPS-only ambiguity-fixed resolutions, respectively. Moreover, the TTFF is reduced by 27% after adding GLONASS observations. Wilcoxon rank sum tests and chi-square two-sample tests are made to examine the significance of the improvement on the positioning accuracy, convergence time and TTFF. PMID:25237901
Combined GPS/GLONASS Precise Point Positioning with Fixed GPS Ambiguities
Directory of Open Access Journals (Sweden)
Lin Pan
2014-09-01
Full Text Available 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.
$β'_{IR}$ at an Infrared Fixed Point in Chiral Gauge Theories
DEFF Research Database (Denmark)
Ryttov, Thomas A.; Shrock, Robert
2018-01-01
We present scheme-independent calculations of the derivative of the beta function, denoted $\\beta'_{IR}$, at a conformally invariant infrared (IR) fixed point, in several asymptotically free chiral gauge theories, namely SO($4k+2$) with $2 \\le k \\le 4$ with respective numbers $N_f$ of fermions...
Common Fixed Points via λ-Sequences in G-Metric Spaces
Directory of Open Access Journals (Sweden)
Yaé Ulrich Gaba
2017-01-01
Full Text Available We use λ-sequences in this article to derive common fixed points for a family of self-mappings defined on a complete G-metric space. We imitate some existing techniques in our proofs and show that the tools employed can be used at a larger scale. These results generalize well known results in the literature.
Establishment of the Co-C Eutectic Fixed-Point Cell for Thermocouple Calibrations at NIMT
Ongrai, O.; Elliott, C. J.
2017-08-01
In 2015, NIMT first established a Co-C eutectic temperature reference (fixed-point) cell measurement capability for thermocouple calibration to support the requirements of Thailand's heavy industries and secondary laboratories. The Co-C eutectic fixed-point cell is a facility transferred from NPL, where the design was developed through European and UK national measurement system projects. In this paper, we describe the establishment of a Co-C eutectic fixed-point cell for thermocouple calibration at NIMT. This paper demonstrates achievement of the required furnace uniformity, the Co-C plateau realization and the comparison data between NIMT and NPL Co-C cells by using the same standard Pt/Pd thermocouple, demonstrating traceability. The NIMT measurement capability for noble metal type thermocouples at the new Co-C eutectic fixed point (1324.06°C) is estimated to be within ± 0.60 K (k=2). This meets the needs of Thailand's high-temperature thermocouple users—for which previously there has been no traceable calibration facility.
Fixed Point of Generalized Eventual Cyclic Gross in Fuzzy Norm Spaces for Contractive Mappings
Directory of Open Access Journals (Sweden)
S. A. M. Mohsenialhosseini
2015-01-01
Full Text Available We define generalized eventual cyclic gross contractive mapping in fuzzy norm spaces, which is a generalization of the eventual cyclic gross contractions. Also we prove the existence of a fixed point for this type of contractive mapping on fuzzy norm spaces.
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Operation of internal transmitter control... Transmitter Control Internal Transmitter Control Systems § 90.473 Operation of internal transmitter control systems through licensed fixed control points. An internal transmitter control system may be operated...
Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation
Directory of Open Access Journals (Sweden)
Berenguer MI
2009-01-01
Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .
Chen, Guiling
2013-01-01
This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study
TARDEC FIXED HEEL POINT (FHP): DRIVER CAD ACCOMMODATION MODEL VERIFICATION REPORT
2017-11-09
Public Release Disclaimer: Reference herein to any specific commercial company, product , process, or service by trade name, trademark, manufacturer , or...not actively engaged HSI until MSB or the Engineering Manufacturing and Development (EMD) Phase, resulting in significant design and cost changes...and shall not be used for advertising or product endorsement purposes. TARDEC Fixed Heel Point (FHP): Driver CAD Accommodation Model Verification
Battuello, M.; Florio, M.; Girard, F.
2010-06-01
An indirect determination of the thermodynamic temperature of the fixed point of copper was made at INRIM by measuring four cells with a Si-based and an InGaAs-based precision radiation thermometer carrying approximated thermodynamic scales realized up to the Ag point. An average value TCu = 1357.840 K was found with a standard uncertainty of 0.047 K. A consequent (T - T90)Cu value of 70 mK can be derived which is 18 mK higher than, but consistent with, the presently available (T - T90)Cu as elaborated by the CCT-WG4.
Optimal Design of Fixed-Point and Floating-Point Arithmetic Units for Scientific Applications
Pongyupinpanich, Surapong
2012-01-01
The challenge in designing a floating-point arithmetic co-processor/processor for scientific and engineering applications is to improve the performance, efficiency, and computational accuracy of the arithmetic unit. The arithmetic unit should efficiently support several mathematical functions corresponding to scientific and engineering computation demands. Moreover, the computations should be performed as fast as possible with a high degree of accuracy. Thus, this thesis proposes algorithm, d...
Study on the fixed point in crustal deformation before strong earthquake
Niu, A.; Li, Y.; Yan, W. Mr
2017-12-01
Usually, scholars believe that the fault pre-sliding or expansion phenomenon will be observed near epicenter area before strong earthquake, but more and more observations show that the crust deformation nearby epicenter area is smallest(Zhou, 1997; Niu,2009,2012;Bilham, 2005; Amoruso et al., 2010). The theory of Fixed point t is a branch of mathematics that arises from the theory of topological transformation and has important applications in obvious model analysis. An important precursory was observed by two tilt-meter sets, installed at Wenchuan Observatory in the epicenter area, that the tilt changes were the smallest compared with the other 8 stations around them in one year before the Wenchuan earthquake. To subscribe the phenomenon, we proposed the minimum annual variation range that used as a topological transformation. The window length is 1 year, and the sliding length is 1 day. The convergence of points with minimum annual change in the 3 years before the Wenchuan earthquake is studied. And the results show that the points with minimum deformation amplitude basically converge to the epicenter region before the earthquake. The possible mechanism of fixed point of crustal deformation was explored. Concerning the fixed point of crust deformation, the liquidity of lithospheric medium and the isostasy theory are accepted by many scholars (Bott &Dean, 1973; Merer et al.1988; Molnar et al., 1975,1978; Tapponnier et al., 1976; Wang et al., 2001). To explain the fixed point of crust deformation before earthquakes, we study the plate bending model (Bai, et al., 2003). According to plate bending model and real deformation data, we have found that the earthquake rupture occurred around the extreme point of plate bending, where the velocities of displacement, tilt, strain, gravity and so on are close to zero, and the fixed points are located around the epicenter.The phenomenon of fixed point of crust deformation is different from former understandings about the
Bojkovski, J.; Veliki, T.; Zvizdić, D.; Drnovšek, J.
2011-08-01
The objective of project EURAMET 1127 (Bilateral comparison of triple point of mercury and melting point of gallium) in the field of thermometry is to compare realization of a triple point of mercury (-38.8344 °C) and melting point of gallium (29.7646 °C) between the Slovenian national laboratory MIRS/UL-FE/LMK and the Croatian national laboratory HMI/FSB-LPM using a long-stem 25 Ω standard platinum resistance thermometer (SPRT). MIRS/UL/FE-LMK participated in a number of intercomparisons on the level of EURAMET. On the other hand, the HMI/LPM-FSB laboratory recently acquired new fixed-point cells which had to be evaluated in the process of intercomparisons. A quartz-sheathed SPRT has been selected and calibrated at HMI/LPM-FSB at the triple point of mercury, the melting point of gallium, and the water triple point. A second set of measurements was made at MIRS/UL/FE-LMK. After its return, the SPRT was again recalibrated at HMI/LPM-FSB. In the comparison, the W value of the SPRT has been used. Results of the bilateral intercomparison confirmed that the new gallium cell of the HMI/LPM-FSB has a value that is within uncertainty limits of both laboratories that participated in the exercise, while the mercury cell experienced problems. After further research, a small leakage in the mercury fixed-point cell has been found.
Bent, J. D.; Sweeney, C.; Tans, P. P.; Newberger, T.; Higgs, J. A.; Wolter, S.
2017-12-01
Accurate estimates of point source gas emissions are essential for reconciling top-down and bottom-up greenhouse gas measurements, but sampling such sources is challenging. Remote sensing methods are limited by resolution and cloud cover; aircraft methods are limited by air traffic control clearances, and the need to properly determine boundary layer height. A new sampling approach leverages the ability of unmanned aerial systems (UAS) to measure all the way to the surface near the source of emissions, improving sample resolution, and reducing the need to characterize a wide downstream swath, or measure to the full height of the planetary boundary layer (PBL). The "Active-AirCore" sampler, currently under development, will fly on a fixed wing UAS in Class G airspace, spiraling from the surface to 1200 ft AGL around point sources such as leaking oil wells to measure methane, carbon dioxide and carbon monoxide. The sampler collects a 100-meter long sample "core" of air in an 1/8" passivated stainless steel tube. This "core" is run on a high-precision instrument shortly after the UAS is recovered. Sample values are mapped to a specific geographic location by cross-referencing GPS and flow/pressure metadata, and fluxes are quantified by applying Gauss's theorem to the data, mapped onto the spatial "cylinder" circumscribed by the UAS. The AirCore-Active builds off the sampling ability and analytical approach of the related AirCore sampler, which profiles the atmosphere passively using a balloon launch platform, but will add an active pumping capability needed for near-surface horizontal sampling applications. Here, we show design elements, laboratory and field test results for methane, describe the overall goals of the mission, and discuss how the platform can be adapted, with minimal effort, to measure other gas species.
Indirect Determination of the Thermodynamic Temperature of a Gold Fixed-Point Cell
Battuello, M.; Girard, F.; Florio, M.
2010-09-01
Since the value T 90(Au) was fixed on the ITS-90, some determinations of the thermodynamic temperature of the gold point have been performed which form, with other renormalized results of previous measurements by radiation thermometry, the basis for the current best estimates of ( T - T 90)Au = 39.9 mK as elaborated by the CCT-WG4. Such a value, even if consistent with the behavior of T - T 90 differences at lower temperatures, is quite influenced by the low values of T Au as determined with few radiometric measurements. At INRIM, an independent indirect determination of the thermodynamic temperature of gold was performed by means of a radiation thermometry approach. A fixed-point technique was used to realize approximated thermodynamic scales from the Zn point up to the Cu point. A Si-based standard radiation thermometer working at 900 nm and 950 nm was used. The low uncertainty presently associated to the thermodynamic temperature of fixed points and the accuracy of INRIM realizations, allowed scales with an uncertainty lower than 0.03 K in terms of the thermodynamic temperature to be realized. A fixed-point cell filled with gold, 99.999 % in purity, was measured, and its freezing temperature was determined by both interpolation and extrapolation. An average T Au = 1337.395 K was found with a combined standard uncertainty of 23 mK. Such a value is 25 mK higher than the presently available value as derived by the CCT-WG4 value of ( T - T 90)Au = 39.9 mK.
Indian Academy of Sciences (India)
eralizing the method of proof of the well known. Cantor's ... Godel's first incompleteness theorem is proved. ... that the number of elements in any finite set is a natural number. ..... proof also has a Godel number; of course, you have to fix.
Flatto, Leopold
2009-01-01
Poncelet's theorem is a famous result in algebraic geometry, dating to the early part of the nineteenth century. It concerns closed polygons inscribed in one conic and circumscribed about another. The theorem is of great depth in that it relates to a large and diverse body of mathematics. There are several proofs of the theorem, none of which is elementary. A particularly attractive feature of the theorem, which is easily understood but difficult to prove, is that it serves as a prism through which one can learn and appreciate a lot of beautiful mathematics. This book stresses the modern appro
Rigorous high-precision enclosures of fixed points and their invariant manifolds
Wittig, Alexander N.
The well established concept of Taylor Models is introduced, which offer highly accurate C0 enclosures of functional dependencies, combining high-order polynomial approximation of functions and rigorous estimates of the truncation error, performed using verified arithmetic. The focus of this work is on the application of Taylor Models in algorithms for strongly non-linear dynamical systems. A method is proposed to extend the existing implementation of Taylor Models in COSY INFINITY from double precision coefficients to arbitrary precision coefficients. Great care is taken to maintain the highest efficiency possible by adaptively adjusting the precision of higher order coefficients in the polynomial expansion. High precision operations are based on clever combinations of elementary floating point operations yielding exact values for round-off errors. An experimental high precision interval data type is developed and implemented. Algorithms for the verified computation of intrinsic functions based on the High Precision Interval datatype are developed and described in detail. The application of these operations in the implementation of High Precision Taylor Models is discussed. An application of Taylor Model methods to the verification of fixed points is presented by verifying the existence of a period 15 fixed point in a near standard Henon map. Verification is performed using different verified methods such as double precision Taylor Models, High Precision intervals and High Precision Taylor Models. Results and performance of each method are compared. An automated rigorous fixed point finder is implemented, allowing the fully automated search for all fixed points of a function within a given domain. It returns a list of verified enclosures of each fixed point, optionally verifying uniqueness within these enclosures. An application of the fixed point finder to the rigorous analysis of beam transfer maps in accelerator physics is presented. Previous work done by
The resolution of field identification fixed points in diagonal coset theories
International Nuclear Information System (INIS)
Fuchs, J.; Schellekens, B.; Schweigert, C.
1995-09-01
The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use ''orbit Lie algebras'' and ''twining characters'', which were introduced in a previous paper. The characters of the primary fields are expressed in terms branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of ''generalized diagonal cosets''. (orig.)
Alignment Solution for CT Image Reconstruction using Fixed Point and Virtual Rotation Axis.
Jun, Kyungtaek; Yoon, Seokhwan
2017-01-25
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.
Emittance and damping of electrons in the neighborhood of resonance fixed points
International Nuclear Information System (INIS)
Crosbie, E.A.
1993-01-01
The stable fixed points generated by nonlinear field harmonics in a cyclic lattice define a multiturn stable orbit. The position of the orbit for each turn in each magnet of the lattice determines the betatron tunes and lattice dispersion functions describing the linear motion of charged particles with respect to the stable orbit. Since the position of the fixed points is dependent in part on the central orbit tune, it turns out that the multiturn orbit dispersion function depends to a large extent on the central orbit chromaticity. In particular, the horizontal partition number can be made to vary from values less than zero (horizontal antidamping for electrons) to values greater than three (longitudinal antidamping). The central orbit chromaticity therefore plays a major role in determining the characteristic emittance of an electron beam with respect to the multiturn orbit
Computing fixed points of nonexpansive mappings by $\\alpha$-dense curves
Directory of Open Access Journals (Sweden)
G. García
2017-08-01
Full Text Available Given a multivalued nonexpansive mapping defined on a convex and compact set of a Banach space, with values in the class of convex and compact subsets of its domain, we present an iteration scheme which (under suitable conditions converges to a fixed point of such mapping. This new iteration provides us another method to approximate the fixed points of a singlevalued nonexpansive mapping, defined on a compact and convex set into itself. Moreover, the conditions for the singlevalued case are less restrictive than for the multivalued case. Our main tool will be the so called $\\alpha$-dense curves, which will allow us to construct such iterations. Some numerical examples are provided to illustrate our results.
1989-01-01
This selection of papers from the Beijing conference gives a cross-section of the current trends in the field of fixed point theory as seen by topologists and analysts. Apart from one survey article, they are all original research articles, on topics including equivariant theory, extensions of Nielsen theory, periodic orbits of discrete and continuous dynamical systems, and new invariants and techniques in topological approaches to analytic problems.
Storti, Mario A.; Nigro, Norberto M.; Paz, Rodrigo R.; Dalcín, Lisandro D.
2009-03-01
In this paper some results on the convergence of the Gauss-Seidel iteration when solving fluid/structure interaction problems with strong coupling via fixed point iteration are presented. The flow-induced vibration of a flat plate aligned with the flow direction at supersonic Mach number is studied. The precision of different predictor schemes and the influence of the partitioned strong coupling on stability is discussed.
Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents
International Nuclear Information System (INIS)
Hasenfratz, P.; Hauswirth, S.; Holland, K.; Joerg, T.; Niedermayer, F.
2002-01-01
In this preliminary study, we examine the chiral properties of the parametrized Fixed-Point Dirac operator D FP , see how to improve its chirality via the Overlap construction, measure the renormalized quark condensate Σ-circumflex and the topological susceptibility χ t , and investigate local chirality of near zero modes of the Dirac operator. We also give a general construction of chiral currents and densities for chiral lattice actions
Energy efficient smartphone-based activity recognition using fixed-point arithmetic
Anguita, Davide; Ghio, Alessandro; Oneto, Luca; Llanas Parra, Francesc Xavier; Reyes Ortiz, Jorge Luis
2013-01-01
In this paper we propose a novel energy efficient approach for the recognition of human activities using smartphones as wearable sensing devices, targeting assisted living applications such as remote patient activity monitoring for the disabled and the elderly. The method exploits fixed-point arithmetic to propose a modified multiclass Support Vector Machine (SVM) learning algorithm, allowing to better pre- serve the smartphone battery lifetime with respect to the conventional flo...
Common Fixed Point of Multivalued Generalized φ-Weak Contractive Mappings
Directory of Open Access Journals (Sweden)
Behzad Djafari Rouhani
2010-01-01
Full Text Available Fixed point and coincidence results are presented for multivalued generalized φ-weak contractive mappings on complete metric spaces, where φ:[0,+∞→[0,+∞ is a lower semicontinuous function with φ(0=0 and φ(t>0 for all t>0. Our results extend previous results by Zhang and Song (2009, as well as by Rhoades (2001, Nadler (1969, and Daffer and Kaneko (1995.
Wähmer, M.; Anhalt, K.; Hollandt, J.; Klein, R.; Taubert, R. D.; Thornagel, R.; Ulm, G.; Gavrilov, V.; Grigoryeva, I.; Khlevnoy, B.; Sapritsky, V.
2017-10-01
Absolute spectral radiometry is currently the only established primary thermometric method for the temperature range above 1300 K. Up to now, the ongoing improvements of high-temperature fixed points and their formal implementation into an improved temperature scale with the mise en pratique for the definition of the kelvin, rely solely on single-wavelength absolute radiometry traceable to the cryogenic radiometer. Two alternative primary thermometric methods, yielding comparable or possibly even smaller uncertainties, have been proposed in the literature. They use ratios of irradiances to determine the thermodynamic temperature traceable to blackbody radiation and synchrotron radiation. At PTB, a project has been established in cooperation with VNIIOFI to use, for the first time, all three methods simultaneously for the determination of the phase transition temperatures of high-temperature fixed points. For this, a dedicated four-wavelengths ratio filter radiometer was developed. With all three thermometric methods performed independently and in parallel, we aim to compare the potential and practical limitations of all three methods, disclose possibly undetected systematic effects of each method and thereby confirm or improve the previous measurements traceable to the cryogenic radiometer. This will give further and independent confidence in the thermodynamic temperature determination of the high-temperature fixed point's phase transitions.
A Fixed Point VHDL Component Library for a High Efficiency Reconfigurable Radio Design Methodology
Hoy, Scott D.; Figueiredo, Marco A.
