The cofinal property of the Reflexive Indecomposable Banach spaces
Argyros, Spiros A.; Raikoftsalis, Theocharis
2010-01-01
It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\\ell_p$ saturated space with $1
Reflexive Operator Algebras on Banach Spaces
Merlevède, Florence; Peligrad, Costel; Peligrad, Magda
2012-01-01
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of finite uniform multiplicity and with the direct sum property, then it is reflexive, i.e. it contains every operator that leaves invariant every closed subspace in the invariant subspace lattice of the algebra. In particular, such algebras coincide with their...
Strict Feasibility of Variational Inequalities in Reflexive Banach Spaces
Institute of Scientific and Technical Information of China (English)
Yi Ran HE; Xiu Zhen MAO; Mi ZHOU
2007-01-01
Strict feasibility is proved to be an equivalent characterization of (dual) variational in-equalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinite-dimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
Every Weakly Compact Set Can Be Uniformly Embedded into a Reflexive Banach Space
Institute of Scientific and Technical Information of China (English)
Li Xin CHENG; Qing Jin CHENG; Zheng Hua LUO; Wen ZHANG
2009-01-01
Based on an application of the Davis-Figiel-Johnson-Pelzy(s)ki procedure,this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space.As its application,we present the recent renorming theorems for reflexive spaces of Odellan arbitrary Banach space.
First and Second Order Convex Sweeping Processes in Reflexive Smooth Banach Spaces
International Nuclear Information System (INIS)
In this paper we establish new characterizations of the normal cone of closed convex sets in reflexive smooth Banach spaces and then we use those results to prove the existence of solutions for first order convex sweeping processes and their variants in reflexive smooth Banach spaces. The case of second order convex sweeping processes is also studied. (author)
On extension results for n-cyclically monotone operators in reflexive Banach spaces
Bot, Radu Ioan
2009-01-01
In this paper we provide some extension results for n-cyclically monotone operators in reflexive Banach spaces by making use of the Fenchel duality. In this way we give a positive answer to a question posed by Bauschke and Wang in [4].
Separably injective Banach spaces
Avilés, Antonio; Castillo, Jesús M F; González, Manuel; Moreno, Yolanda
2016-01-01
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines o...
$\\alpha$-minimal Banach spaces
Rosendal, Christian
2011-01-01
A Banach space with a Schauder basis is said to be $\\alpha$-minimal for some countable ordinal $\\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\\alpha$. We prove a dichotomy that characterises when a Banach space has an $\\alpha$-minimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characteristic subspaces.
Albiac, Fernando
2016-01-01
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f...
Banach spaces of universal disposition
Aviles, Antonio; Castillo, Jesus M F; Gonzalez, Manuel; Moreno, Yolanda
2011-01-01
In this paper we present a method to obtain Banach spaces of universal and almost-universal disposition with respect to a given class $\\mathfrak M$ of normed spaces. The method produces, among other, the Gurari\\u{\\i} space $\\mathcal G$ (the only separable Banach space of almost-universal disposition with respect to the class $\\mathfrak F$ of finite dimensional spaces), or the Kubis space $\\mathcal K$ (under {\\sf CH}, the only Banach space with the density character the continuum which is of universal disposition with respect to the class $\\mathfrak S$ of separable spaces). We moreover show that $\\mathcal K$ is not isomorphic to a subspace of any $C(K)$-space -- which provides a partial answer to the injective space problem-- and that --under {\\sf CH}-- it is isomorphic to an ultrapower of the Gurari\\u{\\i} space. We study further properties of spaces of universal disposition: separable injectivity, partially automorphic character and uniqueness properties.
Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
Bonet Solves, José Antonio; Wright, J. D. Maitland
2012-01-01
In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated.
A pythagorean approach in Banach spaces
Gao Ji
2006-01-01
Let be a Banach space and let be the unit sphere of . Parameters , , , and , where and are introduced and studied. The values of these parameters in the spaces and function spaces are estimated. Among the other results, we proved that a Banach space with , or is uniform nonsquare; and a Banach space with , or has uniform normal structure.
Extremely strict ideals in Banach spaces
Indian Academy of Sciences (India)
T S S R K RAO
2016-08-01
Motivated by the notion of an ideal introduced by Godefroy {\\it et al.} ({\\it Studia Math.} {\\bf 104} (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex $K$, we show that the space of affine continuous functions on $K$ is an extremely strict ideal in the space of continuous functions on $K$. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.
Fusion Frames and -Frames in Banach Spaces
Indian Academy of Sciences (India)
Amir Khosravi; Behrooz Khosravi
2011-05-01
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Smooth analysis in Banach spaces
Hájek, Petr
2014-01-01
This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into in
Tokarev, Eugene
2002-01-01
In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any separable sub B-convex Banach space X may be almost isometrically embedded in a separable Banach space G(X) of the same cotype as X, which has a series of properties. Namely, G(X) is an approximate envelope, i.e. any separable Banach space which is finitely repres...
Characterizing R-duality in Banach spaces
DEFF Research Database (Denmark)
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.......R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces....
Existence of zeros for operators taking their values in the dual of a Banach space
Directory of Open Access Journals (Sweden)
Ricceri Biagio
2004-01-01
Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
Best Simultaneous Approximation to Totally Bounded Sequences in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Xian Fa LUO; Chong LI; Genaro LOPEZ
2008-01-01
This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B
The Connection Between the Metric and Generalized Projection Operators in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Yakov ALBER; Jin Lu LI
2007-01-01
In this paper we study the connection between the metric projection operator PK:B→K,where B is a reflexive Banach space with dual space B* and K is a non-empty closed convex subset of B, and the generalized projection oprators Πk:B→k and πk:B*→k.We also present some results in non-reflexive Banach spaces.