2006-01-01
Advances in Field Programmable Gate Array (FPGA) technologies enable the implementation of reconfigurable radio systems for both ground and space applications. The development of such systems challenges the current design paradigms and requires more robust design techniques to meet the increased system complexity. Among these techniques is the development of component libraries to reduce design cycle time and to improve design verification, consequently increasing the overall efficiency of the project development process while increasing design success rates and reducing engineering costs. This paper describes the reconfigurable radio component library developed at the Software Defined Radio Applications Research Center (SARC) at Goddard Space Flight Center (GSFC) Microwave and Communications Branch (Code 567). The library is a set of fixed-point VHDL components that link the Digital Signal Processing (DSP) simulation environment with the FPGA design tools. This provides a direct synthesis path based on the latest developments of the VHDL tools as proposed by the BEE VBDL 2004 which allows for the simulation and synthesis of fixed-point math operations while maintaining bit and cycle accuracy. The VHDL Fixed Point Reconfigurable Radio Component library does not require the use of the FPGA vendor specific automatic component generators and provide a generic path from high level DSP simulations implemented in Mathworks Simulink to any FPGA device. The access to the component synthesizable, source code provides full design verification capability:
A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point
International Nuclear Information System (INIS)
Lenci, Marco
2016-01-01
Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0, 1], with countably many surjective branches and a strongly neutral fixed point in 0.
Heck, Richard G
2011-01-01
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a
Reliability of High-Temperature Fixed-Point Installations over 8 Years
Elliott, C. J.; Ford, T.; Ongrai, O.; Pearce, J. V.
2017-12-01
At NPL, high-temperature metal-carbon eutectic fixed points have been set up for thermocouple calibration purposes since 2006, for realising reference temperatures above the highest point specified in the International Temperature Scale of 1990 for contact thermometer calibrations. Additionally, cells of the same design have been provided by NPL to other national measurement institutes (NMIs) and calibration laboratories over this period, creating traceable and ISO 17025 accredited facilities around the world for calibrating noble metal thermocouples at 1324 {°}C (Co-C) and 1492 {°}C (Pd-C). This paper shows collections of thermocouple calibration results obtained during use of the high-temperature fixed-point cells at NPL and, as further examples, the use of cells installed at CCPI Europe (UK) and NIMT (Thailand). The lifetime of the cells can now be shown to be in excess of 7 years, whether used on a weekly or monthly basis, and whether used in an NMI or industrial calibration laboratory.
Tail estimates for stochastic fixed point equations via nonlinear renewal theory
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.
2013-01-01
estimate P(V>u)~Cu^{-r} as u tends to infinity, and also present a corresponding Lundberg-type upper bound. To this end, we introduce a novel dual change of measure on a random time interval and analyze the path properties, using nonlinear renewal theory, of the Markov chain resulting from the forward...... iteration of the given stochastic fixed point equation. In the process, we establish several new results in the realm of nonlinear renewal theory for these processes. As a consequence of our techniques, we also establish a new characterization of the extremal index. Finally, we provide some extensions...... of our methods to Markov-driven processes....
(0,2) SCFTs from the Leigh-Strassler fixed point
Energy Technology Data Exchange (ETDEWEB)
Bobev, Nikolay [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5 (Canada); Pilch, Krzysztof; Vasilakis, Orestis [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089 (United States)
2014-06-17
We show that there is a family of two-dimensional (0,2) SCFTs associated with twisted compactifications of the four-dimensional N=1 Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and c-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric AdS{sub 3} solutions that are holographic duals of those two-dimensional (0,2) SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.
1988-01-01
Let K be a subset of a real Banach space X. A mapping T:K → X is called pseudo-contractive if the inequality ||x-y|| ≤ ||(1+r)(x-y)-r(Tx-Ty)|| holds for all x,y in K and r > 0. Fixed points of Lipschitz pseudo-contractive maps are approximated under appropriate conditions, by an iteration process of the type introduced by W.R. Mann. This gives an affirmative answer to the problem stated by T.L. Hicks and J.R. Rubicek (J. Math. Anal. Appl. 59 (1977) 504). (author). 28 refs
(0,2) SCFTs from the Leigh-Strassler fixed point
International Nuclear Information System (INIS)
Bobev, Nikolay; Pilch, Krzysztof; Vasilakis, Orestis
2014-01-01
We show that there is a family of two-dimensional (0,2) SCFTs associated with twisted compactifications of the four-dimensional N=1 Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and c-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric AdS 3 solutions that are holographic duals of those two-dimensional (0,2) SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.
Grand unified theory precursors and nontrivial fixed points in higher-dimensional gauge theories
International Nuclear Information System (INIS)
Dienes, Keith R.; Dudas, Emilian; Gherghetta, Tony
2003-01-01
Within the context of traditional logarithmic grand unification at M GUT ≅10 16 GeV, we show that it is nevertheless possible to observe certain GUT states such as X and Y gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as 'GUT precursors'. These states offer an interesting alternative possibility for new physics at the TeV scale, and could be used to directly probe GUT physics even though the scale of gauge coupling unification remains high. Our results also give rise to a Kaluza-Klein realization of nontrivial fixed points in higher-dimensional gauge theories
Standard map in magnetized relativistic systems: fixed points and regular acceleration.
de Sousa, M C; Steffens, F M; Pakter, R; Rizzato, F B
2010-08-01
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.
Rare event simulation for stochastic fixed point equations related to the smoothing transform
DEFF Research Database (Denmark)
Collamore, Jeffrey F.; Vidyashankar, Anand N.; Xu, Jie
2013-01-01
In several applications arising in computer science, cascade theory, and other applied areas, it is of interest to evaluate the tail probabilities of non-homogeneous stochastic fixed point equations. Recently, techniques have been developed for the related linear recursions, yielding tail estimates...... and importance sampling methods for these recursions. However, such methods do not routinely generalize to non-homogeneous recursions. Drawing on techniques from the weighted branching process literature, we present a consistent, strongly efficient importance sampling algorithm for estimating the tail...
Isotopic effects in the neon fixed point: uncertainty of the calibration data correction
Steur, Peter P. M.; Pavese, Franco; Fellmuth, Bernd; Hermier, Yves; Hill, Kenneth D.; Seog Kim, Jin; Lipinski, Leszek; Nagao, Keisuke; Nakano, Tohru; Peruzzi, Andrea; Sparasci, Fernando; Szmyrka-Grzebyk, Anna; Tamura, Osamu; Tew, Weston L.; Valkiers, Staf; van Geel, Jan
2015-02-01
The neon triple point is one of the defining fixed points of the International Temperature Scale of 1990 (ITS-90). Although recognizing that natural neon is a mixture of isotopes, the ITS-90 definition only states that the neon should be of ‘natural isotopic composition’, without any further requirements. A preliminary study in 2005 indicated that most of the observed variability in the realized neon triple point temperatures within a range of about 0.5 mK can be attributed to the variability in isotopic composition among different samples of ‘natural’ neon. Based on the results of an International Project (EUROMET Project No. 770), the Consultative Committee for Thermometry decided to improve the realization of the neon fixed point by assigning the ITS-90 temperature value 24.5561 K to neon with the isotopic composition recommended by IUPAC, accompanied by a quadratic equation to take the deviations from the reference composition into account. In this paper, the uncertainties of the equation are discussed and an uncertainty budget is presented. The resulting standard uncertainty due to the isotopic effect (k = 1) after correction of the calibration data is reduced to (4 to 40) μK when using neon of ‘natural’ isotopic composition or to 30 μK when using 20Ne. For comparison, an uncertainty component of 0.15 mK should be included in the uncertainty budget for the neon triple point if the isotopic composition is unknown, i.e. whenever the correction cannot be applied.
Non-thermal fixed points and solitons in a one-dimensional Bose gas
International Nuclear Information System (INIS)
Schmidt, Maximilian; Erne, Sebastian; Nowak, Boris; Sexty, Dénes; Gasenzer, Thomas
2012-01-01
Single-particle momentum spectra for a dynamically evolving one-dimensional Bose gas are analysed in the semi-classical wave limit. Representing one of the simplest correlation functions, these provide information on a possible universal scaling behaviour. Motivated by the previously discovered connection between (quasi-) topological field configurations, strong wave turbulence and non-thermal fixed points of quantum field dynamics, soliton formation is studied with respect to the appearance of transient power-law spectra. A random-soliton model is developed for describing the spectra analytically, and the analogies and differences between the emerging power laws and those found in a field theory approach to strong wave turbulence are discussed. The results open a new perspective on solitary wave dynamics from the point of view of critical phenomena far from thermal equilibrium and the possibility of studying this dynamics by experiment without the need for detecting solitons in situ. (paper)
The general problem of the motion of coupled rigid bodies about a fixed point
Leimanis, Eugene
1965-01-01
In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.
Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
Directory of Open Access Journals (Sweden)
P. Pasom
2012-01-01
Full Text Available Let C be a nonempty bounded closed convex subset of a complete CAT(0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmkxk⊕tmkTmnky(m-1k, y(m-1k=(1-t(m-1kxk⊕t(m-1kTm-1nky(m-2k,y(m-2k=(1-t(m-2kxk⊕t(m-2kTm-2nky(m-3k,…,y2k=(1-t2kxk⊕t2kT2nky1k,y1k=(1-t1kxk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.
Acoustic resonator providing fixed points of temperature between 0.1 and 2 K
International Nuclear Information System (INIS)
Salmela, Anssi; Tuoriniemi, Juha; Pentti, Elias; Sebedash, Alexander; Rysti, Juho
2009-01-01
Below 2 K the speed of second sound in mixtures of liquid 3 He and 4 He first increases to a maximum of 30-40 m/s at about 1 K and then decreases again at lower temperatures to values below 15 m/s. The exact values depend on the concentration and pressure of the mixture. This can be exploited to provide fixed points in temperature by utilizing a resonator with appropriate dimensions and frequency to excite standing waves in the resonator cavity filled with helium mixture. We demonstrate that commercially mass produced quartz tuning forks can be used for this purpose. They are meant for frequency standards operating at 32 kHz. Their dimensions are typically of order 1 mm matching the wavelength of the second sound in helium mixtures at certain values of temperature. Due to the complicated geometry, we observe some 20 sharp acoustic resonances in the range 0.1l 2 K having temperature resolution of order 1 μK. The quartz resonators are cheap, compact, simple to implement, easy to measure with great accuracy, and, above all, they are not sensitive to magnetic field, which is a great advantage compared to fixed point devices based on superconductivity transitions. The reproducibility of the resonance pattern upon thermal cycling remains to be verified.
On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems
Directory of Open Access Journals (Sweden)
B.M.B. Krushna
2016-10-01
Full Text Available In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.
The a theorem for Gauge-Yukawa theories beyond Banks-Zaks
DEFF Research Database (Denmark)
Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben
2013-01-01
We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the pres......We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including...
Design and Evaluation of Large-Aperture Gallium Fixed-Point Blackbody
Khromchenko, V. B.; Mekhontsev, S. N.; Hanssen, L. M.
2009-02-01
To complement existing water bath blackbodies that now serve as NIST primary standard sources in the temperature range from 15 °C to 75 °C, a gallium fixed-point blackbody has been recently built. The main objectives of the project included creating an extended-area radiation source with a target emissivity of 0.9999 capable of operating either inside a cryo-vacuum chamber or in a standard laboratory environment. A minimum aperture diameter of 45 mm is necessary for the calibration of radiometers with a collimated input geometry or large spot size. This article describes the design and performance evaluation of the gallium fixed-point blackbody, including the calculation and measurements of directional effective emissivity, estimates of uncertainty due to the temperature drop across the interface between the pure metal and radiating surfaces, as well as the radiometrically obtained spatial uniformity of the radiance temperature and the melting plateau stability. Another important test is the measurement of the cavity reflectance, which was achieved by using total integrated scatter measurements at a laser wavelength of 10.6 μm. The result allows one to predict the performance under the low-background conditions of a cryo-chamber. Finally, results of the spectral radiance comparison with the NIST water-bath blackbody are provided. The experimental results are in good agreement with predicted values and demonstrate the potential of our approach. It is anticipated that, after completion of the characterization, a similar source operating at the water triple point will be constructed.
Directory of Open Access Journals (Sweden)
Coghetto Roland
2015-06-01
Full Text Available Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].
Directory of Open Access Journals (Sweden)
Marek Karaś
2017-12-01
Full Text Available In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets, which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free
Solution of the Stokes system by boundary integral equations and fixed point iterative schemes
International Nuclear Information System (INIS)
Chidume, C.E.; Lubuma, M.S.
1990-01-01
The solution to the exterior three dimensional Stokes problem is sought in the form of a single layer potential of unknown density. This reduces the problem to a boundary integral equation of the first kind whose operator is the velocity component of the single layer potential. It is shown that this component is an isomorphism between two appropriate Sobolev spaces containing the unknown densities and the data respectively. The isomorphism corresponds to a variational problem with coercive bilinear form. The latter property allows us to consider various fixed point iterative schemes that converge to the unique solution of the integral equation. Explicit error estimates are also obtained. The successive approximations are also considered in a more computable form by using the product integration method of Atkinson. (author). 47 refs
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.
'Fixed point' QCD analysis of the CCFR data on deep inelastic neutrino-nucleon scattering
International Nuclear Information System (INIS)
Sidorov, A.V.; Stamenov, D.B.
1995-01-01
The results of LO Fixed point QCD (FP-QCD) analysis of the CCFR data for the nucleon structure function xF 3 (x,Q 2 ) are presented. The predictions of FP-QCD, in which α S (Q 2 ) tends to a nonzero coupling constant α 0 as Q 2 → ∞, are in good agreement with the data. The description of the data is even better than that in the case of LO QCD. The FP-QCD parameter α 0 is determined with a good accuracy: α 0 0.198 ± 0.009. Having in mind the recent QCD fits to the same data we conclude that unlike the high precision and large (x,Q 2 ) kinematic range of the CCFR data they cannot discriminate between QCD and FP-QCD predictions for xF 3 (x,Q 2 ). 11 refs., 1 tab
Point and Fixed Plot Sampling Inventory Estimates at the Savannah River Site, South Carolina.
Energy Technology Data Exchange (ETDEWEB)
Parresol, Bernard, R.
2004-02-01
This report provides calculation of systematic point sampling volume estimates for trees greater than or equal to 5 inches diameter breast height (dbh) and fixed radius plot volume estimates for trees < 5 inches dbh at the Savannah River Site (SRS), Aiken County, South Carolina. The inventory of 622 plots was started in March 1999 and completed in January 2002 (Figure 1). Estimates are given in cubic foot volume. The analyses are presented in a series of Tables and Figures. In addition, a preliminary analysis of fuel levels on the SRS is given, based on depth measurements of the duff and litter layers on the 622 inventory plots plus line transect samples of down coarse woody material. Potential standing live fuels are also included. The fuels analyses are presented in a series of tables.
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.
Directory of Open Access Journals (Sweden)
Phayap Katchang
2010-01-01
Full Text Available The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued maximal monotone mappings and inverse-strongly monotone mappings, and the set of fixed points of a family of finitely nonexpansive mappings in the setting of Hilbert spaces. We propose a new iterative scheme for finding the common element of the above three sets. Our results improve and extend the corresponding results of the works by Zhang et al. (2008, Peng et al. (2008, Peng and Yao (2009, as well as Plubtieng and Sriprad (2009 and some well-known results in the literature.
Finite size scaling of the Higgs-Yukawa model near the Gaussian fixed point
Energy Technology Data Exchange (ETDEWEB)
Chu, David Y.J.; Lin, C.J. David [National Chiao-Tung Univ., Hsinchu, Taiwan (China); Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Knippschild, Bastian [HISKP, Bonn (Germany); Nagy, Attila [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Univ. Berlin (Germany)
2016-12-15
We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility study of our strategy is performed for the pure scalar theory in the weak-coupling regime. Choosing the on-shell renormalisation scheme gives us an advantage to fit the scaling functions against lattice data with only a small number of fit parameters. These formulae can be used to determine the universality of the observed phase transitions, and thus play an essential role in future investigations of Higgs-Yukawa models, in particular in the strong Yukawa coupling region.
Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs
Directory of Open Access Journals (Sweden)
Angelos Charalambidis
2015-09-01
Full Text Available Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point construction defined on a syntactic instantiation of the source program. The relationships between these two approaches had not been investigated until now. In this paper we demonstrate that for a very broad class of programs, namely the class of definitional programs introduced by W. W. Wadge, the two approaches coincide (with respect to ground atoms that involve symbols of the program. On the other hand, we argue that if existential higher-order variables are allowed to appear in the bodies of program rules, the two approaches are in general different. The results of the paper contribute to a better understanding of the semantics of higher-order logic programming.
International Nuclear Information System (INIS)
Cahill, K.
1975-11-01
Local field theory is used to derive formulas that express certain boundary values of the N-point function as sums of products of scattering amplitudes. These formulas constitute a generalization of the optical theorem and facilitate the analysis of multiparticle scattering functions [fr
Debattista, Josephine
2000-01-01
Pythagoras 580 BC was a Greek mathematician who became famous for formulating Pythagoras Theorem but its principles were known earlier. The ancient Egyptians wanted to layout square (90°) corners to their fields. To solve this problem about 2000 BC they discovered the 'magic' of the 3-4-5 triangle.
Converse Barrier Certificate Theorem
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2013-01-01
This paper presents a converse barrier certificate theorem for a generic dynamical system.We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold. Other authors have developed a related result, by assuming that the dynamical system has no singular...... points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work...
New Approach in Filling of Fixed-Point Cells: Case Study of the Melting Point of Gallium
Bojkovski, J.; Hiti, M.; Batagelj, V.; Drnovšek, J.
2008-02-01
The typical way of constructing fixed-point cells is very well described in the literature. The crucible is loaded with shot, or any other shape of pure metal, inside an argon-filled glove box. Then, the crucible is carefully slid into a fused-silica tube that is closed at the top with an appropriate cap. After that, the cell is removed from the argon glove box and melted inside a furnace while under vacuum or filled with an inert gas like argon. Since the metal comes as shot, or in some other shape such as rods of various sizes, and takes more volume than the melted material, it is necessary to repeat the procedure until a sufficient amount of material is introduced into the crucible. With such a procedure, there is the possibility of introducing additional impurities into the pure metal with each cycle of melting the material and putting it back into the glove box to fill the cell. Our new approach includes the use of a special, so-called dry-box system, which is well known in chemistry. The atmosphere inside the dry box contains less than 20 ppm of water and less than 3 ppm of oxygen. Also, the size of the dry box allows it to contain a furnace for melting materials, not only for gallium but for higher-temperature materials as well. With such an approach, the cell and all its parts (pure metal, graphite, fused-silica tube, and cap) are constantly inside the controlled atmosphere, even while melting the material and filling the crucible. With such a method, the possibility of contaminating the cell during the filling process is minimized.
Metal Carbon Eutectics to Extend the Use of the Fixed-Point Technique in Precision IR Thermometry
Battuello, M.; Girard, F.; Florio, M.