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
Lifting bounded approximation properties from Banach spaces to their dual spaces
Oja, Eve
2006-11-01
Based on a new reformulation of the bounded approximation property, we develop a unified approach to the lifting of bounded approximation properties from a Banach space X to its dual X*. This encompasses cases when X has the unique extension property or X is extendably locally reflexive. In particular, it is shown that the unique extension property of X permits to lift the metric -approximation property from X to X*, for any operator ideal , and that there exists a Banach space X such that X,X**,... are extendably locally reflexive, but X*,X***,... are not.
Bloch spaces on bounded symmetric domains in complex Banach spaces
Institute of Scientific and Technical Information of China (English)
DENG; Fangwen
2006-01-01
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.
On Λ-Type Duality of Frames in Banach Spaces
Directory of Open Access Journals (Sweden)
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES
Institute of Scientific and Technical Information of China (English)
Yu Lin
2009-01-01
A generalized Rosenthal's inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and character-izes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.
Boundary Controllability of Integrodifferential Systems in Banach Spaces
Indian Academy of Sciences (India)
K Balachandran; E R Anandhi
2001-02-01
Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
Invariant manifolds for flows in Banach Spaces
Energy Technology Data Exchange (ETDEWEB)
Lu Kening.
1989-01-01
The author considers the existence, smoothness and exponential attractivity of global invariant manifolds for flow in Banach Spaces. He shows that every global invariant manifold can be expressed as a graph of a C{sup k} map, provided that the invariant manifolds are exponentially attractive. Applications go to the Reaction-Diffusion equation, the Kuramoto-Sivashinsky equation, and singular perturbed wave equation.
The Topological Degree in Ordered Banach Spaces
Institute of Scientific and Technical Information of China (English)
Adrian DUMA; Ileana DUMA
2008-01-01
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this frame-work, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
Wang, Min
2016-04-01
This paper aims to establish the Tikhonov regularization method for generalized mixed variational inequalities in Banach spaces. For this purpose, we firstly prove a very general existence result for generalized mixed variational inequalities, provided that the mapping involved has the so-called mixed variational inequality property and satisfies a rather weak coercivity condition. Finally, we establish the Tikhonov regularization method for generalized mixed variational inequalities. Our findings extended the results for the generalized variational inequality problem (for short, GVIP(F, K)) in R^n spaces (He in Abstr Appl Anal, 2012) to the generalized mixed variational inequality problem (for short, GMVIP(F,φ , K) ) in reflexive Banach spaces. On the other hand, we generalized the corresponding results for the generalized mixed variational inequality problem (for short, GMVIP(F,φ ,K) ) in R^n spaces (Fu and He in J Sichuan Norm Univ (Nat Sci) 37:12-17, 2014) to reflexive Banach spaces.
Malliavin calculus and decoupling inequalities in Banach spaces
Maas, Jan
2008-01-01
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the ...
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
Directory of Open Access Journals (Sweden)
Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
Directory of Open Access Journals (Sweden)
Irene Benedetti
2015-01-01
Full Text Available We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.
On the weak uniform rotundity of Banach spaces
Directory of Open Access Journals (Sweden)
Wen D. Chang
2003-01-01
Full Text Available We prove that if Xi,i=1,2,…, are Banach spaces that are weak* uniformly rotund, then their lp product space (p>1 is weak* uniformly rotund, and for any weak or weak* uniformly rotund Banach space, its quotient space is also weak or weak* uniformly rotund, respectively.
Introduction to Banach spaces and algebras
Allan, Graham
2010-01-01
Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be
Spatiality of Derivations of Operator Algebras in Banach Spaces
Directory of Open Access Journals (Sweden)
Quanyuan Chen
2011-01-01
Full Text Available Suppose that A is a transitive subalgebra of B(X and its norm closure A¯ contains a nonzero minimal left ideal I. It is shown that if δ is a bounded reflexive transitive derivation from A into B(X, then δ is spatial and implemented uniquely; that is, there exists T∈B(X such that δ(A=TA−AT for each A∈A, and the implementation T of δ is unique only up to an additive constant. This extends a result of E. Kissin that “if A¯ contains the ideal C(H of all compact operators in B(H, then a bounded reflexive transitive derivation from A into B(H is spatial and implemented uniquely.” in an algebraic direction and provides an alternative proof of it. It is also shown that a bounded reflexive transitive derivation from A into B(X is spatial and implemented uniquely, if X is a reflexive Banach space and A¯ contains a nonzero minimal right ideal I.
The heart of the Banach spaces
Wegner, Sven-Ake
2016-01-01
Let an exact category in the sense of Quillen be given. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their famous 1982 paper, Beilinson, Bernstein and Deligne consider in this situation a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out, that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by...
BANACH CONTRACTION PRINCIPLE ON CONE RECTANGULAR METRIC SPACES
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Ismat Beg
2009-08-01
Full Text Available We introduce the notion of cone rectangular metric space and prove {sc Banach} contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.
Open problems in the geometry and analysis of Banach spaces
Guirao, Antonio J; Zizler, Václav
2016-01-01
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...
An explicit construction of sunny nonexpansive retractions in Banach spaces
Directory of Open Access Journals (Sweden)
Simeon Reich
2005-10-01
Full Text Available An explicit algorithmic scheme for constructing the unique sunny nonexpansive retraction onto the common fixed point set of a nonlinear semigroup of nonexpansive mappings in a Banach space is analyzed and a proof of convergence is given.
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-01-01
Abstract Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a s...
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.
Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
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Sergey Ajiev
2013-05-01
Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.
Banach frames for multivariate alpha-modulation spaces
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2006-01-01
The α-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Ri...
On the WAε Property and g-NUCε Banach Spaces
Institute of Scientific and Technical Information of China (English)
FANG Xi-nian; YANG Yi-min
2001-01-01
The WAε property and g-NUCε, g-NUC Banach spaces are introduced. We prove that the WAε property is equivalent to the WBS property and the g-NUCε (resp., g-NUC) spaces are equivalent to the NUCε (resp., NUC) spaces possessing the BS property. So we obtain a characterization of the NUCε (resp. , NUC) spaces possessing the BS property.
Construction of generalized atomic decompositions in Banach spaces
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Raj Kumar
2014-06-01
Full Text Available G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.
Atomic decompositions of Banach-space-valued martingales
Institute of Scientific and Technical Information of China (English)
刘培德; 侯友良
1999-01-01
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as H_α(X) and _ρ(?)_α in the case 0<α≤1 are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
(s, μ)-similar operators in the Banach spaces
International Nuclear Information System (INIS)
The theory of the operator ideals formed by means of S function is developed. The problem of the construction of the operator acting from one Banach space to another whose S numbers are near to the given ones, is solved. Several conditions, sufficient for that any wholly continuous operator in the Gilbert space were transferred to the given pair of the Banach spaces without distorting too much the values of its S-numbers, are given. All the considered operators are assumed to be linear and continuous ones
Additive maps preserving the reduced minimum modulus of Banach space operators
Bourhim, Abdellatif
2009-01-01
Let ${\\mathcal B}(X)$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space $X$. We prove that an additive surjective map $\\phi$ on ${\\mathcal B}(X)$ preserves the reduced minimum modulus if and only if either there are bijective isometries $U:X\\to X$ and $V:X\\to X$ both linear or both conjugate linear such that $\\phi(T)=UTV$ for all $T\\in{\\mathcal B}(X)$, or $X$ is reflexive and there are bijective isometries $U:X^*\\to X$ and $V:X\\to X^*$ both linear or both conjugate linear such that $\\phi(T)=UT^*V$ for all $T\\in{\\mathcal B}(X)$. As immediate consequences of the ingredients used in the proof of this result, we get the complete description of surjective additive maps preserving the minimum, the surjectivity and the maximum moduli of Banach space operators.
A Banach Space Regularization Approach for Multifrequency Microwave Imaging
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Claudio Estatico
2016-01-01
Full Text Available A method for microwave imaging of dielectric targets is proposed. It is based on a tomographic approach in which the field scattered by an unknown target (and collected in a proper observation domain is inverted by using an inexact-Newton method developed in Lp Banach spaces. In particular, the extension of the approach to multifrequency data processing is reported. The mathematical formulation of the new method is described and the results of numerical simulations are reported and discussed, analyzing the behavior of the multifrequency processing technique combined with the Banach spaces reconstruction method.
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
Indian Academy of Sciences (India)
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
On well posedness of best simultaneous approximation problems in Banach spaces
Institute of Scientific and Technical Information of China (English)
LI; Chong
2001-01-01
［1］Pinkus, A., Uniqueness in vector-valued approximation, J. Approx. Theory, 1993, 73: 17—92.［2］Li, C., Watson, G. A., On best simultaneous approximation, J. Approx. Theory, 1997, 91: 332—348.［3］Tanimoto, S., A characterization of best simultaneous approximations, J. Approx. Theory, 1989, 59: 359—361.［4］Watson, G. A., A characterization of best simultaneous approximations, J. Approx. Theory, 1993, 75: 175—182.［5］Li, C., Watson, G. A., On best simultaneous approximation of a finite set of functions, Computer Math. Applic., 1999, 37: 1—9.［6］Stechkin, S. B., Approximation properties of sets in normed linear spaces, Rev. Roumaine Math. Pures and Appl. (in Russian), 1963, 8: 5—18.［7］Borwein, J. M., Fitzpatrick, S., Existence of nearest points in Banach spaces, Can. J. Math., 1989, 41: 702—720.［8］De Blasi, F. S., Myjak, J., On a generalized best approximation problem, J. Approx. Theory, 1998, 94: 54—72.［9］Georgiev, P. G., The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Anal. Appl., 1988, 131: 1—21.［10］Lau, K. S., Almost Chebyshev subsets in reflexive Banach spaces, Indiana Univ. Math. J., 1978, 27: 791—795.［11］Li, C., On mutually nearest and mutually furthest points in reflexive Banach spaces, J. Approx. Theory, 2000, 103: 1—17.［12］Li, C., On well posed generalized best approximation problems, J. Approx. Thory, 2000, 107: 96—108.［13］Li, C., Almost K-Chebyshev sets, Acta. Math. Sin. (in Chinese), 1990, 33: 251—259.［14］De Blasi, F. S., Myjak, J., Papini, P. L., On mutually nearest and mutually furthest points of sets in Banach spaces, J. Approx. Theory, 1992, 70: 142—155.［15］Dontchev, A., Zolezzi, T., Well Posed Optimization Problems, Lecture Notes in Math., Vol. 1543, New York: Springer-Verlag, 1993.［16］Li, C., Wang, X. H., Almost Chebyshev set with respect to bounded subsets, Science in China, Ser. A, 1997, 40: 375—383.［17］Ni, R
Banach spaces and descriptive set theory selected topics
Dodos, Pandelis
2010-01-01
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
陈果良; 魏木生
2002-01-01
In this paper we show that in error estimates, the condition number κ(T) of any invertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Banach theorem and other related results.
Stochastic Integration in Banach Spaces using a product structure with partial order
Bierkens, Joris
2009-01-01
Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.
Multipliers of pg-Bessel sequences in Banach spaces
Abdollahpour, M. R.; Najati, A.; Gavruta, P.
2015-01-01
In this paper, we introduce (p,q)g-Bessel multipliers in Banach spaces and we show that under some conditions a (p,q)g-Bessel multiplier is invertible. Also, we show the continuous dependency of (p,q)g-Bessel multipliers on their parameters.
Mann Iteration of Weak Convergence Theorems in Banach Space
Institute of Scientific and Technical Information of China (English)
Liang-gen Hu; Jin-ping Wang
2009-01-01
In this paper, by using Mann's iteration process we will establish several weak convergence theorems for approximating a fixed point of κ-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich's theorem from nonexpausive mappings to κ-strict pseudocontractive mappings.