2008-06-01
The high-temperature extension of the fixed-point technique for primary calibration of precision infrared (IR) thermometers was investigated both through mathematical simulations and laboratory investigations. Simulations were performed with Co C (1,324°C) and Pd C (1, 492°C) eutectic fixed points, and a precision IR thermometer was calibrated from the In point (156.5985°C) up to the Co C point. Mathematical simulations suggested the possibility of directly deriving the transition temperature of the Co C and Pd C points by extrapolating the calibration derived from fixed-point measurements from In to the Cu point. Both temperatures, as a result of the low uncertainty associated with the In Cu calibration and the high number of fixed points involved in the calibration process, can be derived with an uncertainty of 0.11°C for Co C and 0.18°C for Pd C. A transition temperature of 1,324.3°C for Co C was determined from the experimental verification, a value higher than, but compatible with, the one proposed by the thermometry community for inclusion as a secondary reference point for ITS-90 dissemination, i.e., 1,324.0°C.
Investigation of the Behavior of the Co C Eutectic Fixed Point
Girard, F.; Battuello, M.; Florio, M.
2007-12-01
The behavior of the Co C eutectic fixed point was investigated at INRIM. Several cells of different design and volume, and filled with cobalt of different purity were constructed and investigated with both Pt/Pd thermocouples and radiation thermometers. The melting behavior was investigated with respect to the melting rate, the pre-freezing rate, and the annealing time. The melting temperatures, as defined, were not significantly affected by the different testing conditions, even if the shape and duration of the plateaux were influenced. Several tens of melt and freeze cycles were performed with the different cells. The spread in the results for all of the different conditions was very limited in extent, giving rise to a standard deviation of less than 0.04 °C; a repeatability of better than 0.02 °C was found with both Pt/Pd thermocouples and radiation thermometers. The results of our measurements are encouraging and confirm the suitability of Co C as a reference point for the high-temperature range in a possible future temperature scale. Investigations of long-term stability remain ongoing.
Analyzing survival curves at a fixed point in time for paired and clustered right-censored data
Su, Pei-Fang; Chi, Yunchan; Lee, Chun-Yi; Shyr, Yu; Liao, Yi-De
2018-01-01
In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Rather than comparing entire survival curves, researchers can focus on the comparison at fixed time points that may have a clinical utility for patients. For two independent samples of right-censored data, Klein et al. (2007) compared survival probabilities at a fixed time point by studying a number of tests based on some transformations of the Kaplan-Meier estimators of the survival function. However, to compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, their approach would need to be modified. In this paper, we extend the statistics to accommodate the possible within-paired correlation and within-clustered correlation, respectively. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets. PMID:29456280
Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities
Directory of Open Access Journals (Sweden)
Chidume CO
2008-01-01
Full Text Available Abstract Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.
A note on the proof of Bertrand's theorem
Directory of Open Access Journals (Sweden)
Jovanović Vladimir
2015-01-01
Full Text Available In this paper we fill a common gap in the proof of Bertrand' theorem present both the in Bertrand's original paper Théorème relatif au movement d'un point attiré vers un centre fixe and in the Arnold's book Mathematical methods of classical mechanics, by providing missing details which pertain to the problem of how to single out elastic and gravitational potentials among the power law ones.
There is no non-zero stable fixed point for dense networks in the homogeneous Kuramoto model
International Nuclear Information System (INIS)
Taylor, Richard
2012-01-01
This paper is concerned with the existence of multiple stable fixed point solutions of the homogeneous Kuramoto model. We develop a necessary condition for the existence of stable fixed points for the general network Kuramoto model. This condition is applied to show that for sufficiently dense n-node networks, with node degrees at least 0.9395(n−1), the homogeneous (equal frequencies) model has only one stable fixed point solution over the full space of phase angles in the range −π to π. This is the zero fixed point solution defined by all phase angle differences being zero. This result, together with existing research, proves a conjecture of Verwoerd and Mason (2007 Proc. of the American Control Conf. pp 4613–8) that for the complete network and the homogeneous model, the zero fixed point has a basin of attraction consisting of the entire space minus a set of measure zero. The necessary conditions are also tested to see how close to sufficiency they might be by applying them to a class of regular degree networks studied by Wiley et al (2006 Chaos 16 015103). (paper)
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.
Development of large-area high-temperature fixed-point blackbodies for photometry and radiometry
Khlevnoy, Boris; Grigoryeva, Irina; Anhalt, Klaus; Waehmer, Martin; Ivashin, Evgeniy; Otryaskin, Denis; Solodilov, Maxim; Sapritsky, Victor
2018-04-01
Large-area high-temperature fixed-point (HTFP) blackbodies with working temperatures of approximately 2748 K and 3021 K, based on an Re-C eutectic and a WC-C peritectic respectively, have been developed and investigated. The blackbodies have an emissivity of 0.9997, show high-quality phase-transition plateaus and have high repeatability of the melting temperatures, but demonstrate temperature differences (from 0.2 K to 0.6 K) compared with small-cell blackbodies of the same HTFP. We associate these temperature differences with the temperature drop effect, which may differ from cell to cell. The large radiating cavity diameter of 14 mm allows developed HTFP blackbodies to be used for photometric and radiometric applications in irradiance mode with uncertainties as small as 0.12% (k = 1) in the visible. A photometer and an irradiance-mode filter radiometer (visible range), previously calibrated at VNIIOFI, were used to measure illuminance and irradiance of the HTFP blackbodies equipped with a precise outer aperture. The values measured by the detectors agreed with those based on the blackbody calculation to within 0.2%. The large-area HTFP blackbodies will be used in a joint PTB-VNIIOFI experiment on measuring thermodynamic temperature.
Higgs and supersymmetric particle signals at the infrared fixed point of the top quark mass
International Nuclear Information System (INIS)
Carena, M.; Wagner, C.E.M.
1995-01-01
We study the properties of the Higgs and supersymmetric particle spectrum, associated with the infrared fixed point solution of the top quark mass in the Minimal Supersymmetric Standard Model. We concentrate on the possible detection of these particles, analysing the deviations from the Standard Model predictions for the leptonic and hadronic variables measured at LEP and for the b→sγ decay rate. We consider the low and moderate tan β regime, imposing the constraints derived from a proper radiative SU(2) L xU(1) Y symmetry breaking, and we study both the cases of universal and non-universal soft supersymmetry-breaking parameters at high energies. In the first case, for any given value of the top quark mass, the Higgs and supersymmetric particle spectrum is completely determined as a function of only two soft supersymmetry-breaking parameters, implying very definite experimental signatures. In the case of non-universal mass parameters at M GUT , instead, the strong correlations between the sparticle masses are relaxed, allowing a richer structure for the precision data variables. As a general feature, whenever a significant deviation from the Standard Model value of the precision data parameters is predicted, a light sparticle, which should be visible at LEP2, appears in the model. (orig.)
Stabilizing unstable fixed points of chaotic maps via minimum entropy control
Energy Technology Data Exchange (ETDEWEB)
Salarieh, Hassan [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics and Automation, Department of Mechanical Engineering, Sharif University of Technology, P.O. Box 11365-9567, Tehran (Iran, Islamic Republic of)
2008-08-15
In this paper the problem of chaos control in nonlinear maps using minimization of entropy function is investigated. Invariant probability measure of a chaotic dynamics can be used to produce an entropy function in the sense of Shannon. In this paper it is shown that how the entropy control technique is utilized for chaos elimination. Using only the measured states of a chaotic map the probability measure of the system is numerically estimated and this estimated measure is used to obtain an estimation for the entropy of the chaotic map. The control variable of the chaotic system is determined in such a way that the entropy function descends until the chaotic trajectory of the map is replaced with a regular one. The proposed idea is applied for stabilizing the fixed points of the logistic and the Henon maps as some cases of study. Simulation results show the effectiveness of the method in chaos rejection when only the statistical information is available from the under-study systems.
CPN-1 models with a θ term and fixed point action
International Nuclear Information System (INIS)
Burkhalter, Rudolf; Imachi, Masahiro; Shinno, Yasuhiko; Yoneyama, Hiroshi
2001-01-01
The topological charge distribution P(Q) is calculated for lattice CP N-1 models. In order to suppress lattice cutoff effects, we employ a fixed point (FP) action. Through transformation of P(Q), we calculate the free energy F(θ) as a function of the θ parameter. For N=4, scaling behavior is observed for P(Q) and F(θ), as well as the correlation lengths ξ(Q). For N=2, however, scaling behavior is not observed, as expected. For comparison, we also make a calculation for the CP 3 model with a standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For this purpose, we carefully consider the behavior of γ eff , which is an effective power of P(Q) (∼exp (-CQ γeff )), and reflects the local behavior of P(Q) as a function of Q. We study γ eff for two cases, the dilute gas approximation based on the Poisson distribution of instantons and the Debye-Hueckel approximation of instanton quarks. In both cases, we find behavior similar to that observed in numerical simulations. (author)
Directory of Open Access Journals (Sweden)
Ibrahim Karahan
2016-04-01
Full Text Available Let C be a nonempty closed convex subset of a real Hilbert space H. Let {T_{n}}:C›H be a sequence of nearly nonexpansive mappings such that F:=?_{i=1}^{?}F(T_{i}?Ø. Let V:C›H be a ?-Lipschitzian mapping and F:C›H be a L-Lipschitzian and ?-strongly monotone operator. This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem. It is shown that under certain approximate assumptions on the operators and parameters, the modified iterative sequence {x_{n}} converges strongly to x^{*}?F which is also the unique solution of the following variational inequality: ?0, ?x?F. As a special case, this projection method can be used to find the minimum norm solution of above variational inequality; namely, the unique solution x^{*} to the quadratic minimization problem: x^{*}=argmin_{x?F}?x?². The results here improve and extend some recent corresponding results of other authors.
Piñeiro Orioli, Asier; Boguslavski, Kirill; Berges, Jürgen
2015-07-01
We investigate universal behavior of isolated many-body systems far from equilibrium, which is relevant for a wide range of applications from ultracold quantum gases to high-energy particle physics. The universality is based on the existence of nonthermal fixed points, which represent nonequilibrium attractor solutions with self-similar scaling behavior. The corresponding dynamic universality classes turn out to be remarkably large, encompassing both relativistic as well as nonrelativistic quantum and classical systems. For the examples of nonrelativistic (Gross-Pitaevskii) and relativistic scalar field theory with quartic self-interactions, we demonstrate that infrared scaling exponents as well as scaling functions agree. We perform two independent nonperturbative calculations, first by using classical-statistical lattice simulation techniques and second by applying a vertex-resummed kinetic theory. The latter extends kinetic descriptions to the nonperturbative regime of overoccupied modes. Our results open new perspectives to learn from experiments with cold atoms aspects about the dynamics during the early stages of our universe.
DEFF Research Database (Denmark)
Beltran, H.; Perez, E.; Chen, Zhe
2009-01-01
This paper describes a Fixed Maximum Power Point analog control used in a step-down Pulse Width Modulated power converter. The DC/DC converter drives a DC motor used in small water pumping installations, without any electric storage device. The power supply is provided by PV panels working around....... The proposed Optimal Power Point fix voltage control system is analyzed in comparison to other complex controls....... their maximum power point, with a fixed operating voltage value. The control circuit implementation is not only simple and cheap, but also robust and reliable. System protections and adjustments are also proposed. Simulations and hardware are reported in the paper for a 150W water pumping application system...
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.
Ragay-Enot, Monalisa; Lee, Young Hee; Kim, Yong-Gyoo
2017-07-01
A mini multi-fixed-point cell (length 118 mm, diameter 33 mm) containing three materials (In-Zn eutectic (mass fraction 3.8% Zn), Sn and Pb) in a single crucible was designed and fabricated for the easy and economical fixed-point calibration of industrial platinum resistance thermometers (IPRTs) for use in industrial temperature measurements. The melting and freezing behaviors of the metals were investigated and the phase transition temperatures were determined using a commercial dry-block calibrator. Results showed that the melting plateaus are generally easy to realize and are reproducible, flatter and of longer duration. On the other hand, the freezing process is generally difficult, especially for Sn, due to the high supercooling required to initiate freezing. The observed melting temperatures at optimum set conditions were 143.11 °C (In-Zn), 231.70 °C (Sn) and 327.15 °C (Pb) with expanded uncertainties (k = 2) of 0.12 °C, 0.10 °C and 0.13 °C, respectively. This multi-fixed-point cell can be treated as a sole reference temperature-generating system. Based on the results, the realization of melting points of the mini multi-fixed-point cell can be recommended for the direct calibration of IPRTs in industrial applications without the need for a reference thermometer.
Co-C and Pd-C Eutectic Fixed Points for Radiation Thermometry and Thermocouple Thermometry
Wang, L.
2017-12-01
Two Co-C and Pd-C eutectic fixed point cells for both radiation thermometry and thermocouple thermometry were constructed at NMC. This paper describes details of the cell design, materials used, and fabrication of the cells. The melting curves of the Co-C and Pd-C cells were measured with a reference radiation thermometer realized in both a single-zone furnace and a three-zone furnace in order to investigate furnace effect. The transition temperatures in terms of ITS-90 were determined to be 1324.18 {°}C and 1491.61 {°}C with the corresponding combined standard uncertainty of 0.44 {°}C and 0.31 {°}C for Co-C and Pd-C, respectively, taking into account of the differences of two different types of furnaces used. The determined ITS-90 temperatures are also compared with that of INRIM cells obtained using the same reference radiation thermometer and the same furnaces with the same settings during a previous bilateral comparison exercise (Battuello et al. in Int J Thermophys 35:535-546, 2014). The agreements are within k=1 uncertainty for Co-C cell and k = 2 uncertainty for Pd-C cell. Shapes of the plateaus of NMC cells and INRIM cells are compared too and furnace effects are analyzed as well. The melting curves of the Co-C and Pd-C cells realized in the single-zone furnace are also measured by a Pt/Pd thermocouple, and the preliminary results are presented as well.
Castro, P.; Machin, G.; Bloembergen, P.; Lowe, D.; Whittam, A.
2014-07-01
This study forms part of the European Metrology Research Programme project implementing the New Kelvin to assign thermodynamic temperatures to a selected set of high-temperature fixed points (HTFPs), Cu, Co-C, Pt-C, and Re-C. A realistic thermal model of these HTFPs, developed in finite volume software ANSYS FLUENT, was constructed to quantify the uncertainty associated with the temperature drop across the back wall of the cell. In addition, the widely applied software package, STEEP3 was used to investigate the influence of cell emissivity. The temperature drop, , relates to the temperature difference due to the net loss of heat from the aperture of the cavity between the back wall of the cavity, viewed by the thermometer, defining the radiance temperature, and the solid-liquid interface of the alloy, defining the transition temperature of the HTFP. The actual value of can be used either as a correction (with associated uncertainty) to thermodynamic temperature evaluations of HTFPs, or as an uncertainty contribution to the overall estimated uncertainty. In addition, the effect of a range of furnace temperature profiles on the temperature drop was calculated and found to be negligible for Cu, Co-C, and Pt-C and small only for Re-C. The effective isothermal emissivity is calculated over the wavelength range from 450 nm to 850 nm for different assumed values of surface emissivity. Even when furnace temperature profiles are taken into account, the estimated emissivities change only slightly from the effective isothermal emissivity of the bare cell. These emissivity calculations are used to estimate the uncertainty in the temperature assignment due to the uncertainty in the emissivity of the blackbody.
Optimal design of a beam-based dynamic vibration absorber using fixed-points theory
Hua, Yingyu; Wong, Waion; Cheng, Li
2018-05-01
The addition of a dynamic vibration absorber (DVA) to a vibrating structure could provide an economic solution for vibration suppressions if the absorber is properly designed and located onto the structure. A common design of the DVA is a sprung mass because of its simple structure and low cost. However, the vibration suppression performance of this kind of DVA is limited by the ratio between the absorber mass and the mass of the primary structure. In this paper, a beam-based DVA (beam DVA) is proposed and optimized for minimizing the resonant vibration of a general structure. The vibration suppression performance of the proposed beam DVA depends on the mass ratio, the flexural rigidity and length of the beam. In comparison with the traditional sprung mass DVA, the proposed beam DVA shows more flexibility in vibration control design because it has more design parameters. With proper design, the beam DVA's vibration suppression capability can outperform that of the traditional DVA under the same mass constraint. The general approach is illustrated using a benchmark cantilever beam as an example. The receptance theory is introduced to model the compound system consisting of the host beam and the attached beam-based DVA. The model is validated through comparisons with the results from Abaqus as well as the Transfer Matrix method (TMM) method. Fixed-points theory is then employed to derive the analytical expressions for the optimum tuning ratio and damping ratio of the proposed beam absorber. A design guideline is then presented to choose the parameters of the beam absorber. Comparisons are finally presented between the beam absorber and the traditional DVA in terms of the vibration suppression effect. It is shown that the proposed beam absorber can outperform the traditional DVA by following this proposed guideline.
Influence of the Cavity Length on the Behavior of Hybrid Fixed-Point Cells Constructed at INRIM
Battuello, M.; Girard, F.; Florio, M.
2015-03-01
Hybrid cells with double carbon/carbon sheets are used at the Istituto Nazionale di Ricerca Metrologica (INRIM) for the realization of both pure metal fixed points and high-temperature metal-carbon eutectic points. Cells for the Cu and Co-C fixed points have been prepared to be used in the high-temperature fixed-point project of the Comité Consultatif de Thermométrie. The results of the evaluation processes were not completely satisfactory for the INRIM cells because of their low transition temperatures with respect to the best cells, and of a rather large melting range for the Co-C cell. A new design of the cells was devised, and considerable improvements were achieved with respect to the transition temperature, and the plateau shape and duration. As for the Cu point, the duration of the freezing plateaux increased by more than 50 % and the freezing temperature increased by 18 mK. As for the Co-C point, the melting temperature, expressed in terms of the point of inflection of the melting curve, increased by about 70 mK. The melting range of the plateaux, expressed as a difference was reduced from about 180 mK to about 130 mK, with melting times increased by about 50 %, as a consequence of an improvement of flatness and run-off of the plateaux.
Free-time and fixed end-point multi-target optimal control theory: Application to quantum computing
International Nuclear Information System (INIS)
Mishima, K.; Yamashita, K.