MULTI-VALUED QUASI VARLATIONAL INCLUSIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
张石生
2004-01-01
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces.By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established.The results generalize,improve and unify a number of Noor's and others' recent results.
A NOTE ON REARRANGEMENTS OF SERIES IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
ZhongHuaijie
1994-01-01
We generalize Kadec's and Yan Zikun's resuhs in [1],[2] to prove; in every infinite dimensional real Banach space Y there exist an infinite dimensional subspace X and a series ∑xn such that ∑xn has property(N) in X. but(the domain of sums of this series) S(∑xn) is not a convex set.
Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces
Directory of Open Access Journals (Sweden)
Lu-Chuan Ceng
2014-01-01
Full Text Available We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.
Improved bounds in the metric cotype inequality for Banach spaces
Giladi, Ohad; Naor, Assaf
2010-01-01
It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m X we have \\sum_{j=1}^n \\Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] n^{(1/2)+(1/q)}.
Banach空间中的Xd Bessel列%Sequences of Xd Bessel for a Banach space
Institute of Scientific and Technical Information of China (English)
王亚丽; 曹怀信; 张巧卫
2011-01-01
研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基.证明了当Xd为BK-空间时,(BXXd,‖·‖)是数域F上的Banach空间；当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B(X*,Xd)之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据.最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的.%Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X ate introduced and discussed. It is proved that (Bxxd || ? || ) is a Banach space when Xd is a BK-space. By de fining an operator Tf, an isometric isomorphism from Bxxd to B(X* ,Xd) is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ ent Xd frames and Xd Riesz bases for a Banach space X are the same.
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Kraus, Michal
2015-01-01
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
Integrals and Banach spaces for finite order distributions
Talvila, Erik
2011-01-01
Let $\\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\\infty$. Let $\\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\\infty$. Define $\\acn$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\\Bc$. Similarly with $\\arn$ from $\\Br$. A type of integral is defined on distributions in $\\acn$ and $\\arn$. The multipliers are iterated integrals of functions of bounded variation. For each $n\\in\\N$, the spaces $\\acn$ and $\\arn$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\\Bc$ and $\\Br$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\\ac^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\\ar^1$ contains all finite signed Borel measure...
Geometric properties of Banach spaces and nonlinear iterations
Chidume, Charles
2009-01-01
Nonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent,...
Some Properties of the Injective Tensor Product of Banach Spaces
Institute of Scientific and Technical Information of China (English)
Xiao Ping XUE; Yong Jin LI; Qing Ying BU
2007-01-01
Let X and Y be Banach spaces such that X has an unconditional basis. Then X?Y, the injective tensor product of X and Y, has the Radon-Nikodym property (respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness) if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw
2012-01-01
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n dimensional space X_n \\subset X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width d_n(F)_X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method fo...
The Hilbert Inequality in Banach Spaces%Banach空间上的Hilbert不等式
Institute of Scientific and Technical Information of China (English)
华柳斌; 黎永锦
2011-01-01
Some Hilbert's inequalities in Hilbert spaces and Banach spaces were discussed by inner and functional. The Hilbert spaces and Banach space version of Hilbert's inequalities were established.%利用内积和泛函,在Hilbert空间和Banach空间中讨论Hilbert不等式,建立了抽象空间的Hilbert不等式.
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald
2013-02-26
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.
Some Banach spaces of Dirichlet series
Bailleul, Maxime; Lefèvre, Pascal
2013-01-01
The Hardy spaces of Dirichlet series denoted by ${\\cal H}^p$ ($p\\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces denoted ${\\cal A}^p$ and ${\\cal B}^p$. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p = 2. We also show that the...
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
An approximation problem of the finite rank operator in Banach spaces
Institute of Scientific and Technical Information of China (English)
王玉文; 潘少荣
2003-01-01
By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.
Institute of Scientific and Technical Information of China (English)
Adrian PETRU(S)EL; Jen-Chih YAO
2009-01-01
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation
Brzezniak, Z.; Van Neerven, J.M.A.M.; Veraar, M.C.; Weis, L.
2008-01-01
Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results
On sets minimizing their weighted length in uniformly convex separable Banach spaces
De Pauw, Thierry; Lemenant, Antoine; Millot, Vincent
2013-01-01
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show $C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.
Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Zi Hou ZHANG; Yu ZHOU; Chun Yan LIU
2016-01-01
The authors discuss the dual relation of nearly very convexity and property WS.By two kinds of near convexities and two kinds of near smoothness,the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact.They show a sufficient condition such that a Banach space X is a Asplund space.Using upper semi-continuity of duality mapping,the authors also give two characterizations of property WS and property S.
Maximal regularity of second order delay equations in Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We give necessary and sufficient conditions of Lp-maximal regularity(resp.B sp ,q-maximal regularity or F sp ,q-maximal regularity) for the second order delay equations:u″(t)=Au(t) + Gu’t + F u t + f(t), t ∈ [0, 2π] with periodic boundary conditions u(0)=u(2π), u′(0)=u′(2π), where A is a closed operator in a Banach space X,F and G are delay operators on Lp([-2π, 0];X)(resp.Bsp ,q([2π, 0];X) or Fsp,q([-2π, 0;X])).
Linearization of class C1 for contractions on Banach spaces
Rodrigues, Hildebrando M.; Solà-Morales, J.
In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.
Iterative solutions of nonlinear equations in smooth Banach spaces
International Nuclear Information System (INIS)
Let E be a smooth Banach space over the real field, φ not= K is contained in E closed convex and bounded, T:K → K uniformly continuous and strongly pseudo-contractive. It is proved that the Ishikawa iteration process converges strongly to the unique fixed point of T. Applications of this result to the operator equations Au=f or u+Au=f where A is a strongly accretive mapping of E into itself and under various continuity assumptions on A are also given. (author). 41 refs
FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS
Institute of Scientific and Technical Information of China (English)
S. S. Panday
2004-01-01
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
ZHANG WEIRONG; MA JIPU
2005-01-01
Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
Homomorphisms and functional calculus on algebras on entire functions on Banach spaces
Directory of Open Access Journals (Sweden)
H. M. Pryimak
2015-07-01
Full Text Available The paper is devoted to study homomorphisms of algebras of entire functionson Banach spaces to a commutative Banach algebra. In particular, it is proposed amethod to construct homomorphisms vanishing on homogeneouspolynomials of degree less or equal that a fixed number $n.$
Stochastic integration in Banach spaces theory and applications
Mandrekar, Vidyadhar
2015-01-01
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...
A SUPER-HALLEY TYPE APPROXIMATION IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
J.A. Ezquerro; M.A. Hernández
2001-01-01
The Super-Halley method is one of the best known third-orderiteration for solving nonlinear equations. A Newton-like method which is an approximation of this method is studied. Our approach yields a fourth R-order iterative process which is more efficient than its classical predecessor. We establish a Newton-Kantorovich-type convergence theorem using a new system of recurrence relations, and give an explicit expression for the a priori error bounds of the iteration.CLC Number：O17 Document ID：AAuthor Resume：J.A. Ezquerro,e-mail : jezquer@siur. unirioja. es mahernan@siur. unirioja. es References：[1]Argyros,I.K. ,Chen,D. andQian,Q. ,An Inverse-Free Jarratt Type Approximation in a Banach Space,J. Appr. Th. Appl.,12(1996),No. 1,19-30.[2]Argyros,I. K. ,Chen,D. And Qian,Q. ,The Jarratt Method in Banach Space Setting,J.Comput. Appl. Math.,51(1994),103-106.[3]Candela,V. And Marquina,A. ,Recurrence Relations for Rational Cubic Methods I: The Halley Method,Computing,44(1990),169- 184.[4]Candela,V. And Marquina,A. ,Recurrence Relations for Rational Cubic Method I : TheChebyshev Method,Computing,45(1990),355-[3]67.[5]Chen,D.,Argyros,I.K.andQian,Q.,ALocalConvergenceTheoremfortheSuper-HalleyMethodinaBanachSpace,Appl.Math.Lett.,7(1994),No.5,49-52.[6]Hernández,M.A.,Newton-Raphson'sMethodandConvexity,Zb.Rad.Prirod.Mat.Fak.Ser.Mat.,22(1992),No.1,1591-66.[7]Kantorovich,L.V.,TheMajorantPrincipleforNewton'sMethod,Dokl.Akad.Nauk,SSSR,76(1951),17-20.[8]Potra,F.A.adnPták,V.,NondiscreteInductionandIterativeProcesses,Pitman,NewYork,1984.[9]Rall,L.B.,ComputationalSolutionofNonlinearOperatorEquations,JohnWiley&-Sons,NewYork,1979.[10]Safiev,R.A.,OnSomeIterativeProcesses,Z,Vyccisl.Mat.Fiz.,4,193-143(TranslatedintoEnglishbyL.B.RallasMRCTechnicalSummaryReport,No.649,Univ.Wisconsin-Madison,1966).Manuscript Received：1998年10月20日Published：2001年9月1日
Directory of Open Access Journals (Sweden)
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
A New Class of Banach Spaces with Uniform Normal Structure
Institute of Scientific and Technical Information of China (English)
GAO Ji
2001-01-01
Let X be a Banach space, S (X) be the unit sphere of X, ψ be a function: S ( X)→ S ( X * )such that ψ(x)∈ x, and vψ(ε)=inf ,0 ≤ ε ≤ 2, where x is the set of norm 1 supporting functionals of S (X) at x. A geometric concept,modulus of V-convexity V(ε) = sup{ Vψ(ε), for all ψ: S(X)→ S(X* )}, is introduced; the properties of V( ε ) and the relationship between V(ε ) and other geometric concepts are discussed. The main result is that V(1/2)＞0 implies normal structure.
Approximative compactness and continuity of metric projector in Banach spaces and applications
Institute of Scientific and Technical Information of China (English)
HUDZIK; Henryk; KOWALEWSKI; Wojciech; WISLA; Marek
2008-01-01
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
Exponential dichotomies for linear discrete-time systems in Banach spaces
Directory of Open Access Journals (Sweden)
Ioan-Lucian Popa
2012-04-01
Full Text Available In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarify the relations between these concepts.
On Property () in Banach Lattices, Calderón–Lozanowskiĭ and Orlicz–Lorentz Spaces
Indian Academy of Sciences (India)
Paweł Kolwicz
2001-08-01
The geometry of Calderón–Lozanowskiĭ spaces, which are strongly connected with the interpolation theory, was essentially developing during the last few years (see [4, 9, 10, 12, 13, 17]). On the other hand many authors investigated property () in Banach spaces (see [7, 19, 20, 21, 25, 26]). The first aim of this paper is to study property () in Banach function lattices. Namely a criterion for property () in Banach function lattice is presented. In particular we get that in Banach function lattice property () implies uniform monotonicity. Moreover, property () in generalized Calderón–Lozanowskiĭ function spaces is studied. Finally, it is shown that in Orlicz–Lorentz function spaces property () and uniform convexity coincide.
Institute of Scientific and Technical Information of China (English)
张石生
2001-01-01
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.
Restrictive metric regularity and generalized differential calculus in Banach spaces
Directory of Open Access Journals (Sweden)
Bingwu Wang
2004-10-01
Full Text Available We consider nonlinear mappings f:XÃ¢Â†Â’Y between Banach spaces and study the notion of restrictive metric regularity of f around some point xÃ‚Â¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at xÃ‚Â¯ but its strict derivative Ã¢ÂˆÂ‡f(xÃ‚Â¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.
On quasi-convex mappings of order α in the unit ball of a complex Banach space
Institute of Scientific and Technical Information of China (English)
LIU Taishun; XU Qinghua
2006-01-01
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.