2011-01-01
Graphical abstract: The two-state Deutsch-Jozsa algortihm used to demonstrate the utility of free-time and fixed-end point multi-target optimal control theory. Research highlights: → Free-time and fixed-end point multi-target optimal control theory (FRFP-MTOCT) was constructed. → The features of our theory include optimization of the external time-dependent perturbations with high transition probabilities, that of the temporal duration, the monotonic convergence, and the ability to optimize multiple-laser pulses simultaneously. → The advantage of the theory and a comparison with conventional fixed-time and fixed end-point multi-target optimal control theory (FIFP-MTOCT) are presented by comparing data calculated using the present theory with those published previously [K. Mishima, K. Yamashita, Chem. Phys. 361 (2009) 106]. → The qubit system of our interest consists of two polar NaCl molecules coupled by dipole-dipole interaction. → The calculation examples show that our theory is useful for minor adjustment of the external fields. - Abstract: An extension of free-time and fixed end-point optimal control theory (FRFP-OCT) to monotonically convergent free-time and fixed end-point multi-target optimal control theory (FRFP-MTOCT) is presented. The features of our theory include optimization of the external time-dependent perturbations with high transition probabilities, that of the temporal duration, the monotonic convergence, and the ability to optimize multiple-laser pulses simultaneously. The advantage of the theory and a comparison with conventional fixed-time and fixed end-point multi-target optimal control theory (FIFP-MTOCT) are presented by comparing data calculated using the present theory with those published previously [K. Mishima, K. Yamashita, Chem. Phys. 361, (2009), 106]. The qubit system of our interest consists of two polar NaCl molecules coupled by dipole-dipole interaction. The calculation examples show that our theory is useful for minor
Itou, Etsuko
2013-08-01
We report the nonperturbative behavior of the twisted Polyakov loop (TPL) coupling constant for the SU(3) gauge theories defined by the ratio of Polyakov loop correlators in finite volume with twisted boundary condition. We reveal the vacuum structures and the phase structure for the lattice gauge theory with the twisted boundary condition. Carrying out the numerical simulations, we determine the nonperturbative running coupling constant in this renormalization scheme for the quenched QCD and N_f=12 SU(3) gauge theories. First, we study the quenched QCD theory using the plaquette gauge action. The TPL coupling constant has a fake fixed point in the confinement phase. We discuss this fake fixed point of the TPL scheme and obtain the nonperturbative running coupling constant in the deconfinement phase, where the magnitude of the Polyakov loop shows the nonzero values. We also investigate the system coupled to fundamental fermions. Since we use the naive staggered fermion with the twisted boundary condition in our simulation, only multiples of 12 are allowed for the number of flavors. According to the perturbative two-loop analysis, the N_f=12 SU(3) gauge theory might have a conformal fixed point in the infrared region. However, recent lattice studies show controversial results for the existence of the fixed point. We point out possible problems in previous work, and present our careful study. Finally, we find the infrared fixed point (IRFP) and discuss the robustness of the nontrivial IRFP of a many-flavor system under the change of the analysis method. Some preliminary results were reported in the proceedings [E. Bilgici et al., PoS(Lattice 2009), 063 (2009); Itou et al., PoS(Lattice 2010), 054 (2010)] and the letter paper [T. Aoyama et al., arXiv:1109.5806 [hep-lat
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Kiêu, K
1994-01-01
Unbiased stereological estimators of d-dimensional volume in R(n) are derived, based on information from an isotropic random r-slice through a specified point. The content of the slice can be subsampled by means of a spatial grid. The estimators depend only on spatial distances. As a fundamental ...... lemma, an explicit formula for the probability that an isotropic random r-slice in R(n) through 0 hits a fixed point in R(n) is given....
Directory of Open Access Journals (Sweden)
Kazuhiko W. Nakamura
2018-06-01
Full Text Available In order to foster leaders and supporters of fixed-point observation for sustainable forest management, it is considered effective to focus on students who have demonstrated potential for fixed-point observations of forests in the universal education stage. This study aims to identify the characteristics of students who frequently conduct plant observations, which is the basis for the fixed-point observation of forests, including methods involving photography. We conducted a questionnaire survey, which consisted of 19 questions that provided insight into junior high school students’ experiences, opportunities, and interests related to plant observation. We compared students who have conducted plant observations with those who have not, using Fisher’s exact test and multiple comparisons using the Benjamini and Hochberg method. The ratio of students who frequently conducted plant observations was significantly higher among female students than male students, and their characteristics differed by gender. The significant characteristics of male students included farm work experience and niche hobbies such as camping and lighting a bonfire, as well as using digital single-lens reflex cameras for photography; female students had relatively niche hobbies such as enjoying science. Students who increased the frequency of plant observations after the lecture about fixed-point observations of forests had an inclination toward social studies and tended not to use a smartphone for photography.
Directory of Open Access Journals (Sweden)
Yazheng Dang
2013-01-01
Full Text Available Inspired by the Moudafi (2010, we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.
Directory of Open Access Journals (Sweden)
Urriza I
2010-01-01
Full Text Available Abstract This paper presents a word length selection method for the implementation of digital controllers in both fixed-point and floating-point hardware on FPGAs. This method uses the new types defined in the VHDL-2008 fixed-point and floating-point packages. These packages allow customizing the word length of fixed and floating point representations and shorten the design cycle simplifying the design of arithmetic operations. The method performs bit-true simulations in order to determine the word length to represent the constant coefficients and the internal signals of the digital controller while maintaining the control system specifications. A mixed-signal simulation tool is used to simulate the closed loop system as a whole in order to analyze the impact of the quantization effects and loop delays on the control system performance. The method is applied to implement a digital controller for a switching power converter. The digital circuit is implemented on an FPGA, and the simulations are experimentally verified.
Convergence theorems for strictly hemi-contractive maps
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-04-01
It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the L p (or l p ) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs
International Nuclear Information System (INIS)
Palmer, R.
1994-06-01
Electromagnetic fields can be separated into near and far components. Near fields are extensions of static fields. They do not radiate, and they fall off more rapidly from a source than far fields. Near fields can accelerate particles, but the ratio of acceleration to source fields at a distance R, is always less than R/λ or 1, whichever is smaller. Far fields can be represented as sums of plane parallel, transversely polarized waves that travel at the velocity of light. A single such wave in a vacuum cannot give continuous acceleration, and it is shown that no sums of such waves can give net first order acceleration. This theorem is proven in three different ways; each method showing a different aspect of the situation
The quantitative Morse theorem
Loi, Ta Le; Phien, Phan
2013-01-01
In this paper, we give a proof of the quantitative Morse theorem stated by {Y. Yomdin} in \\cite{Y1}. The proof is based on the quantitative Sard theorem, the quantitative inverse function theorem and the quantitative Morse lemma.
Theorems of Tarski's Undefinability and Godel's Second Incompleteness - Computationally
Salehi, Saeed
2015-01-01
We present a version of Godel's Second Incompleteness Theorem for recursively enumerable consistent extensions of a fixed axiomatizable theory, by incorporating some bi-theoretic version of the derivability conditions (first discussed by M. Detlefsen 2001). We also argue that Tarski's theorem on the Undefinability of Truth is Godel's First Incompleteness Theorem relativized to definable oracles; here a unification of these two theorems is given.
Merzlikin, Boris S.; Shapiro, Ilya L.; Wipf, Andreas; Zanusso, Omar
2017-12-01
Using covariant methods, we construct and explore the Wetterich equation for a nonminimal coupling F (ϕ )R of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered nonminimal coupling ξ ϕ2R as a special case. We consider the truncations without and with scale- and field-dependent wave-function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the nonminimal coupling in the symmetric and spontaneously broken phases with vanishing and nonvanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension d =4 .
Fröb, Markus B.
2018-02-01
We study a proposal for gauge-invariant correlation functions in perturbative quantum gravity, which are obtained by fixing the geodesic distance between points in the fluctuating geometry. These correlation functions are non-local and strongly divergent, and we show how to renormalise them by performing a ‘wave function renormalisation’ of the geodesic embedding coordinates. The result is finite and gauge-independent, but displays unusual features such as double logarithms at one-loop order.
Directory of Open Access Journals (Sweden)
Wei Han
2008-01-01
Full Text Available Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.
Convergence Theorem for Finite Family of Total Asymptotically Nonexpansive Mappings
Directory of Open Access Journals (Sweden)
E.U. Ofoedu
2015-11-01
Full Text Available In this paper we introduce an explicit iteration process and prove strong convergence of the scheme in a real Hilbert space $H$ to the common fixed point of finite family of total asymptotically nonexpansive mappings which is nearest to the point $u \\in H$. Our results improve previously known ones obtained for the class of asymptotically nonexpansive mappings. As application, iterative method for: approximation of solution of variational Inequality problem, finite family of continuous pseudocontractive mappings, approximation of solutions of classical equilibrium problems and approximation of solutions of convex minimization problems are proposed. Our theorems unify and complement many recently announced results.
Small copper fixed-point cells of the hybrid type to be used in place of normal larger cells
Battuello, M.; Girard, F.; Florio, M.
2012-10-01
Two small cells for the realization of the fixed point of copper were constructed and investigated at INRIM. They are of the same hybrid design generally adopted for the eutectic high-temperature fixed-point cells, namely a structure with a sacrificial graphite sleeve and a layer of flexible carbon-carbon composite sheet (C/C sheet). Because of the largely different design with respect to the cells normally adopted for the construction of pure metal fixed points, they were compared and characterized with respect to the normal cells used at INRIM for the ITS-90 realization. Two different furnaces were used to compare hybrid and normal cells. One of the hybrid cells was also used in different configurations, i.e. without the C/C sheet and with two layers of sheet. The cells were compared with different operative conditions, i.e. temperature settings of the furnaces for inducing the freeze, and repeatability and reproducibility were investigated. Freezing temperature and shape of the plateaux obtained under the different conditions were analysed. As expected the duration of the plateaux obtained with the hybrid cells is considerably shorter than with the normal cell, but this does not affect the results in terms of freezing temperature. Measurements with the modified cell showed that the use of a double C/C sheet may improve both repeatability and reproducibility of the plateaux.
Small copper fixed-point cells of the hybrid type to be used in place of normal larger cells
International Nuclear Information System (INIS)
Battuello, M; Girard, F; Florio, M
2012-01-01
Two small cells for the realization of the fixed point of copper were constructed and investigated at INRIM. They are of the same hybrid design generally adopted for the eutectic high-temperature fixed-point cells, namely a structure with a sacrificial graphite sleeve and a layer of flexible carbon–carbon composite sheet (C/C sheet). Because of the largely different design with respect to the cells normally adopted for the construction of pure metal fixed points, they were compared and characterized with respect to the normal cells used at INRIM for the ITS-90 realization. Two different furnaces were used to compare hybrid and normal cells. One of the hybrid cells was also used in different configurations, i.e. without the C/C sheet and with two layers of sheet. The cells were compared with different operative conditions, i.e. temperature settings of the furnaces for inducing the freeze, and repeatability and reproducibility were investigated. Freezing temperature and shape of the plateaux obtained under the different conditions were analysed. As expected the duration of the plateaux obtained with the hybrid cells is considerably shorter than with the normal cell, but this does not affect the results in terms of freezing temperature. Measurements with the modified cell showed that the use of a double C/C sheet may improve both repeatability and reproducibility of the plateaux. (paper)
Directory of Open Access Journals (Sweden)
Svetoslav Ganchev Nikolov
2015-07-01
Full Text Available The study of the dynamic behavior of a rigid body with one fixed point (gyroscope has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1 to outline the characteristic features of the theory of dynamical systems and 2 to reveal the specific properties of the motion of a rigid body with one fixed point (gyroscope.This article consists of six sections. The first section addresses the main concepts of the theory of dynamical systems. Section two presents the main theoretical results (obtained so far concerning the dynamic behavior of a solid with one fixed point (gyroscope. Section three examines the problem of gyroscopic stabilization. Section four deals with the non-linear (chaotic dynamics of the gyroscope. Section five is a brief analysis of the gyroscope applications in engineering. The final section provides conclusions and generalizations on why the theory of dynamical systems should be used in the study of the movement of gyroscopic systems.
Energy Technology Data Exchange (ETDEWEB)
Laurie, M.; Vlahovic, L.; Rondinella, V.V. [European Commission, Joint Research Centre, Institute for Transuranium Elements, P.O. Box 2340, D-76125 Karlsruhe, (Germany); Sadli, M.; Failleau, G. [Laboratoire Commun de Metrologie, LNE-Cnam, Saint-Denis, (France); Fuetterer, M.; Lapetite, J.M. [European Commission, Joint Research Centre, Institute for Energy and Transport, P.O. Box 2, NL-1755 ZG Petten, (Netherlands); Fourrez, S. [Thermocoax, 8 rue du pre neuf, F-61100 St Georges des Groseillers, (France)
2015-07-01
Temperature measurements in the nuclear field require a high degree of reliability and accuracy. Despite their sheathed form, thermocouples subjected to nuclear radiations undergo changes due to radiation damage and transmutation that lead to significant EMF drift during long-term fuel irradiation experiment. For the purpose of a High Temperature Reactor fuel irradiation to take place in the High Flux Reactor Petten, a dedicated fixed-point cell was jointly developed by LNE-Cnam and JRC-IET. The developed cell to be housed in the irradiation rig was tailor made to quantify the thermocouple drift during the irradiation (about two year duration) and withstand high temperature (in the range 950 deg. C - 1100 deg. C) in the presence of contaminated helium in a graphite environment. Considering the different levels of temperature achieved in the irradiation facility and the large palette of thermocouple types aimed at surveying the HTR fuel pebble during the qualification test both copper (1084.62 deg. C) and gold (1064.18 deg. C) fixed-point materials were considered. The aim of this paper is to first describe the fixed-point mini-cell designed to be embedded in the reactor rig and to discuss the preliminary results achieved during some out of pile tests as much as some robustness tests representative of the reactor scram scenarios. (authors)
International Nuclear Information System (INIS)
Ma Zhongqi
2006-01-01
The Levinson theorem is a fundamental theorem in quantum scattering theory, which shows the relation between the number of bound states and the phase shift at zero momentum for the Schroedinger equation. The Levinson theorem was established and developed mainly with the Jost function, with the Green function and with the Sturm-Liouville theorem. In this review, we compare three methods of proof, study the conditions of the potential for the Levinson theorem and generalize it to the Dirac equation. The method with the Sturm-Liouville theorem is explained in some detail. References to development and application of the Levinson theorem are introduced. (topical review)
The EuroSITES network: Integrating and enhancing fixed-point open ocean observatories around Europe
Lampitt, Richard S.; Larkin, Kate E.; EuroSITES Consortium
2010-05-01
EuroSITES is a 3 year (2008-2011) EU collaborative project (3.5MEuro) with the objective to integrate and enhance the nine existing open ocean fixed point observatories around Europe (www.eurosites.info). These observatories are primarily composed of full depth moorings and make multidisciplinary in situ observations within the water column as the European contribution to the global array OceanSITES (www.oceansites.org). In the first 18 months, all 9 observatories have been active and integration has been significant through the maintenance and enhancement of observatory hardware. Highlights include the enhancement of observatories with sensors to measure O2, pCO2, chlorophyll, and nitrate in near real-time from the upper 1000 m. In addition, some seafloor missions are also actively supported. These include seafloor platforms currently deployed in the Mediterranean, one for tsunami detection and one to monitor fluid flow related to seismic activity and slope stability. Upcoming seafloor science missions in 2010 include monitoring benthic biological communities and associated biogeochemistry as indicators of climate change in both the Northeast Atlantic and Mediterranean. EuroSITES also promotes the development of innovative sensors and samplers in order to progress capability to measure climate-relevant properties of the ocean. These include further developing current technologies for autonomous long-term monitoring of oxygen consumption in the mesopelagic, pH and mesozooplankton abundance. Many of these science missions are directly related to complementary activities in other European projects such as EPOCA, HYPOX and ESONET. In 2010 a direct collaboration including in situ field work will take place between ESONET and EuroSITES. The demonstration mission MODOO (funded by ESONET) will be implemented in 2010 at the EuroSITES PAP observatory. Field work will include deployment of a seafloor lander system with various sensors which will send data to shore in real
Dermíšek, Radovan; McGinnis, Navin
2018-03-01
We use the IR fixed point predictions for gauge couplings and the top Yukawa coupling in the minimal supersymmetric model (MSSM) extended with vectorlike families to infer the scale of vectorlike matter and superpartners. We quote results for several extensions of the MSSM and present results in detail for the MSSM extended with one complete vectorlike family. We find that for a unified gauge coupling αG>0.3 vectorlike matter or superpartners are expected within 1.7 TeV (2.5 TeV) based on all three gauge couplings being simultaneously within 1.5% (5%) from observed values. This range extends to about 4 TeV for αG>0.2 . We also find that in the scenario with two additional large Yukawa couplings of vectorlike quarks the IR fixed point value of the top Yukawa coupling independently points to a multi-TeV range for vectorlike matter and superpartners. Assuming a universal value for all large Yukawa couplings at the grand unified theory scale, the measured top quark mass can be obtained from the IR fixed point for tan β ≃4 . The range expands to any tan β >3 for significant departures from the universality assumption. Considering that the Higgs boson mass also points to a multi-TeV range for superpartners in the MSSM, adding a complete vectorlike family at the same scale provides a compelling scenario where the values of gauge couplings and the top quark mass are understood as a consequence of the particle content of the model.
Directory of Open Access Journals (Sweden)
B. Kuyper
2018-04-01
Full Text Available Bromoform mixing ratios in marine air were measured at Cape Point Global Atmospheric Watch Station, South Africa. This represents the first such bromoform data set recorded at this location. Manual daily measurements were made during a month-long field campaign (austral spring 2011 using a gas chromatograph-electron capture detector (GC-ECD with a custom-built front end thermal desorption trap. The measured concentrations ranged between 4.4 and 64.6 (± 22.2 % ppt with a mean of 24.8 ± 14.8 ppt. The highest mixing ratios recorded here occurred at, or shortly after, low tide. The diurnal cycle exhibited a morning and evening maximum with lower concentrations throughout the rest of the day. Initial analysis of the data presented indicates that the local kelp beds were the dominant source of the bromoform reported. A concentration-weighted trajectory analysis of the bromoform measurements suggests that two offshore source areas may exist. These source areas appear to be centred on the Agulhas retroflection and extend from St Helena Bay to the southwest.
Kuyper, Brett; Palmer, Carl J.; Labuschagne, Casper; Reason, Chris J. C.
2018-04-01
Bromoform mixing ratios in marine air were measured at Cape Point Global Atmospheric Watch Station, South Africa. This represents the first such bromoform data set recorded at this location. Manual daily measurements were made during a month-long field campaign (austral spring 2011) using a gas chromatograph-electron capture detector (GC-ECD) with a custom-built front end thermal desorption trap. The measured concentrations ranged between 4.4 and 64.6 (± 22.2 %) ppt with a mean of 24.8 ± 14.8 ppt. The highest mixing ratios recorded here occurred at, or shortly after, low tide. The diurnal cycle exhibited a morning and evening maximum with lower concentrations throughout the rest of the day. Initial analysis of the data presented indicates that the local kelp beds were the dominant source of the bromoform reported. A concentration-weighted trajectory analysis of the bromoform measurements suggests that two offshore source areas may exist. These source areas appear to be centred on the Agulhas retroflection and extend from St Helena Bay to the southwest.
On large N fixed points of a U(N) symmetric (phisup(*)xphi)3sub(D=3) model coupled to fermions
International Nuclear Information System (INIS)
Nissimov, E.R.; Pacheva, S.J.
1984-01-01
The three-dimensional U(N) symmetric eta(phisup(*) x phi) 3 model coupled to N component fermions is considered within the 1/N expansion. In contrast to the purely bosonic case, here we find in the large N limit only a (nonperturbative) ultraviolet fixed point at eta=etasup(*) approx.= 179, whereas infrared fixed points are absent. (orig.)
Directory of Open Access Journals (Sweden)
Sol Swords
2011-10-01
Full Text Available Interactive theorem proving requires a lot of human guidance. Proving a property involves (1 figuring out why it holds, then (2 coaxing the theorem prover into believing it. Both steps can take a long time. We explain how to use GL, a framework for proving finite ACL2 theorems with BDD- or SAT-based reasoning. This approach makes it unnecessary to deeply understand why a property is true, and automates the process of admitting it as a theorem. We use GL at Centaur Technology to verify execution units for x86 integer, MMX, SSE, and floating-point arithmetic.
The g-theorem and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo [Centro Atómico Bariloche and CONICET,S.C. de Bariloche, Río Negro, R8402AGP (Argentina)
2016-10-25
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.
Stacked spheres and lower bound theorem
Indian Academy of Sciences (India)
BASUDEB DATTA
2011-11-20
Nov 20, 2011 ... Preliminaries. Lower bound theorem. On going work. Definitions. An n-simplex is a convex hull of n + 1 affinely independent points. (called vertices) in some Euclidean space R. N . Stacked spheres and lower bound theorem. Basudeb Datta. Indian Institute of Science. 2 / 27 ...
The divergence theorem for unbounded vector fields
De Pauw, Thierry; Pfeffer, Washek F.
2007-01-01
In the context of Lebesgue integration, we derive the divergence theorem for unbounded vector. elds that can have singularities at every point of a compact set whose Minkowski content of codimension greater than two is. nite. The resulting integration by parts theorem is applied to removable sets of holomorphic and harmonic functions.
Investigations on Two Co-C Fixed-Point Cells Prepared at INRIM and LNE-Cnam
Battuello, M.; Florio, M.; Sadli, M.; Bourson, F.
2011-08-01
INRIM and LNE-Cnam agreed to undertake a collaboration aimed to verify, through the use of metal-carbon eutectic fixed-point cells, methods and facilities used for defining the transition temperature of eutectic fixed points and manufacturing procedures of cells. To this purpose and as a first step of the cooperation, a Co-C cell manufactured at LNE-Cnam was measured at INRIM and compared with a local cell. The two cells were of different designs: the INRIM cell of 10 cm3 inner volume and the LNE-Cnam one of 3.9 cm3. The external dimensions of the two cells were noticeably different, namely, 40 mm in length and 24 mm in diameter for the LNE-Cnam cell 3Co4 and 110 mm in length and 42 mm in diameter for the INRIM cell. Consequently, the investigation of the effect of temperature distributions in the heating furnace was undertaken by implementing the cells inside single-zone and three-zone furnaces. The transition temperature of the cell was determined at the two institutes making use of different techniques: at INRIM radiation scales at 900 nm, 950 nm, and 1.6 μm were realized from In to Cu and then used to define T 90(Co-C) by extrapolation. At LNE-Cnam, a radiance comparator based on a grating monochromator was used for the extrapolation from the Cu fixed point. This paper presents a comparative description of the cells and the manufacturing methods and the results in terms of equivalence between the two cells and melting temperatures determined at INRIM and LNE-Cnam.
International Nuclear Information System (INIS)
Znojil, M.
1986-01-01
The radial Schroedinger equation and its bound-state solutions for the interaction V(r)=Vsub(coulomb)+Vsub(Pade), where Vsub(Pade)(r)=(b+cr)/(1+drsup(2)) are considered. In order to construct exactly the Feshbach effective Hamiltonian Hsup(eff), the fixed-point-substraction technique is employed and its simplification is proposed. The first two terms in the resulting asymptotic expansions of PSIsub(n) and Hsup(eff) are calculated and interpreted as a new type of perturbation theory
Zhao, Jing; Zong, Haili
2018-01-01
In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.
Fermat's Last Theorem A Theorem at Last!
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Fermat's Last Theorem A Theorem at Last! C S Yogananda. General Article Volume 1 Issue 1 January 1996 pp 71-79. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0071-0079 ...
International Nuclear Information System (INIS)
Kainz, K; Prah, D; Ahunbay, E; Li, X
2014-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Kainz, K; Prah, D; Ahunbay, E; Li, X [Medical College of Wisconsin, Milwaukee, WI (United States)
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.
Directory of Open Access Journals (Sweden)
Eleonora Pantano
2013-05-01
Full Text Available The current advances in information and communications technologies developed new tools for retailers to innovate. In fact, the increasing computing capacity and the advancements in networking systems provided a new ubiquitous scenario that can be adapted for retailing in order to develop innovative shopping environments. The aim of this paper is to deeply understand the emergence of the ubiquitous retailing phenomenon and the possible shift from the physical point of sale to a ubiquitous one, by analysing this radical innovation and the main consequences for frms and market.
Energy Technology Data Exchange (ETDEWEB)
Ancsin, J. [National Research Council of Canada, Ottawa, ON (Canada). Inst. for National Measurement Standards; Mendez-Lango, E. [Centro Nacional de Metrologia (CENAM), Div. Termometria, Queretaro (Mexico)
1999-07-01
The reproducibility of some thermometric fixed points and the accuracy of four platinum resistance thermometers (PRTs) were studied. It was found that the fixed points of aluminium (Al), zinc (Zn), tin (Sn), indium (In) and gallium (Ga) were realized reproducibly within {+-}0.17 mK; {+-}0.11 mK; {+-}0.10 mK; {+-}0.13 mK and {+-}0.12 mK, respectively. Because the actual impurities and their concentration in our samples (of 99.9999 % or 99.999 99 % purity) are unknown, the systematic uncertainly due to impurities cannot be estimated. However, any of the samples of Ga, In, Sn, Zn and Al is consistent with the rest within {+-}0.2 mK, using a cubic or quadratic deviation function, in the temperature range 0 deg C to 660 deg C. This indicates that the effect of impurities is negligible. Four PRTs were selected at random. They were calibrated repeatedly, first up to the Zn point and then up to the Al point. The resistance of each PRT drifted. From time to time, for each PRT, a seemingly well-established resistance drift suddenly and unpredictably changed to a different rate of drift. Occasionally, the resistance of the PRTs shifted. Such unpredictable changes obviously limit the accuracy of temperature measurements using PRTs no matter what the accuracy of their calibrations. In the case of our four PRTs, the uncertainty of temperature measurements near 660 deg C ranged from about {+-}1 mK to about {+-}2,5 mK even though they were all calibrated at all fixed points well within {+-}0.25 mK uncertainty. Possible explanations are offered for the apparently permanent drifts and the erratic shifts in the resistance of the PRTs. Some comments are made concerning the ambiguity of 'immersion tests' in general. The furnaces of the National Research Council of Canada used in this work are high-temperature adiabatic calorimeters. (authors)
Theorems of Leray-Schauder type and applications
Precup, Radu
2002-01-01
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis. This volume will appeal to graduate students and researchers in mathematical analysis and its applications.
International Nuclear Information System (INIS)
Sidorov, A.V.; Stamenov, D.B.
1996-01-01
The results of LO fixed point QCD (FP-QCD) analysis of the CCFR data for the nucleon structure function xF 3 (x,Q 2 ) are presented. The predictions of FR-QCD, in which the Callan-Symanzik β-function admits a second order ultraviolet zero at α=α 0 are in good agreement with the data. Constraints on possible values of the β-function parameter b regulating how fast α s (Q 2 ) tends to its asymptotic value α 0 ≠0 are found from the data. The corresponding values of α 0 are also determined. Having in mind our recent 'first-order fixed point' QCD fit to the same data we conclude that in spite of a high precision and a large (x,Q 2 ) kinematic range of the CCFR data they cannot discriminate between QCD and FP-QCD predictions for xF 3 (x,Q 2 ). 14 refs., 1 tab
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We introduce and analyze a hybrid iterative algorithm by virtue of Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, and averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs, the solution set of finitely many variational inequality problems (VIPs, the solution set of general system of variational inequalities (GSVI, and the set of minimizers of convex minimization problem (CMP, which is just a unique solution of a triple hierarchical variational inequality (THVI in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solve a hierarchical fixed point problem with constraints of finitely many GMEPs, finitely many VIPs, GSVI, and CMP. The results obtained in this paper improve and extend the corresponding results announced by many others.
Convergence theorems for quasi-contractive maps in uniformly convex spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-04-01
Let K be a nonempty closed convex and bounded subset of a real uniformly convex Banach space E of modulus of convexity of power type q≥2. Let T by a quasi-contractive mapping of K into itself. It is proved that each of two well known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly, without any compactness assumption on the domain of the map, to the unique fixed point of T in K. Our theorems generalize important known results. (author). 22 refs
Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
Chidume, C.E.; Osilike, M.O.
1992-05-01
Let K be a nonempty closed and convex subset of a real uniformly smooth Banach space, E, with modulus of smoothness of power type q>1. Let T be a mapping of K into itself, T is an element of C (in the notion of Browder and Petryshyn; and Rhoades). It is proved that the Mann iteration process, under suitable conditions, converges strongly to the unique fixed point of T. If K is also bounded, then the Ishikawa iteration process converges to the fixed point of T. While our theorems generalize important known results, our method is also of independent interest. (author). 14 refs
The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
Energy Technology Data Exchange (ETDEWEB)
Gliozzi, Ferdinando [Dipartimento di Fisica, Università di Torino andIstituto Nazionale di Fisica Nucleare - sezione di Torino,Via P. Giuria 1, I-10125 Torino (Italy); Guerrieri, Andrea L. [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); I.N.F.N. Sezione di Roma Tor Vergata,Via della Ricerca Scientifica, I-00133 Roma (Italy); Petkou, Anastasios C. [Institute of Theoretical Physics, Aristotle University of Thessaloniki,54124 Thessaloniki (Greece); Wen, Congkao [Walter Burke Institute for Theoretical Physics, California Institute of Technology,Pasadena, CA 91125 (United States); Mani L. Bhaumik Institute for Theoretical Physics,Department of Physics and Astronomy, UCLA,Los Angeles, CA 90095 (United States)
2017-04-11
We describe in detail the method used in our previous work https://arxiv.org/abs/1611.10344 to study the Wilson-Fisher critical points nearby generalized free CFTs, exploiting the analytic structure of conformal blocks as functions of the conformal dimension of the exchanged operator. Our method is equivalent to the mechanism of conformal multiplet recombination set up by null states. We compute, to the first non-trivial order in the ϵ-expansion, the anomalous dimensions and the OPE coefficients of infinite classes of scalar local operators using just CFT data. We study single-scalar and O(N)-invariant theories, as well as theories with multiple deformations. When available we agree with older results, but we also produce a wealth of new ones. Unitarity and crossing symmetry are not used in our approach and we are able to apply our method to non-unitary theories as well. Some implications of our results for the study of the non-unitary theories containing partially conserved higher-spin currents are briefly mentioned.
Construction of Home-Made Tin Fixed-Point Cell at TUBITAK UME
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.
Expansion of a stochastic stationary optical field at a fixed point
International Nuclear Information System (INIS)
Martinez-Herrero, R.; Mejias, P.M.
1984-01-01
An important problem in single and multifold photoelectron statistics is to determine the statistical properties of a totally polarized optical field at some point →r from the photoelectron counts registered by the detector. The solution to this problem may be found in the determination of the statistical properties of an integral over a stochastic process; a complicated and formidable task. This problem can be solved in some cases of interest by expanding the process V(t) (which represents the field at →r) in a set of complete orthonormal deterministic functions, resulting in the so-called Karhunen-Loeve expansion of V(t). Two disadvantages are that the process must be defined over a finite time interval, and that each term of the series does not represent any special optical field. Taking into account these limitations of the expansion, the purpose of this work is to find another alternative expansion of stationary optical fields defined over the infinite time interval, and whose terms represent stochastic fields
Levinson, N
1940-01-01
A typical gap theorem of the type discussed in the book deals with a set of exponential functions { \\{e^{{{i\\lambda}_n} x}\\} } on an interval of the real line and explores the conditions under which this set generates the entire L_2 space on this interval. A typical gap theorem deals with functions f on the real line such that many Fourier coefficients of f vanish. The main goal of this book is to investigate relations between density and gap theorems and to study various cases where these theorems hold. The author also shows that density- and gap-type theorems are related to various propertie
2016-04-01
AND ROTORCRAFT FROM DISCRETE -POINT LINEAR MODELS Eric L. Tobias and Mark B. Tischler Aviation Development Directorate Aviation and Missile...Stitching Architecture for Continuous Full Flight-Envelope Simulation of Fixed-Wing Aircraft and Rotorcraft from Discrete -Point Linear Models 5...of discrete -point linear models and trim data. The model stitching simulation architecture is applicable to any aircraft configuration readily
De la Sen, M.
2015-01-01
In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilistic α-fuzzy fixed points under some types of probabilistic contractive conditions.
Directory of Open Access Journals (Sweden)
Cai Gang
2009-01-01
Full Text Available We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asymptotically nonexpansive mappings. Our results improve and extend the results announced by many others.
DEFF Research Database (Denmark)
Filipiuk, Piotr; Nielson, Flemming; Nielson, Hanne Riis
2012-01-01
We present a logic for the specification of static analysis problems that goes beyond the logics traditionally used. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive specifications of properties. Two main theoretical contributions...... are a Moore Family result and a parametrized worst case time complexity result. We show that the logic and the associated solver can be used for rapid prototyping of analyses and illustrate a wide variety of applications within Static Analysis, Constraint Satisfaction Problems and Model Checking. In all cases...
The Infrared Fixed Points of 3d $\\mathcal{N}=4$ $USp(2N)$ SQCD Theories arXiv
Assel, Benjamin
We derive the algebraic description of the Coulomb branch of 3d $\\mathcal{N}=4$ $USp(2N)$ SQCD theories with $N_f$ fundamental hypermultiplets and determine their low energy physics in any vacuum from the local geometry of the moduli space, identifying the interacting SCFTs which arise at singularities and possible extra free sectors. The SCFT with the largest moduli space arises at the most singular locus on the Coulomb branch. For $N_f>2N$ (good theories) it sits at the origin of the conical variety as expected. For $N_f =2N$ we find two separate most singular points, from which the two isomorphic components of the Higgs branch of the UV theory emanate. The SCFTs sitting at any of these two vacua have only odd dimensional Coulomb branch generators, which transform under an accidental $SU(2)$ global symmetry. We provide a direct derivation of their moduli spaces of vacua, and propose a Lagrangian mirror theory for these fixed points. For $2 \\le N_f < 2N$ the most singular locus has one or two extended com...
The Patchwork Divergence Theorem
Dray, Tevian; Hellaby, Charles
1994-01-01
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PA...
Lectures on Fermat's last theorem
International Nuclear Information System (INIS)
Sury, B.
1993-09-01
The report presents the main ideas involved in the approach towards the so-called Fermat's last theorem (FLT). The discussion leads to the point where recent work of A. Wiles starts and his work is not discussed. After a short history of the FLT and of the present approach, are discussed the elliptic curves and the modular forms with their relations, the Taniyama-Shimura-Well conjecture and the FLT
Pythagoras Theorem and Relativistic Kinematics
Mulaj, Zenun; Dhoqina, Polikron
2010-01-01
In two inertial frames that move in a particular direction, may be registered a light signal that propagates in an angle with this direction. Applying Pythagoras theorem and principles of STR in both systems, we can derive all relativistic kinematics relations like the relativity of simultaneity of events, of the time interval, of the length of objects, of the velocity of the material point, Lorentz transformations, Doppler effect and stellar aberration.
Metrical theorems on systems of small inhomogeneous linear forms
DEFF Research Database (Denmark)
Hussain, Mumtaz; Kristensen, Simon
In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.......In this paper we establish complete Khintchine-Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed....
Directory of Open Access Journals (Sweden)
Douglas Scott C
2007-01-01
Full Text Available We derive new fixed-point algorithms for the blind separation of complex-valued mixtures of independent, noncircularly symmetric, and non-Gaussian source signals. Leveraging recently developed results on the separability of complex-valued signal mixtures, we systematically construct iterative procedures on a kurtosis-based contrast whose evolutionary characteristics are identical to those of the FastICA algorithm of Hyvarinen and Oja in the real-valued mixture case. Thus, our methods inherit the fast convergence properties, computational simplicity, and ease of use of the FastICA algorithm while at the same time extending this class of techniques to complex signal mixtures. For extracting multiple sources, symmetric and asymmetric signal deflation procedures can be employed. Simulations for both noiseless and noisy mixtures indicate that the proposed algorithms have superior finite-sample performance in data-starved scenarios as compared to existing complex ICA methods while performing about as well as the best of these techniques for larger data-record lengths.
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!!!
International Nuclear Information System (INIS)
Singh, Vimal
2007-01-01
In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters
Yang, Chen; Li, Bingyi; Chen, Liang; Wei, Chunpeng; Xie, Yizhuang; Chen, He; Yu, Wenyue
2017-06-24
With the development of satellite load technology and very large scale integrated (VLSI) circuit technology, onboard real-time synthetic aperture radar (SAR) imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS) SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT), which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array-application-specific integrated circuit (FPGA-ASIC) hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS) technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.
Directory of Open Access Journals (Sweden)
Chen Yang
2017-06-01
Full Text Available With the development of satellite load technology and very large scale integrated (VLSI circuit technology, onboard real-time synthetic aperture radar (SAR imaging systems have become a solution for allowing rapid response to disasters. A key goal of the onboard SAR imaging system design is to achieve high real-time processing performance with severe size, weight, and power consumption constraints. In this paper, we analyse the computational burden of the commonly used chirp scaling (CS SAR imaging algorithm. To reduce the system hardware cost, we propose a partial fixed-point processing scheme. The fast Fourier transform (FFT, which is the most computation-sensitive operation in the CS algorithm, is processed with fixed-point, while other operations are processed with single precision floating-point. With the proposed fixed-point processing error propagation model, the fixed-point processing word length is determined. The fidelity and accuracy relative to conventional ground-based software processors is verified by evaluating both the point target imaging quality and the actual scene imaging quality. As a proof of concept, a field- programmable gate array−application-specific integrated circuit (FPGA-ASIC hybrid heterogeneous parallel accelerating architecture is designed and realized. The customized fixed-point FFT is implemented using the 130 nm complementary metal oxide semiconductor (CMOS technology as a co-processor of the Xilinx xc6vlx760t FPGA. A single processing board requires 12 s and consumes 21 W to focus a 50-km swath width, 5-m resolution stripmap SAR raw data with a granularity of 16,384 × 16,384.
Hahl, Sayuri K; Kremling, Andreas
2016-01-01
In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still
Dimensional analysis beyond the Pi theorem
Zohuri, Bahman
2017-01-01
Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First ...