Institute of Scientific and Technical Information of China (English)
Robert F.Allen
2014-01-01
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient condi-tions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ”computable” estimates on the operator norm.
On well posedness of best simultaneous approximation problems in Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points in E(G) such that the best simultaneous approximation problems are not well posed is a σ-porous set in E(G) when X is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
On Best Approximations from RS-sets in Complex Banach Spaces
Institute of Scientific and Technical Information of China (English)
Chong LI
2005-01-01
The concept of an RS-set in a complex Banach Space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established.
Hybrid Iteration Method for Fixed Points of Nonexpansive Mappings in Arbitrary Banach Spaces
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P. U. Nwokoro
2008-02-01
Full Text Available We prove that recent results of Wang (2007 concerning the iterative approximation of fixed points of nonexpansive mappings using a hybrid iteration method in Hilbert spaces can be extended to arbitrary Banach spaces without the strong monotonicity assumption imposed on the hybrid operator.
Integrals with values in Banach spaces and locally convex spaces
Mikusinski, Piotr
2014-01-01
The purpose of this article is to present the construction and basic properties of the general Bochner integral. The approach presented here is based on the ideas from the book The Bochner Integral by J. Mikusinski where the integral is presented for functions defined on $\\mathbb{R}^N$. In this article we present a more general and simplified construction of the Bochner integral on abstract measure spaces. An extension of the construction to functions with values in a locally convex space is ...
Institute of Scientific and Technical Information of China (English)
Xie Ping DING
2012-01-01
Some classes of mixed equilibrium problems and bilevel mixed equilibrium problems are introduced and studied in reflexive Banach spaces.First,by using a minimax inequality,some new existence results of solutious and the behavior of solution set for the mixed equilibrium problems and the bilevel mixed equilibrium problems are proved under suitable assumptions without the coercive conditions.Next,by using auxiliary principle technique,some new iterative algorithms for solving the mixed equilibrium problems and the bilevel mixed equilibrium problems are suggested and analyzed.The strong convergence of the iterative sequences generated by the proposed algorithms is proved under suitable assumptions without the coercive conditions.These results are new and generalize some recent results in this field.
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety
Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
Directory of Open Access Journals (Sweden)
2009-02-01
Full Text Available We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.
The generalized hardy operator with kernel and variable integral limits in banach function spaces
Lang J; Gogatishvill A
1999-01-01
Let we have an integral operator where and are nondecreasing functions, and are non-negative and finite functions, and is nondecreasing in , nonincreasing in and for and . We show that the integral operator where and are Banach functions spaces with -condition is bounded if and only if . Where and
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Psi-exponential dichotomy for linear differential equations in a Banach space
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Atanaska Georgieva
2013-07-01
Full Text Available In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banach space. With these two concepts we prove the existence of psi-bounded solutions of the appropriate inhomogeneous equation. A roughness of the psi-dichotomy is also considered.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE
Institute of Scientific and Technical Information of China (English)
M.I.Gil＇
2004-01-01
The nonlocal initial problem for nonlinear nonautonomous evolution equations in a Banach space is considered. It is assumed that the nonlinearities have the local Lipschitz properties. The existence and uniqueness of mild solutions are proved. Applications to integro-differential equations are discussed. The main tool in the paper is the normalizing mapping (the generalized norm).
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Bound and periodic solutions of the Riccati equation in Banach space
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A. Ya. Dorogovtsev
1995-01-01
Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.
Some G-M-type Banach spaces and K-groups of operator algebras on them
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ZHONG Huaijie; CHEN Dongxiao; CHEN Jianlan
2004-01-01
By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
Strong convergence theorems for nonexpansive semi-groups in Banach spaces
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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
Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras
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HUANG Hua-ping; XU Shao-yuan; LIU Qiu-hua; MING Wei
2016-01-01
In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover, we give an example to support the main assertions.
Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Institute of Scientific and Technical Information of China (English)
Hai Yun ZHOU
2004-01-01
In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces
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Lin Wei-Wei
2010-01-01
Full Text Available The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to -strict pseudocontractions in -uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.
The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space
Institute of Scientific and Technical Information of China (English)
Liping Yang
2007-01-01
Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method,it is proved that the convergence of Mann,Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration.The results of this paper extend the results of Rhoades and Soltuz in some aspects.
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
Murthy, S; Arunkumar, M; V. Govindan
2015-01-01
In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized n-type additive-quadratic functional equation. g(x + 2y; u + 2v) + g(x 2y; u 2v) = 4[g(x + y; u + v) + g(x y; u v)] 6g(x; u) + g(2y; 2v) + g(2y;2v) 4g(y; v) 4g(y;v) Where is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.
ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
Chen Dongyang
2006-01-01
Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p+1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.
Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras
Muscat, Joseph
2014-01-01
This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields. Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.
Institute of Scientific and Technical Information of China (English)
Boulbeba Abdelmoumen; Aref Jeribi; Maher Mnif
2012-01-01
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space
Lemle, Ludovic Dan
2008-01-01
Let $({\\cal X},\\|\\:.\\:\\|)$ be a Banach space. In general, for a $C_0$-semigroup \\semi on $({\\cal X},\\|\\:.\\:\\|)$, its adjoint semigroup \\semia is no longer strongly continuous on the dual space $({\\cal X}^{*},\\|\\:.\\:\\|^{*})$. Consider on ${\\cal X}^{*}$ the topology of uniform convergence on compact subsets of $({\\cal X},\\|\\:.\\:\\|)$ denoted by ${\\cal C}({\\cal X}^{*},{\\cal X})$, for which the usual semigroups in literature becomes $C_0$-semigroups.\\\\ The main purpose of this paper is to prove th...
Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
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Messaoud Bounkhel
2013-01-01
Full Text Available In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t∈F(t,x(t a.e. on I, x(t∈S, ∀t∈I, x(0=x0∈S, (*, where S is a closed subset in a Banach space , I=[0,T], (T>0, F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x⊂c(tx+xp, ∀(t,x∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+. The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.