Bellver-Cebreros, Consuelo; Rodriguez-Danta, Marcelo
2009-01-01
An apparently unnoticed analogy between the torque-free motion of a rotating rigid body about a fixed point and the propagation of light in anisotropic media is stated. First, a new plane construction for visualizing this torque-free motion is proposed. This method uses an intrinsic representation alternative to angular momentum and independent of…
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
Wigner's Symmetry Representation Theorem
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...
Nonextensive Pythagoras' Theorem
Dukkipati, Ambedkar
2006-01-01
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And hence, this property is referred to as Pythagoras' theorem of relative-entropy minimization or triangle equality and plays a fundamental role in geometrical approaches of statistical estimation theory like information geometry. Equvalent of Pythagoras' theo...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Abstract. The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose K is a compact set in the complex plane and 0 belongs to the boundary ∂K. Let A(K) denote the space of all functions f on K such that f is holo- morphic in a neighborhood of K and f(0) = 0. Also for any given positive integer ...
Existence of positive solutions for a multi-point four-order boundary-value problem
Directory of Open Access Journals (Sweden)
Le Xuan Truong
2011-10-01
Full Text Available The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differential equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
Triple solutions for multi-point boundary-value problem with p-Laplace operator
Directory of Open Access Journals (Sweden)
Yansheng Liu
2009-11-01
Full Text Available Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained.
Directory of Open Access Journals (Sweden)
Tian Zhou Xu
2010-01-01
Full Text Available Using the fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation f(x+ky+f(x−ky=k2f(x+y+k2f(x−y+2(1−k2f(x+((k4−k2/12[f(2y+f(−2y−4f(y−4f(−y] for a fixed integer k with k≠0,±1 in non-Archimedean normed spaces.
Complex proofs of real theorems
Lax, Peter D
2011-01-01
Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Müntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Żelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime ...
DEFF Research Database (Denmark)
Törnquist, Asger Dag; Weiss, W.
2009-01-01
We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible.......We prove the following descriptive set-theoretic analogue of a theorem of R. 0. Davies: Every σ function f:ℝ × ℝ → ℝ can be represented as a sum of rectangular Σ functions if and only if all reals are constructible....
The Fluctuation Theorem and Dissipation Theorem for Poiseuille Flow
International Nuclear Information System (INIS)
Brookes, Sarah J; Reid, James C; Evans, Denis J; Searles, Debra J
2011-01-01
The fluctuation theorem and the dissipation theorem provide relationships to describe nonequilibrium systems arbitrarily far from, or close to equilibrium. They both rely on definition of a central property, the dissipation function. In this manuscript we apply these theorems to examine a boundary thermostatted system undergoing Poiseuille flow. The relationships are verified computationally and show that the dissipation theorem is potentially useful for study of boundary thermostatted systems consisting of complex molecules undergoing flow in the nonlinear regime.
Bell's theorem and the nature of reality
International Nuclear Information System (INIS)
Bertlmann, R.A.
1988-01-01
We rediscuss the Einstein-Podolsky-Rosen paradox in Bohm's spin version and oppose to it Bohr's controversial point of view. Then we explain Bell's theorem, Bell inequalities and its consequences. We describe the experiment of Aspect, Dalibard and Roger in detail. Finally we draw attention to the nonlocal structure of the underlying theory. 61 refs., 8 tabs. (Author)
On Viviani's Theorem and Its Extensions
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…
Another look at the second incompleteness theorem
Visser, A.
2017-01-01
In this paper we study proofs of some general forms of the Second Incompleteness Theorem. These forms conform to the Feferman format, where the proof predicate is xed and the representation of the axiom set varies. We extend the Feferman framework in one important point: we allow the interpretation
Dalen, D. van
The following pages make form a new chapter for the book Logic and Structure. This chapter deals with the incompleteness theorem, and contains enough basic material for the treatment of the required notions of computability, representability and the like. This chapter will appear in the next
Saikia, Manjil P.
2013-01-01
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \\cite{thales}, \\cite{wiki} and \\cite{wiki2} for the historical comments and sources.
Converse Barrier Certificate Theorems
DEFF Research Database (Denmark)
Wisniewski, Rafael; Sloth, Christoffer
2016-01-01
This paper shows that a barrier certificate exists for any safe dynamical system. Specifically, we prove converse barrier certificate theorems for a class of structurally stable dynamical systems. Other authors have developed a related result by assuming that the dynamical system has neither...
Virial theorem and hypervirial theorem in a spherical geometry
International Nuclear Information System (INIS)
Li Yan; Chen Jingling; Zhang Fulin
2011-01-01
The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)
Discovering the Theorem of Pythagoras
Lattanzio, Robert (Editor)
1988-01-01
In this 'Project Mathematics! series, sponsored by the California Institute of Technology, Pythagoraus' theorem a(exp 2) + b(exp 2) = c(exp 2) is discussed and the history behind this theorem is explained. hrough live film footage and computer animation, applications in real life are presented and the significance of and uses for this theorem are put into practice.
Balle, C; Fortescue-Beck, E; Vauthier, N
2013-01-01
The cernox™ sensor is delivered with a 3-point resistance versus temperature cal-ibration that permits the construction of an individual interpolation table by using the data in the CERN thermometer database. For instance at the 4.2 K point, the individual calibration and the manufacturer data are within +/-0.1 K for 99.39% of a sample population of about 5700 sensors. Preliminary results also indicate that accuracies of 0.1 K and 1 K can be obtained below respectively 5 K and 77 K.
International Nuclear Information System (INIS)
Veltman, H.
1990-01-01
The equivalence theorem states that, at an energy E much larger than the vector-boson mass M, the leading order of the amplitude with longitudinally polarized vector bosons on mass shell is given by the amplitude in which these vector bosons are replaced by the corresponding Higgs ghosts. We prove the equivalence theorem and show its validity in every order in perturbation theory. We first derive the renormalized Ward identities by using the diagrammatic method. Only the Feynman-- 't Hooft gauge is discussed. The last step of the proof includes the power-counting method evaluated in the large-Higgs-boson-mass limit, needed to estimate the leading energy behavior of the amplitudes involved. We derive expressions for the amplitudes involving longitudinally polarized vector bosons for all orders in perturbation theory. The fermion mass has not been neglected and everything is evaluated in the region m f ∼M much-lt E much-lt m Higgs
Fully Quantum Fluctuation Theorems
Åberg, Johan
2018-02-01
Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
Multivariable Chinese Remainder Theorem
Indian Academy of Sciences (India)
IAS Admin
to sleep. The 3rd thief wakes up and finds the rest of the coins make 7 equal piles excepting a coin which he pockets. If the total number of coins they stole is not more than 200, what is the exact number? With a bit of hit and miss, one can find that 157 is a possible number. The Chinese remainder theorem gives a systematic ...
Directory of Open Access Journals (Sweden)
Shihuang Hong
2009-01-01
Full Text Available We present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.
Unified quantum no-go theorems and transforming of quantum pure states in a restricted set
Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun
2017-12-01
The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.
International Nuclear Information System (INIS)
Lloyd, Mark Anthony
1999-01-01
We in the nuclear power industry consider ourselves to be at the forefront of civilised progress. Yet, all too often, even we ourselves don't believe our public relations statements about nuclear power. Why is this? Let us approach the question by considering Godel's Theorem. Godel's Theorem is extremely complicated mathematically, but for our purposes can be simplified to the maxim that one cannot validate a system from within that system. Scientists, especially those in the fields of astronomy and nuclear physics, have long realised the implications of Godel's Theorem. The people to whom we must communicate look to us, who officially know everything about our industry, to comfort and reassure them. And we forget that we can only comfort them by addressing their emotional needs, not by demonstrating our chilling o bjectivity . Let us try something completely new in communication. Instead of looking for incremental rules which will help us marginally differentiate the way we communicate about minor or major incidents, let us leapfrog across 'objectivity' to meaning and relevance. If we truly believe that nuclear energy is a good thing, this leap should not be difficult. Finally, if we as communicators are not prepared to be meaningful and relevant - not prepared to leapfrog beyond weasel terms like 'minor incident' - what does that say about the kinds of people we believe the nuclear community to be? Are nuclear people a group apart, divisible from the rest of the human race by their evil? In fact the nuclear community is a living, laughing, normal part of a whole society; and is moreover a good contributor to the technological progress that society demands. When we ourselves recognise this, we will start to communicate nuclear issues in the same language as the rest of society. We will start to speak plainly and convincingly, and our conviction will leapfrog our audience into being able to believe us
Soft theorems for shift-symmetric cosmologies
Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca
2018-03-01
We derive soft theorems for single-clock cosmologies that enjoy a shift symmetry. These so-called consistency conditions arise from a combination of a large diffeomorphism and the internal shift symmetry and fix the squeezed limit of all correlators with a soft scalar mode. As an application, we show that our results reproduce the squeezed bispectrum for ultra-slow-roll inflation, a particular shift-symmetric, nonattractor model which is known to violate Maldacena's consistency relation. Similar results have been previously obtained by Mooij and Palma using background-wave methods. Our results shed new light on the infrared structure of single-clock cosmological spacetimes.
Topological interpretation of Luttinger theorem
Seki, Kazuhiro; Yunoki, Seiji
2017-01-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because i) the Luttinger volume is represented as the winding number of the single-particle Green's function and thus ii) the deviation of the theorem, expressed with a ratio between the interacting and n...
Bertrand's theorem and virial theorem in fractional classical mechanics
Yu, Rui-Yan; Wang, Towe
2017-09-01
Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
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.
A note on the weighted Khintchine-Groshev Theorem
DEFF Research Database (Denmark)
Hussain, Mumtaz; Yusupova, Tatiana
Let W(m,n;ψ−−) denote the set of ψ1,…,ψn-approximable points in Rmn. The classical Khintchine-Groshev theorem assumes a monotonicity condition on the approximating functions ψ−−. Removing monotonicity from the Khintchine-Groshev theorem is attributed to different authors for different cases of m...... and n. It can not be removed for m=n=1 as Duffin-Shcaeffer provided the counter example. We deal with the only remaining case m=2 and thereby remove all unnecessary conditions from the Khintchine-Groshev theorem....
Direct and converse theorems the elements of symbolic logic
Gradshtein, I S; Stark, M; Ulam, S
1963-01-01
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chap
Directory of Open Access Journals (Sweden)
F. O. Isiogugu
2016-01-01
Full Text Available The strong convergence of a hybrid algorithm to a common element of the fixed point sets of multivalued strictly pseudocontractive-type mappings and the set of solutions of an equilibrium problem in Hilbert spaces is obtained using a strict fixed point set condition. The obtained results improve, complement, and extend the results on multivalued and single-valued mappings in the contemporary literature.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
The Non-Signalling theorem in generalizations of Bell's theorem
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Probability densities and the radon variable transformation theorem
International Nuclear Information System (INIS)
Ramshaw, J.D.
1985-01-01
D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
Geometry of the Adiabatic Theorem
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.…
Braun, Jens; Leonhardt, Marc; Pospiech, Martin
2018-04-01
Nambu-Jona-Lasinio-type models are often employed as low-energy models for the theory of the strong interaction to analyze its phase structure at finite temperature and quark chemical potential. In particular, at low temperature and large chemical potential, where the application of fully first-principles approaches is currently difficult at best, this class of models still plays a prominent role in guiding our understanding of the dynamics of dense strong-interaction matter. In this work, we consider a Fierz-complete version of the Nambu-Jona-Lasinio model with two massless quark flavors and study its renormalization group flow and fixed-point structure at leading order of the derivative expansion of the effective action. Sum rules for the various four-quark couplings then allow us to monitor the strength of the breaking of the axial UA(1 ) symmetry close to and above the phase boundary. We find that the dynamics in the ten-dimensional Fierz-complete space of four-quark couplings can only be reduced to a one-dimensional space associated with the scalar-pseudoscalar coupling in the strict large-Nc limit. Still, the interacting fixed point associated with this one-dimensional subspace appears to govern the dynamics at small quark chemical potential even beyond the large-Nc limit. At large chemical potential, corrections beyond the large-Nc limit become important, and the dynamics is dominated by diquarks, favoring the formation of a chirally symmetric diquark condensate. In this regime, our study suggests that the phase boundary is shifted to higher temperatures when a Fierz-complete set of four-quark interactions is considered.
An extension of Pohlmeyer's theorem
International Nuclear Information System (INIS)
Rosten, Oliver J
2010-01-01
Applying the exact renormalization group to scalar field theory in Euclidean space of general (not necessarily integer) dimension, it is proven that the only fixed point with vanishing anomalous dimension is the Gaussian one. The proof requires positivity of the two-point connected correlation function together with a technical assumption concerning solutions of the flow equation. The method, in which the representation of the flow equation as a heat equation plays a central role, extends directly to non-gauge theories with arbitrary matter content (though nonlinear sigma models are beyond the scope of the current method).
A Decomposition Theorem for Finite Automata.
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)
Testing subleading multiple soft graviton theorem for CHY prescription
Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay
2018-01-01
In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.
A variational proof of Thomson's theorem
Energy Technology Data Exchange (ETDEWEB)
Fiolhais, Miguel C.N., E-mail: miguel.fiolhais@cern.ch [Department of Physics, City College of the City University of New York, 160 Convent Avenue, New York, NY 10031 (United States); Department of Physics, New York City College of Technology, 300 Jay Street, Brooklyn, NY 11201 (United States); LIP, Department of Physics, University of Coimbra, 3004-516 Coimbra (Portugal); Essén, Hanno [Department of Mechanics, Royal Institute of Technology (KTH), Stockholm SE-10044 (Sweden); Gouveia, Tomé M. [Cavendish Laboratory, 19 JJ Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-08-12
Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.
Directory of Open Access Journals (Sweden)
Zhou Yinying
2014-01-01
Full Text Available We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009, Min and Chang (2012, Plubtieng and Punpaeng (2007, S. Takahashi and W. Takahashi (2007, Tada and Takahashi (2007, Gang and Changsong (2009, Ying (2013, Y. Yao and J. C. Yao (2007, and Yong-Cho and Kang (2012.
Smorynski, Craig
2017-01-01
This book is about the rise and supposed fall of the mean value theorem. It discusses the evolution of the theorem and the concepts behind it, how the theorem relates to other fundamental results in calculus, and modern re-evaluations of its role in the standard calculus course. The mean value theorem is one of the central results of calculus. It was called “the fundamental theorem of the differential calculus” because of its power to provide simple and rigorous proofs of basic results encountered in a first-year course in calculus. In mathematical terms, the book is a thorough treatment of this theorem and some related results in the field; in historical terms, it is not a history of calculus or mathematics, but a case study in both. MVT: A Most Valuable Theorem is aimed at those who teach calculus, especially those setting out to do so for the first time. It is also accessible to anyone who has finished the first semester of the standard course in the subject and will be of interest to undergraduate mat...
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
Energy Technology Data Exchange (ETDEWEB)
Kijima, K; Murata, W; Furukawa, Y [Kyushu University, Fukuoka (Japan). Faculty of Engineering
1997-10-01
The control system for keeping the fixed-point of ships against disturbance was designed by applying an ILQ (Inverse Linear Quadratic) control (possible to specify the response of controlled systems with time constant) theory, to study the effect of different time constants as design parameter on a fixed-point keeping performance. It was assumed that the controlled ship is equipped with two bow thrusters and one stern thruster of 30ton in output to generate a control force. For fixed-point keeping control, the state equation was derived to slave the controlled system to a target input. The ILQ design method uses the result of the inverse problem of optimum regulators. For designing control systems by using the ILQ control theory, the smallest time constant should be selected according to the most severe disturbance condition considering the response performance of controllers, to achieve fixed-point keeping of ships. In fixed-point keeping, it is also essential to put the initial position as close as possible to the target point. 2 refs., 6 figs., 2 tabs.
Energy Technology Data Exchange (ETDEWEB)
Bloembergen, P.; Yamada, Y.; Sasajima, N.; Yamamoto, N. [National Metrology Institute of Japan (NMIJ), AIST, Tsukuba (Japan); Torizuka, S.; Yoshida, N. [National Institute for Materials Science (NIMS), Tsukuba (Japan)
2004-12-01
A survey will be given of metal-carbon (M-C) and metal carbide-carbon (MC-C) systems presently in development for applications in thermometry in the range from 1000 K to about 3500 K. The advantages of these systems as fixed points at high temperatures as compared to systems relying on pure metals will be elucidated. Purification of the components making up the M-C or MC-C systems is a prerequisite to their implementation as reference fixed points in thermometry, requiring a high level of reproducibility of the eutectic temperature. To set an example a study on the effect of impurities on the eutectic transition of Fe-C is included in the survey. Experimentally obtained melting curves are compared with the curves calculated on the basis of a thermodynamic model, which includes the impurities in question as components. The calculations of the melting curves are based upon: (1) the Equilibrium solidification model and (2) the Scheil-Gulliver solidification model, which handle the effects of the impurities on the transition process in such a way that they may be assumed to set lower and upper boundaries to the associated melting ranges, respectively. We will conclude pointing out fields of common interest to materials science and thermometry within the realm of ultra-pure materials. (authors)
Directory of Open Access Journals (Sweden)
Houzeng Han
2016-07-01
Full Text Available Precise Point Positioning (PPP makes use of the undifferenced pseudorange and carrier phase measurements with ionospheric-free (IF combinations to achieve centimeter-level positioning accuracy. Conventionally, the IF ambiguities are estimated as float values. To improve the PPP positioning accuracy and shorten the convergence time, the integer phase clock model with between-satellites single-difference (BSSD operation is used to recover the integer property. However, the continuity and availability of stand-alone PPP is largely restricted by the observation environment. The positioning performance will be significantly degraded when GPS operates under challenging environments, if less than five satellites are present. A commonly used approach is integrating a low cost inertial sensor to improve the positioning performance and robustness. In this study, a tightly coupled (TC algorithm is implemented by integrating PPP with inertial navigation system (INS using an Extended Kalman filter (EKF. The navigation states, inertial sensor errors and GPS error states are estimated together. The troposphere constrained approach, which utilizes external tropospheric delay as virtual observation, is applied to further improve the ambiguity-fixed height positioning accuracy, and an improved adaptive filtering strategy is implemented to improve the covariance modelling considering the realistic noise effect. A field vehicular test with a geodetic GPS receiver and a low cost inertial sensor was conducted to validate the improvement on positioning performance with the proposed approach. The results show that the positioning accuracy has been improved with inertial aiding. Centimeter-level positioning accuracy is achievable during the test, and the PPP/INS TC integration achieves a fast re-convergence after signal outages. For troposphere constrained solutions, a significant improvement for the height component has been obtained. The overall positioning accuracies
Strong versions of Bell's theorem
International Nuclear Information System (INIS)
Stapp, H.P.
1994-01-01
Technical aspects of a recently constructed strong version of Bell's theorem are discussed. The theorem assumes neither hidden variables nor factorization, and neither determinism nor counterfactual definiteness. It deals directly with logical connections. Hence its relationship with modal logic needs to be described. It is shown that the proof can be embedded in an orthodox modal logic, and hence its compatibility with modal logic assured, but that this embedding weakens the theorem by introducing as added assumptions the conventionalities of the particular modal logic that is adopted. This weakening is avoided in the recent proof by using directly the set-theoretic conditions entailed by the locality assumption
Green's theorem and Gorenstein sequences
Ahn, Jeaman; Migliore, Juan C.; Shin, Yong-Su
2016-01-01
We study consequences, for a standard graded algebra, of extremal behavior in Green's Hyperplane Restriction Theorem. First, we extend his Theorem 4 from the case of a plane curve to the case of a hypersurface in a linear space. Second, assuming a certain Lefschetz condition, we give a connection to extremal behavior in Macaulay's theorem. We apply these results to show that $(1,19,17,19,1)$ is not a Gorenstein sequence, and as a result we classify the sequences of the form $(1,a,a-2,a,1)$ th...
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Complex integration and Cauchy's theorem
Watson, GN
2012-01-01
This brief monograph by one of the great mathematicians of the early twentieth century offers a single-volume compilation of propositions employed in proofs of Cauchy's theorem. Developing an arithmetical basis that avoids geometrical intuitions, Watson also provides a brief account of the various applications of the theorem to the evaluation of definite integrals.Author G. N. Watson begins by reviewing various propositions of Poincaré's Analysis Situs, upon which proof of the theorem's most general form depends. Subsequent chapters examine the calculus of residues, calculus optimization, the
Deviations from Wick's theorem in the canonical ensemble
Schönhammer, K.
2017-07-01
Wick's theorem for the expectation values of products of field operators for a system of noninteracting fermions or bosons plays an important role in the perturbative approach to the quantum many-body problem. A finite-temperature version holds in the framework of the grand canonical ensemble, but not for the canonical ensemble appropriate for systems with fixed particle number such as ultracold quantum gases in optical lattices. Here we present formulas for expectation values of products of field operators in the canonical ensemble using a method in the spirit of Gaudin's proof of Wick's theorem for the grand canonical case. The deviations from Wick's theorem are examined quantitatively for two simple models of noninteracting fermions.
Some commutativity theorems for a certain class of rings
International Nuclear Information System (INIS)
Khan, M.A.
1994-08-01
In the present paper we first establish the commutativity theorem for semiprime ring satisfying the polynomial identity [x n ,y]x r = ±y s [x,y m ]y t for all x,y in R, where m,n,r,s and t are fixed nonnegative integers, and further, we investigate commutativity of rings with unity under some additional hypothesis. Moreover, it is also shown that the above result is true for s-unital. Also, we provide some counter examples which show that the hypothesis of our theorems are not altogether superfluous. The results of this paper generalize some of the well-known commutativity theorems for rings which are right s-unital. (author). 21 refs
A general product measurability theorem with applications to variational inequalities
Directory of Open Access Journals (Sweden)
Kenneth L. Kuttler
2016-03-01
Full Text Available This work establishes the existence of measurable weak solutions to evolution problems with randomness by proving and applying a novel theorem on product measurability of limits of sequences of functions. The measurability theorem is used to show that many important existence theorems within the abstract theory of evolution inclusions or equations have straightforward generalizations to settings that include random processes or coefficients. Moreover, the convex set where the solutions are sought is not fixed but may depend on the random variables. The importance of adding randomness lies in the fact that real world processes invariably involve randomness and variability. Thus, this work expands substantially the range of applications of models with variational inequalities and differential set-inclusions.
The Levy sections theorem revisited
International Nuclear Information System (INIS)
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Silva, Sergio Da
2007-01-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets
Ortiz, Guillermo P.; Mochán, W. Luis
2018-02-01
Keller’s theorem relates the components of the macroscopic dielectric response of a binary two-dimensional composite system with those of the reciprocal system obtained by interchanging its components. We present a derivation of the theorem that, unlike previous ones, does not employ the common assumption that the response function relates an irrotational to a solenoidal field and that is valid for dispersive and dissipative anisotropic systems. We show that the usual statement of Keller’s theorem in terms of the conductivity is strictly valid only at zero frequency and we obtain a new generalization for finite frequencies. We develop applications of the theorem to the study of the optical properties of systems such as superlattices, 2D isotropic and anisotropic metamaterials and random media, to test the accuracy of theories and computational schemes, and to increase the accuracy of approximate calculations.
The Levy sections theorem revisited
Figueiredo, Annibal; Gleria, Iram; Matsushita, Raul; Da Silva, Sergio
2007-06-01
This paper revisits the Levy sections theorem. We extend the scope of the theorem to time series and apply it to historical daily returns of selected dollar exchange rates. The elevated kurtosis usually observed in such series is then explained by their volatility patterns. And the duration of exchange rate pegs explains the extra elevated kurtosis in the exchange rates of emerging markets. In the end, our extension of the theorem provides an approach that is simpler than the more common explicit modelling of fat tails and dependence. Our main purpose is to build up a technique based on the sections that allows one to artificially remove the fat tails and dependence present in a data set. By analysing data through the lenses of the Levy sections theorem one can find common patterns in otherwise very different data sets.
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
Soft theorems from conformal field theory
International Nuclear Information System (INIS)
Lipstein, Arthur E.
2015-01-01
Strominger and collaborators recently proposed that soft theorems for gauge and gravity amplitudes can be interpreted as Ward identities of a 2d CFT at null infinity. In this paper, we will consider a specific realization of this CFT known as ambitwistor string theory, which describes 4d Yang-Mills and gravity with any amount of supersymmetry. Using 4d ambtwistor string theory, we derive soft theorems in the form of an infinite series in the soft momentum which are valid to subleading order in gauge theory and sub-subleading order in gravity. Furthermore, we describe how the algebra of soft limits can be encoded in the braiding of soft vertex operators on the worldsheet and point out a simple relation between soft gluon and soft graviton vertex operators which suggests an interesting connection to color-kinematics duality. Finally, by considering ambitwistor string theory on a genus one worldsheet, we compute the 1-loop correction to the subleading soft graviton theorem due to infrared divergences.
Generalized Dandelin’s Theorem
Kheyfets, A. L.
2017-11-01
The paper gives a geometric proof of the theorem which states that in case of the plane section of a second-order surface of rotation (quadrics of rotation, QR), such conics as an ellipse, a hyperbola or a parabola (types of conic sections) are formed. The theorem supplements the well-known Dandelin’s theorem which gives the geometric proof only for a circular cone and applies the proof to all QR, namely an ellipsoid, a hyperboloid, a paraboloid and a cylinder. That’s why the considered theorem is known as the generalized Dandelin’s theorem (GDT). The GDT proof is based on a relatively unknown generalized directrix definition (GDD) of conics. The work outlines the GDD proof for all types of conics as their necessary and sufficient condition. Based on the GDD, the author proves the GDT for all QR in case of a random position of the cutting plane. The graphical stereometric structures necessary for the proof are given. The implementation of the structures by 3d computer methods is considered. The article shows the examples of the builds made in the AutoCAD package. The theorem is intended for the training course of theoretical training of elite student groups of architectural and construction specialties.
The Second Noether Theorem on Time Scales
Directory of Open Access Journals (Sweden)
Agnieszka B. Malinowska
2013-01-01
Full Text Available We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for the h-calculus and the second Noether theorem for the q-calculus.
Factor and Remainder Theorems: An Appreciation
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…
Lowe, David; Machin, Graham
2012-06-01
The future mise en pratique for the realization of the kelvin will be founded on the melting temperatures of particular metal-carbon eutectic alloys as thermodynamic temperature references. However, at the moment there is no consensus on what should be taken as the melting temperature. An ideal melting or freezing curve should be a completely flat plateau at a specific temperature. Any departure from the ideal is due to shortcomings in the realization and should be accommodated within the uncertainty budget. However, for the proposed alloy-based fixed points, melting takes place over typically some hundreds of millikelvins. Including the entire melting range within the uncertainties would lead to an unnecessarily pessimistic view of the utility of these as reference standards. Therefore, detailed analysis of the shape of the melting curve is needed to give a value associated with some identifiable aspect of the phase transition. A range of approaches are or could be used; some purely practical, determining the point of inflection (POI) of the melting curve, some attempting to extrapolate to the liquidus temperature just at the end of melting, and a method that claims to give the liquidus temperature and an impurity correction based on the analytical Scheil model of solidification that has not previously been applied to eutectic melting. The different methods have been applied to cobalt-carbon melting curves that were obtained under conditions for which the Scheil model might be valid. In the light of the findings of this study it is recommended that the POI continue to be used as a pragmatic measure of temperature but where required a specified limits approach should be used to define and determine the melting temperature.
Subsubleading soft theorems of gravitons and dilatons in the bosonic string
International Nuclear Information System (INIS)
Vecchia, Paolo Di; Marotta, Raffaele; Mojaza, Matin
2016-01-01
Starting from the amplitude with an arbitrary number of massless closed states of the bosonic string, we compute the soft limit when one of the states becomes soft to subsubleading order in the soft momentum expansion, and we show that when the soft state is a graviton or a dilaton, the full string amplitude can be expressed as a soft theorem through subsubleading order. It turns out that there are string corrections to the field theoretical limit in the case of a soft graviton, while for a soft dilaton the string corrections vanish. We then show that the new soft theorems, including the string corrections, can be simply obtained from the exchange diagrams where the soft state is attached to the other external states through the three-point string vertex of three massless states. In the soft-limit, the propagator of the exchanged state is divergent, and at tree-level these are the only divergent contributions to the full amplitude. However, they do not form a gauge invariant subset and must be supplemented with extra non-singular terms. The requirement of gauge invariance then fixes the complete amplitude through subsubleading order in the soft expansion, reproducing exactly what one gets from the explicit calculation in string theory. From this it is seen that the string corrections at subsubleading order arise as a consequence of the three-point amplitude having string corrections in the bosonic string. When specialized to a soft dilaton, it remarkably turns out that the string corrections vanish and that the non-singular piece of the subsubleading term of the dilaton soft theorem is the generator of space-time special conformal transformation.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
On the inverse of the Pomeranchuk theorem
International Nuclear Information System (INIS)
Nagy, E.
1977-04-01
The Pomeranchuk theorem is valid only for bounded total cross sections at infinite energies, and for arbitrarily rising cross sections one cannot prove the zero asymptotic limit of the difference of the particle and antiparticle total cross sections. In the paper the problem is considered from the inverse point of view. It is proved using dispersion relations that if the total cross sections rise with some power of logarithm and the difference of the particle and antiparticle total cross sections remain finite, then the real to imaginary ratios of both the particle and antiparticle forward scattering amplitudes are bounded. (Sz.N.Z.)
Paraconsistent Probabilities: Consistency, Contradictions and Bayes’ Theorem
Directory of Open Access Journals (Sweden)
Juliana Bueno-Soler
2016-09-01
Full Text Available This paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs. We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes’ theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.
Indian Academy of Sciences (India)
such that '[q,p) lies inside of G and '(p,rj lies outside of G. Now suppose, is a polygonal arc and G is a circle, such that. , crosses G at least once and the end points, a and b, of, lie. 'outside' C. If we start 'moving' from a towards b along " let a be the first crossing and b the last. At every point p in. C - {a, b} we attach a direction ...
Preservation theorems on finite structures
International Nuclear Information System (INIS)
Hebert, M.
1994-09-01
This paper concerns classical Preservation results applied to finite structures. We consider binary relations for which a strong form of preservation theorem (called strong interpolation) exists in the usual case. This includes most classical cases: embeddings, extensions, homomorphisms into and onto, sandwiches, etc. We establish necessary and sufficient syntactic conditions for the preservation theorems for sentences and for theories to hold in the restricted context of finite structures. We deduce that for all relations above, the restricted theorem for theories hold provided the language is finite. For the sentences the restricted version fails in most cases; in fact the ''homomorphism into'' case seems to be the only possible one, but the efforts to show that have failed. We hope our results may help to solve this frustrating problem; in the meantime, they are used to put a lower bound on the level of complexity of potential counterexamples. (author). 8 refs
Houston, Louis M.
2012-01-01
Sign data are the signs of signal added to noise. It is well known that a constant signal can be recovered from sign data. In this paper, we show that an integral over variant signal can be recovered from an integral over sign data based on the variant signal. We refer to this as a generalized sign data average. We use this result to derive a Green's theorem for sign data. Green's theorem is important to various seismic processing methods, including seismic migration. Results in this paper ge...
Scale symmetry and virial theorem
International Nuclear Information System (INIS)
Westenholz, C. von
1978-01-01
Scale symmetry (or dilatation invariance) is discussed in terms of Noether's Theorem expressed in terms of a symmetry group action on phase space endowed with a symplectic structure. The conventional conceptual approach expressing invariance of some Hamiltonian under scale transformations is re-expressed in alternate form by infinitesimal automorphisms of the given symplectic structure. That is, the vector field representing scale transformations leaves the symplectic structure invariant. In this model, the conserved quantity or constant of motion related to scale symmetry is the virial. It is shown that the conventional virial theorem can be derived within this framework
Nonperturbative Adler-Bardeen theorem
International Nuclear Information System (INIS)
Mastropietro, Vieri
2007-01-01
The Adler-Bardeen theorem has been proven only as a statement valid at all orders in perturbation theory, without any control on the convergence of the series. In this paper we prove a nonperturbative version of the Adler-Bardeen theorem in d=2 by using recently developed technical tools in the theory of Grassmann integration. The proof is based on the assumption that the boson propagator decays fast enough for large momenta. If the boson propagator does not decay, as for Thirring contact interactions, the anomaly in the WI (Ward Identities) is renormalized by higher order contributions
Natural relations and Appelquist-Carazzone decoupling theorem
International Nuclear Information System (INIS)
Grzadkowski, B.; Krawczyk, P.; Pokorski, S.
1984-01-01
It is pointed out that in some cases violation of the Appelquist-Carazzone decoupling theorem in spontaneously broken gauge theories is related to the presence in such theories of the so-called natural zeroth-order relations. In this context heavy-fermion effects in the Glashow-Salam-Weinberg model are discussed
Hamiltonian Noether theorem for gauge systems and two time physics
International Nuclear Information System (INIS)
Villanueva, V M; Nieto, J A; Ruiz, L; Silvas, J
2005-01-01
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
On the Robinson theorem and shearfree geodesic null congruences
International Nuclear Information System (INIS)
Tafel, J.
1985-01-01
Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)
Kolmogorov-Arnold-Moser Theorem
Indian Academy of Sciences (India)
system (not necessarily the 2-body system). Kolmogorov was the first to provide a solution to the above general problem in a theorem formulated in 1954 (see Suggested. Reading). However, he provided only an outline of the proof. The actual proof (with all the details) turned to be quite difficult and was provided by Arnold ...
Dynamic Newton-Puiseux Theorem
DEFF Research Database (Denmark)
Mannaa, Bassel; Coquand, Thierry
2013-01-01
A constructive version of Newton-Puiseux theorem for computing the Puiseux expansions of algebraic curves is presented. The proof is based on a classical proof by Abhyankar. Algebraic numbers are evaluated dynamically; hence the base field need not be algebraically closed and a factorization...
Opechowski's theorem and commutator groups
International Nuclear Information System (INIS)
Caride, A.O.; Zanette, S.I.
1985-01-01
It is shown that the conditions of application of Opechowski's theorem for double groups of subgroups of O(3) are directly associated to the structure of their commutator groups. Some characteristics of the structure of classes are also discussed. (Author) [pt
Shell theorem for spontaneous emission
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Mortensen, Jakob Egeberg; Lodahl, Peter
2013-01-01
and therefore is given exactly by the dipole approximation theory. This surprising result is a spontaneous emission counterpart to the shell theorems of classical mechanics and electrostatics and provides insights into the physics of mesoscopic emitters as well as great simplifications in practical calculations....
KLN theorem and infinite statistics
International Nuclear Information System (INIS)
Grandou, T.
1992-01-01
The possible extension of the Kinoshita-Lee-Nauenberg (KLN) theorem to the case of infinite statistics is examined. It is shown that it appears as a stable structure in a quantum field theory context. The extension is provided by working out the Fock space realization of a 'quantum algebra'. (author) 2 refs
The Geometric Mean Value Theorem
de Camargo, André Pierro
2018-01-01
In a previous article published in the "American Mathematical Monthly," Tucker ("Amer Math Monthly." 1997; 104(3): 231-240) made severe criticism on the Mean Value Theorem and, unfortunately, the majority of calculus textbooks also do not help to improve its reputation. The standard argument for proving it seems to be applying…
Fermion fractionization and index theorem
International Nuclear Information System (INIS)
Hirayama, Minoru; Torii, Tatsuo
1982-01-01
The relation between the fermion fractionization and the Callias-Bott-Seeley index theorem for the Dirac operator in the open space of odd dimension is clarified. Only the case of one spatial dimension is discussed in detail. Sum rules for the expectation values of various quantities in fermion-fractionized configurations are derived. (author)
The Completeness Theorem of Godel
Indian Academy of Sciences (India)
GENERAL I ARTICLE. The Completeness Theorem of Godel. 2. Henkin's Proof for First Order Logic. S M Srivastava is with the. Indian Statistical,. Institute, Calcutta. He received his PhD from the Indian Statistical. Institute in 1980. His research interests are in descriptive set theory. I Part 1. An Introduction to Math- ematical ...
Angle Defect and Descartes' Theorem
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.)
Optical theorem and its history
International Nuclear Information System (INIS)
Newton, R.G.
1978-01-01
A translation is presented of a paper submitted to the symposium ''Concepts and methods in microscopic physics'' held at Washington University in 1974. A detailed description is given of the history of the optical theorem, its various formulations and derivations and its use in the scattering theory. (Z.J.)
On the Fourier integral theorem
Koekoek, J.
1987-01-01
Introduction. In traditional proofs of convergence of Fourier series and of the Fourier integraI theorem basic tools are the theory of Dirichlet integraIs and the Riemann-Lebesgue lemma. Recently CHERNOFF [I) and REoIlEFFER (2) gave new proofs of convergenceof Fourier series which make no use of the
A landing theorem for entire functions with bounded post-singular sets
Benini, Anna Miriam; Rempe-Gillen, Lasse
2017-01-01
The Douady-Hubbard landing theorem for periodic external rays is one of the cornerstones of the study of polynomial dynamics. It states that, for a complex polynomial with bounded postcritical set, every periodic external ray lands at a repelling or parabolic periodic point, and conversely every repelling or parabolic point is the landing point of at least one periodic external ray. We prove an analogue of this theorem for an entire function with bounded postsingular set: every periodic dread...
The Classical Version of Stokes' Theorem Revisited
DEFF Research Database (Denmark)
Markvorsen, Steen
2005-01-01
Using only fairly simple and elementary considerations - essentially from first year undergraduate mathematics - we prove that the classical Stokes' theorem for any given surface and vector field in $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... of the vector field in a tubular shell around the given surface. The intuitive appeal of the divergence theorem is thus applied to bootstrap a corresponding intuition for Stokes' theorem. The two stated classical theorems are (like the fundamental theorem of calculus) nothing but shadows of the general version...... to above. Our proof that Stokes' theorem follows from Gauss' divergence theorem goes via a well known and often used exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together...