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Qinghai He
2013-01-01
Full Text Available In general Banach spaces, we consider a vector optimization problem (SVOP in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP. In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.
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Cholamjiak Prasit
2009-01-01
Full Text Available The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-strongly monotone operator and the set of fixed points of relatively quasi-nonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space.
Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Choonkil BAAK
2006-01-01
Let X, Y be vector spaces. It is shown that if a mapping f: X → Y satisfiesf(x+y/2+z)+f(x-y/2+z)=f(x)+2f(z), (0.1)f(x+y/2+z)-f(x-y/2+z)= f(y), (0.2)or2f(x+y/2+z)=f(x)+f(y)+2f(z) (0.3)for all x, y, z ∈ X, then the mapping f: X → Y is Cauchy additive.Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebra.
Landweber-Kaczmarz method in Banach spaces with inexact inner solvers
Jin, Qinian
2016-10-01
In recent years the Landweber-Kaczmarz method has been proposed for solving nonlinear ill-posed inverse problems in Banach spaces using general convex penalty functions. The implementation of this method involves solving a (nonsmooth) convex minimization problem at each iteration step and the existing theory requires its exact resolution which in general is impossible in practical applications. In this paper we propose a version of the Landweber-Kaczmarz method in Banach spaces in which the minimization problem involved in each iteration step is solved inexactly. Based on the \\varepsilon -subdifferential calculus we give a convergence analysis of our method. Furthermore, using Nesterov's strategy, we propose a possible accelerated version of the Landweber-Kaczmarz method. Numerical results on computed tomography and parameter identification in partial differential equations are provided to support our theoretical results and to demonstrate our accelerated method.
Tomonari Suzuki
2006-01-01
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Saeidi Shahram
2008-01-01
Abstract Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space into with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let , , and be sequences in (0, 1) such that , for all . Let , for all . Then, under suitable hypotheses on the constants, we show that converges stron...
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
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Su Yongfu
2008-01-01
Full Text Available Abstract The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping and a finite family of nonexpansive mappings , respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space
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Zhanfei Zuo
2011-01-01
Full Text Available It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where ∶=∩∞=0( stands for the common fixed-point set of the family of multivalued nonexpansive mapping {}.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
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Huimin He
2010-01-01
Full Text Available Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0∈K, xn=αnxn-1+(1-αnyn, yn∈Txn, n≥1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
Nonlinear Evolution Governed by Accretive Operators in Banach Spaces: Error Control and Applications
Nochetto, Ricardo H; Savare, Giuseppe
2001-01-01
Nonlinear evolution equations governed by $m$-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order $O(sqrttau)$. Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in $L^1$, as well as to Hamilton-Jacobi equations in $C^...
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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
ON A FAMILY OF CHEBYSHEV-HALLEY TYPE METHODS IN BANACH SPACE UNDER WEAKER SMALE CONDITION
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, we discuss local convergence of a family of Chebychev-Halley type methods with a parameter θ∈[0,1] in Banach space using Smale-type δ criterion under 2-th γ-condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.
Institute of Scientific and Technical Information of China (English)
CHEN Fang-qi; TIAN Rui-lan; CHEN Yu-shu
2006-01-01
Under loose conditions, the existence of solutions to initial value problem are studied for second order impulsive integro-differential equation with infinite moments of impulse effect on the positive half real axis in Banach spaces. By the use of recurrence method, Tonelii sequence and the locally convex topology, the new existence theorems are achieved, which improve the related results obtained by Guo Da-jun.
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Xin-dong Liu
2012-01-01
Full Text Available A new hybrid projection algorithm is considered for a λ-strict asymptotically pseudocontractive mapping. Using the metric projection, a strong convergence theorem is obtained in a uniformly convex and 2-uniformly smooth Banach spaces. The result presented in this paper mainly improves and extends the corresponding results of Matsushita and Takahashi (2008, Dehghan (2011 Kang and Wang (2011, and many others.
On a New Geometric Constant Related to the Modulus of Smoothness of a Banach Space
Institute of Scientific and Technical Information of China (English)
Yasuji TAKAHASHI; Mikio KATO
2014-01-01
We shall introduce a new geometric constant A(X) of a Banach space X, which is closely related to the modulus of smoothnessρX(τ), and investigate it in relation with the constant A2(X) by Baronti et al., the von Neumann-Jordan constant CN J (X ) and the James constant J (X ). A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.
A reinterpretation of set differential equations as differential equations in a Banach space
Rasmussen, Martin; Rieger, Janosch; Webster, Kevin
2015-01-01
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example,...
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
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Martin Väth
2004-12-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
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Suzuki Tomonari
2006-01-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Directory of Open Access Journals (Sweden)
Yun-zhi Zou
2012-01-01
Full Text Available A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.
From Hahn-Banach to monotonicity
Simons, Stephen
2008-01-01
In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach spac...
Hytonen, Tuomas; van Neerven, Jan; Portal, Pierre
2007-01-01
We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\\infty})-functional calculus on these spaces. This provides a new way of proving functional ...
On Linear Isometries of Banach Lattices in $\\mathcal{C}_0()$-Spaces
Indian Academy of Sciences (India)
José M Isidro
2009-11-01
Consider the space $\\mathcal{C}_0()$ endowed with a Banach lattice-norm $\\|\\cdot p\\|$ that is not assumed to be the usual spectral norm $\\|\\cdot p\\|_∞$ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice $(\\mathcal{C}_0(),\\|\\cdot p\\|)$ induces a partition of into a family of finite subsets $S\\subset$ along with a bijection $T:→$ which preserves cardinality, and a family $[u(S):S\\in]$ of surjective linear maps $u(S):\\mathcal{C}(T(S))→\\mathcal{C}(S)$ of the finite-dimensional *-algebras $\\mathcal{C}(S)$ such that $$(U f)|_{T(S)}=u(S)(f|_S) \\quad \\forall f\\in\\mathcal{C}_0() \\quad \\forall S\\in.$$ Here we endow the space of finite sets $S\\subset$ with a topology for which the bijection and the map are continuous, thus completing the analogy with the classical result.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
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Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Delta-semidefinite and delta-convex quadratic forms in Banach spaces
Kalton, N.; Konyagin, S. V.; Vesely, L.