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
Directory of Open Access Journals (Sweden)
Mesloub Said
2008-01-01
Full Text Available This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.
An extended characterisation theorem for quantum logics
International Nuclear Information System (INIS)
Sharma, C.S.; Mukherjee, M.K.
1977-01-01
Two theorems are proved. In the first properties of an important mapping from an orthocomplemented lattice to itself are studied. In the second the characterisation theorem of Zierler (Pacific J. Math.; 11:1151 (1961)) is extended to obtain a very useful theorem characterising orthomodular lattices. Since quantum logics are merely sigma-complete orthomodular lattices, the principal result is, for application in quantum physics, a characterisation theorem for quantum logics. (author)
Hadronic interactions of the J/ψ and Adler's theorem
International Nuclear Information System (INIS)
Bourque, A.; Gale, C.; Haglin, K.L.
2004-01-01
Effective Lagrangian models of charmonium have recently been used to estimate dissociation cross sections with light hadrons. Detailed study of the symmetry properties reveals possible shortcomings relative to chiral symmetry. We therefore propose a new Lagrangian and point out distinguishing features amongst the different approaches. Moreover, we test the models against Adler's theorem, which requires, in the appropriate limit, the decoupling of pions from the theory for the normal parity sector. Using the newly proposed Lagrangian, which exhibits SU L (N f )xSU R (N f ) symmetry and complies with Adler's theorem, we find dissociation cross sections with pions that are reduced in an energy-dependent way, with respect to cases where the theorem is not fulfilled
A note on generalized Weyl's theorem
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.
A definability theorem for first order logic
Butz, C.; Moerdijk, I.
1997-01-01
In this paper we will present a definability theorem for first order logic This theorem is very easy to state and its proof only uses elementary tools To explain the theorem let us first observe that if M is a model of a theory T in a language L then clearly any definable subset S M ie a subset S
Tight closure and vanishing theorems
International Nuclear Information System (INIS)
Smith, K.E.
2001-01-01
Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric
The de Finetti theorem for test spaces
International Nuclear Information System (INIS)
Barrett, Jonathan; Leifer, Matthew
2009-01-01
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.
A Randomized Central Limit Theorem
International Nuclear Information System (INIS)
Eliazar, Iddo; Klafter, Joseph
2010-01-01
The Central Limit Theorem (CLT), one of the most elemental pillars of Probability Theory and Statistical Physics, asserts that: the universal probability law of large aggregates of independent and identically distributed random summands with zero mean and finite variance, scaled by the square root of the aggregate-size (√(n)), is Gaussian. The scaling scheme of the CLT is deterministic and uniform - scaling all aggregate-summands by the common and deterministic factor √(n). This Letter considers scaling schemes which are stochastic and non-uniform, and presents a 'Randomized Central Limit Theorem' (RCLT): we establish a class of random scaling schemes which yields universal probability laws of large aggregates of independent and identically distributed random summands. The RCLT universal probability laws, in turn, are the one-sided and the symmetric Levy laws.
Bell's theorem, accountability and nonlocality
International Nuclear Information System (INIS)
Vona, Nicola; Liang, Yeong-Cherng
2014-01-01
Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)
Fluctuation theorems and atypical trajectories
International Nuclear Information System (INIS)
Sahoo, M; Lahiri, S; Jayannavar, A M
2011-01-01
In this work, we have studied simple models that can be solved analytically to illustrate various fluctuation theorems. These fluctuation theorems provide symmetries individually to the distributions of physical quantities such as the classical work (W c ), thermodynamic work (W), total entropy (Δs tot ) and dissipated heat (Q), when the system is driven arbitrarily out of equilibrium. All these quantities can be defined for individual trajectories. We have studied the number of trajectories which exhibit behaviour unexpected at the macroscopic level. As the time of observation increases, the fraction of such atypical trajectories decreases, as expected at the macroscale. The distributions for the thermodynamic work and entropy production in nonlinear models may exhibit a peak (most probable value) in the atypical regime without violating the expected average behaviour. However, dissipated heat and classical work exhibit a peak in the regime of typical behaviour only.
Comment on non-renormalization theorem in the four dimensional superstrings
International Nuclear Information System (INIS)
Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.
1987-10-01
We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)
International Nuclear Information System (INIS)
Park, Mu-In
2008-01-01
Hawking's area theorem can be understood from a quasi-stationary process in which a black hole accretes positive energy matter, independent of the details of the gravity action. I use this process to study the dynamics of the inner as well as the outer horizons for various black holes which include the recently discovered exotic black holes and three-dimensional black holes in higher derivative gravities as well as the usual BTZ black hole and the Kerr black hole in four dimensions. I find that the area for the inner horizon 'can decrease', rather than increase, with the quasi-stationary process. However, I find that the area for the outer horizon 'never decreases' such that the usual area theorem still works in our examples, though this is quite non-trivial in general. There exists an instability problem of the inner horizons but it seems that the instability is not important in my analysis. I also find a generalized area theorem by combining those of the outer and inner horizons
Contraction theorems in fuzzy metric space
International Nuclear Information System (INIS)
Farnoosh, R.; Aghajani, A.; Azhdari, P.
2009-01-01
In this paper, the results on fuzzy contractive mapping proposed by Dorel Mihet will be proved for B-contraction and C-contraction in the case of George and Veeramani fuzzy metric space. The existence of fixed point with weaker conditions will be proved; that is, instead of the convergence of subsequence, p-convergence of subsequence is used.
2008-01-01
Ansambel Fix peab 13. detsembril Tallinnas Saku Suurhallis oma 40. sünnipäeva. Kontserdi erikülaline on ansambel Apelsin, kaastegevad Jassi Zahharov ja HaleBopp Singers. Õhtut juhib Tarmo Leinatamm
Bell's "Theorem": loopholes vs. conceptual flaws
Kracklauer, A. F.
2017-12-01
An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.
Theorem Proving in Intel Hardware Design
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
Expanding the Interaction Equivalency Theorem
Directory of Open Access Journals (Sweden)
Brenda Cecilia Padilla Rodriguez
2015-06-01
Full Text Available 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 study sought to apply this theorem to the corporate sector, and to expand it to include other indicators of course effectiveness: satisfaction, knowledge transfer, business results and return on expectations. A large Mexican organisation participated in this research, with 146 learners, 30 teachers and 3 academic assistants. Three versions of an online course were designed, each emphasising a different type of interaction. Data were collected through surveys, exams, observations, activity logs, think aloud protocols and sales records. All course versions yielded high levels of effectiveness, in terms of satisfaction, learning and return on expectations. Yet, course design did not dictate the types of interactions in which students engaged within the courses. Findings suggest that the interaction equivalency theorem can be reformulated as follows: In corporate settings, an online course can be effective in terms of satisfaction, learning, knowledge transfer, business results and return on expectations, as long as (a at least one of three types of interaction (learner-content, learner-teacher or learner-learner features prominently in the design of the course, and (b course delivery is consistent with the chosen type of interaction. Focusing on only one type of interaction carries a high risk of confusion, disengagement or missed learning opportunities, which can be managed by incorporating other forms of interactions.
Confinement, diquarks and goldstone's theorem
International Nuclear Information System (INIS)
Roberts, C.D.
1996-01-01
Determinations of the gluon propagator in the continuum and in lattice simulations are compared. A systematic truncation procedure for the quark Dyson-Schwinger and bound state Bethe-Salpeter equations is described. The procedure ensures the flavor-octet axial- vector Ward identity is satisfied order-by-order, thereby guaranteeing the preservation of Goldstone's theorem; and identifies a mechanism that simultaneously ensures the absence of diquarks in QCD and their presence in QCD N c =2 , where the color singlet diquark is the ''baryon'' of the theory
Comparison theorems in Riemannian geometry
Cheeger, Jeff
2008-01-01
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re
Bernstein Lethargy Theorem and Reflexivity
Aksoy, Asuman Güven; Peng, Qidi
2018-01-01
In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued sequence $\\{d_n\\}_{n\\ge1}$ decrease to $0$. Suppose that $\\{Y_n\\}_{n\\ge1}$ is a system of strictly nested subspaces of $X$ such that $\\overline Y_n \\subset Y_{n+1}$ for all $n\\ge1$ and for each $n\\ge1$, there exists $y_n\\in Y_{n+1}\\backslash Y_n$ such that ...
Cyclic graphs and Apery's theorem
International Nuclear Information System (INIS)
Sorokin, V N
2002-01-01
This is a survey of results about the behaviour of Hermite-Pade approximants for graphs of Markov functions, and a survey of interpolation problems leading to Apery's result about the irrationality of the value ζ(3) of the Riemann zeta function. The first example is given of a cyclic graph for which the Hermite-Pade problem leads to Apery's theorem. Explicit formulae for solutions are obtained, namely, Rodrigues' formulae and integral representations. The asymptotic behaviour of the approximants is studied, and recurrence formulae are found
Abstract decomposition theorem and applications
Grossberg, R; Grossberg, Rami; Lessmann, Olivier
2005-01-01
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies a main gap result for the class K. The setting is general enough to cover \\aleph_0-stable first-order theories (proved by Shelah in 1982), Excellent Classes of atomic models of a first order tehory (proved Grossberg and Hart 1987) and the class of submodels of a large sequentially homogenuus \\aleph_0-stable model (which is new).
Symbolic logic and mechanical theorem proving
Chang, Chin-Liang
1969-01-01
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Equivalent conserved currents and generalized Noether's theorem
International Nuclear Information System (INIS)
Gordon, T.J.
1984-01-01
A generalized Noether theorem is presented, relating symmetries and equivalence classes of local) conservation laws in classical field theories; this is contrasted with the standard theorem. The concept of a ''Noether'' field theory is introduced, being a theory for which the generalized theorem applies; not only does this include the cases of Lagrangian and Hamiltonian field theories, these structures are ''derived'' from the Noether property in a natural way. The generalized theorem applies to currents and symmetries that contain derivatives of the fields up to an arbitrarily high order
Virial Theorem for Nonrelativistic Quantum Fields in D Spatial Dimensions
International Nuclear Information System (INIS)
Lin, Chris L.; Ordóñez, Carlos R.
2015-01-01
The virial theorem for nonrelativistic complex fields in D spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in low-dimensional systems. The potential appearance of a Jacobian J due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the J=1 case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, J=1, is not natural, and the generalization to the case J≠1 is briefly presented
Quantum no-singularity theorem from geometric flows
Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag
2018-04-01
In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
The BRST quantization and the no-ghost theorem for AdS3
International Nuclear Information System (INIS)
Asano, Masako; Natsuume, Makoto
2003-01-01
In our previous papers, we prove the no-ghost theorem without light-cone directions. We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS 3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS 3 . The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form. (author)
The Birth of Model Theory Lowenheim's Theorem in the Frame of the Theory of Relatives
Badesa, Calixto
2008-01-01
Löwenheim's theorem reflects a critical point in the history of mathematical logic, for it marks the birth of model theory--that is, the part of logic that concerns the relationship between formal theories and their models. However, while the original proofs of other, comparably significant theorems are well understood, this is not the case with Löwenheim's theorem. For example, the very result that scholars attribute to Löwenheim today is not the one that Skolem--a logician raised in the algebraic tradition, like Löwenheim--appears to have attributed to him. In The Birth of Model Theory, Cali
Applications of the theorem of Pythagoras in R3
Srinivasan, V. K.
2010-01-01
Three distinct points ? and ? with ? are taken, respectively on the x, y and the z-axes of a rectangular coordinate system in ? Using the converse of the theorem of Pythagoras, it is shown that the triangle ? can never be a right-angled triangle. The result seems to be intuitive, but nevertheless requires a proof. As an application, some intuitive results about a tetrahedron are confirmed.
Approximation Theorems for q- Analouge of a Linear Positive Operator by A. Lupas
Directory of Open Access Journals (Sweden)
Karunesh Kumar Singh
2016-08-01
Full Text Available The purpose of the present paper is to introduce $q-$ analouge of a sequence of linear and positive operators which was introduced by A. Lupas [2]. First, we estimate moments of the operators and then prove a basic convergence theorem. Next, a local direct approximation theorem is established. Further, we study the rate of convergence and point-wise estimate using the Lipschitz type maximal function.
Howell, Russell W.; Schrohe, Elmar
2017-01-01
Rouché's Theorem is a standard topic in undergraduate complex analysis. It is usually covered near the end of the course with applications relating to pure mathematics only (e.g., using it to produce an alternate proof of the Fundamental Theorem of Algebra). The "winding number" provides a geometric interpretation relating to the…
Other trigonometric proofs of Pythagoras theorem
Luzia, Nuno
2015-01-01
Only very recently a trigonometric proof of the Pythagoras theorem was given by Zimba \\cite{1}, many authors thought this was not possible. In this note we give other trigonometric proofs of Pythagoras theorem by establishing, geometrically, the half-angle formula $\\cos\\theta=1-2\\sin^2 \\frac{\\theta}{2}$.
Borghi, Riccardo
2014-03-01
In the present letter, Newton’s theorem for the gravitational field outside a uniform spherical shell is considered. In particular, a purely geometric proof of proposition LXXI/theorem XXXI of Newton’s Principia, which is suitable for undergraduates and even skilled high-school students, is proposed. Minimal knowledge of elementary calculus and three-dimensional Euclidean geometry are required.
Theorems of low energy in Compton scattering
International Nuclear Information System (INIS)
Chahine, J.
1984-01-01
We have obtained the low energy theorems in Compton scattering to third and fouth order in the frequency of the incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes. (Author) [pt
A density Corradi-Hajnal theorem
Czech Academy of Sciences Publication Activity Database
Allen, P.; Böttcher, J.; Hladký, Jan; Piguet, D.
2015-01-01
Roč. 67, č. 4 (2015), s. 721-758 ISSN 0008-414X Institutional support: RVO:67985840 Keywords : extremal graph theory * Mantel's theorem * Corradi-Hajnal theorem Subject RIV: BA - General Mathematics Impact factor: 0.618, year: 2015 http://cms.math.ca/10.4153/CJM-2014-030-6
Visualizing the Central Limit Theorem through Simulation
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 Classical Version of Stokes' Theorem Revisited
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…
The Pomeranchuk theorem and its modifications
International Nuclear Information System (INIS)
Fischer, J.; Saly, R.
1980-01-01
A review of the various modifications and improvements of the Pomeranchuk theorem and also of related statements is given. The present status of the Pomeranchuk relation based on dispersion relation is discussed. Numerous problems related to the Pomeranchuk theorem and some answers to these problems are collected in a clear table
Coalgebraic Lindström Theorems
Kurz, A.; Venema, Y.
2010-01-01
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance,
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Riemannian and Lorentzian flow-cut theorems
Headrick, Matthew; Hubeny, Veronika E.
2018-05-01
We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.
OTTER, Resolution Style Theorem Prover
International Nuclear Information System (INIS)
McCune, W.W.
2001-01-01
1 - Description of program or function: OTTER (Other Techniques for Theorem-proving and Effective Research) is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyper-resolution, UR-resolution, and binary para-modulation. These inference rules take as small set of clauses and infer a clause. If the inferred clause is new and useful, it is stored and may become available for subsequent inferences. Other capabilities are conversion from first-order formulas to clauses, forward and back subsumption, factoring, weighting, answer literals, term ordering, forward and back demodulation, and evaluable functions and predicates. 2 - Method of solution: For its inference process OTTER uses the given-clause algorithm, which can be viewed as a simple implementation of the set of support strategy. OTTER maintains three lists of clauses: axioms, sos (set of support), and demodulators. OTTER is not automatic. Even after the user has encoded a problem into first-order logic or into clauses, the user must choose inference rules, set options to control the processing of inferred clauses, and decide which input formulae or clauses are to be in the initial set of support and which, if any, equalities are to be demodulators. If OTTER fails to find a proof, the user may try again different initial conditions. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 characters in an input string, 64 distinct variables in a clause, 51 characters in any symbol. The maxima can be changed by finding the appropriate definition in the header.h file, increasing the limit, and recompiling OTTER. There are a few constraints on the order of commands
A non-renormalization theorem for conformal anomalies
International Nuclear Information System (INIS)
Petkou, Anastasios; Skenderis, Kostas
1999-01-01
We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the AdS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a 'generalized Adler-Bardeen theorem' holds. We further show that recent arguments connecting the non-renormalizability of the above-mentioned correlation functions to a bonus U(1) Y symmetry are incomplete due to possible U(1) Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above-mentioned correlation functions, however, will follow only if these contact terms saturate by free fields
Graph-like continua, augmenting arcs, and Menger's theorem
DEFF Research Database (Denmark)
Thomassen, Carsten; Vella, Antoine
2008-01-01
We show that an adaptation of the augmenting path method for graphs proves Menger's Theorem for wide classes of topological spaces. For example, it holds for locally compact, locally connected, metric spaces, as already known. The method lends itself particularly well to another class of spaces......, connected graph. While closed subsets of such a space behave nicely in that they are compact and locally connected (and therefore locally arcwise connected), the general subspaces do not: They may be connected without being arcwise connected. Nevertheless, they satisfy Menger's Theorem......., namely the locally arcwise connected, hereditarily locally connected, metric spaces. Finally, it applies to every space where every point can be separated from every closed set not containing it by a finite set, in particular to every subspace of the Freudenthal compactification of a locally finite...
Induction, bounding, weak combinatorial principles, and the homogeneous model theorem
Hirschfeldt, Denis R; Shore, Richard A
2017-01-01
Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model.
Strong-Weak CP Hierarchy from Non-Renormalization Theorems
Energy Technology Data Exchange (ETDEWEB)
Hiller, Gudrun
2002-01-28
We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
Directory of Open Access Journals (Sweden)
FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
One-loop soft theorems via dual superconformal symmetry
Energy Technology Data Exchange (ETDEWEB)
Brandhuber, Andreas; Hughes, Edward; Spence, Bill; Travaglini, Gabriele [Centre for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)
2016-03-14
We study soft theorems at one loop in planar N = 4 super Yang-Mills theory through finite order in the infrared regulator and to subleading order in the soft parameter δ. In particular, we derive a universal constraint from dual superconformal symmetry, which we use to bootstrap subleading log δ behaviour. Moreover, we determine the complete infrared-finite subleading soft contribution of n-point MHV amplitudes using momentum twistors. Finally, we compute the subleading log δ behaviour of one-loop NMHV ratio functions at six and seven points, finding that universality holds within but not between helicity sectors.
The classical version of Stokes' Theorem revisited
DEFF Research Database (Denmark)
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 $\\mathbb{R}^{3}$ follows from an application of Gauss' divergence theorem to a suitable modification...... exercise, which simply relates the concepts of divergence and curl on the local differential level. The rest of the paper uses only integration in $1$, $2$, and $3$ variables together with a 'fattening' technique for surfaces and the inverse function theorem....