2006-01-01
A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator $T\\colon X\\to X^*$ factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if $T$ is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional $...
Existence results for a class of parabolic evolution equations in Banach spaces
Institute of Scientific and Technical Information of China (English)
WangJing; XueXingmei
2003-01-01
We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Avigad, Jeremy; Rute, Jason
2012-01-01
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded from above and below: for any increasing sequence (t_k)_{k in N} of natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
International Nuclear Information System (INIS)
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
Hanke-Raus heuristic rule for variational regularization in Banach spaces
Jin, Qinian
2016-08-01
We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of the Bregman distance. By imposing certain conditions on the random noise, we establish four convergence results; one relies on the source conditions and the other three do not depend on any source conditions. Numerical results are presented to illustrate the performance.
C0-semigroups of linear operators on some ultrametric Banach spaces
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Toka Diagana
2006-01-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
Basic Properties of Banach Space Xμ%Banach空间Xμ的基本性质
Institute of Scientific and Technical Information of China (English)
郑列
2005-01-01
研究了Banach空间Xμ={c=(ci)i≥1:‖c‖μ=def ∞∑ i=1 iμ|Ci|∞},μ≥1.讨论了它的范数,紧性以及强收敛和弱收敛之间的关系.%Banach space Xμ= {c= (ci)i≥1: ‖c‖μ=def ∞∑ i=1 iμ|ci|∞},μ≥1. is studied. Our results relate to norm,compactness and the relation between strong convergence and weak * convergence.
Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces
International Nuclear Information System (INIS)
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
A model of CT dose profiles in Banach space; with applications to CT dosimetry
Weir, Victor J.
2016-07-01
In this paper the scatter component of computed tomography dose profiles is modeled using the solution to a nonlinear ordinary differential equation. This scatter function is summed with a modeled primary function of approximate trapezoidal shape. The primary dose profile is modeled to include the analytic continuation of the Heaviside step function. A mathematical theory is developed in a Banach space. The modeled function is used to accurately fit data from a 256-slice GE Revolution scanner. A 60 cm long body phantom is assembled and used for data collection with both a pencil chamber and a Farmer-type chamber.
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
Institute of Scientific and Technical Information of China (English)
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
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Yu Wen WANG; Jian ZHANG; Yun An CUI
2012-01-01
Let X,Y be Banach spaces and M be a linear subspace in X × Y ={{x,y}|x ∈ X,y ∈ Y}.We may view M as a multi-valued linear operator from X to Y by taking M(x) ={y|{x,y} ∈ M}.In this paper,we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M.The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.
On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
Institute of Scientific and Technical Information of China (English)
ZHANG; Wenjun(张文俊); LIU; Taishun(刘太顺)
2002-01-01
A class of biholomorphic mappings named "quasi-convex mapping" is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the "quasi-convexmapping" is exactly the "quasi-convex mapping of type A" introduced by K. A. Roper and T. J. Suffridge.
Isomorphisms on weighed Banach spaces of harmonic and holomorphic functions
Jorda Mora, Enrique; ZARCO GARCIA, ANA MARIA
2013-01-01
For an arbitrary open subset U subset of R-d or U subset of C-d and a continuous function v : U ->]0,infinity[ we show that the space h(v0) (U) of weighed harmonic functions is almost isometric to a (closed) subspace of c(0), thus extending a theorem due to Bonet and Wolf for spaces of holomorphic functions H-v0 (U) on open sets U subset of C-d. Inspired by recent work of Boyd and Rueda, we characterize in terms of the extremal points of the dual of h(v0) (U) when h(v0) (U) is isometric to a ...
Banach SSD spaces and classes of monotone sets
Simons, Stephen
2009-01-01
In this paper, we unify the theory of SSD spaces and the theory of strongly representable sets, and we apply our results to the theory of the various classes of maximally monotone sets. In particular, we prove that type (ED), dense type, type (D) and type (NI) are identical.
A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space
Kaltenbacher, B.
2015-01-01
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss-Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings.
Institute of Scientific and Technical Information of China (English)
Shi-sheng ZHANG
2009-01-01
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
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Jiancai Huang
2012-01-01
Full Text Available We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
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Rongfei Lin
2013-01-01
Full Text Available Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.
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Qiaohong Jiang
2014-01-01
Full Text Available Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.
（1.2） INVERSES OF OPERATORS BETWEEN BANACH SPACES AND LOCAL CONJUGACY THEOREM
Institute of Scientific and Technical Information of China (English)
MAJIPU
1999-01-01
Let E and F be Banach spaces and f non-linear C1 map from E into F. The main result is Theorem 2.2, in which a connection between local conjugacy problem of f at x0 ∈ E and a local fine property of f'(x) at x0(see the Definition 1.1 in this paper) are obtained. This theorem includes as special cases the two known theorems: the finite rank theorem and Berger's Theorem for non-linear Fredholm operators. Moreover: the theorem gives rise the further results for some non-linear semi-Fredholm maps and for all non-linear semi-Fredholm maps when E and F are Hilbert spaces. Thus Theorem 2.2 not only just unifies the above known theorems but also really generalizes them.
On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces
Institute of Scientific and Technical Information of China (English)
Chong LI; Ren Xing NI
2004-01-01
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let K(X) denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let KG(X) denote the closure of the set {A ∈ K(X): A∩G =φ}. We prove that the set of all A ∈KG(X) (resp. A ∈ K(X)), such that the minimization (resp. maximization) problem min(A, G) (resp. max(A, G)) is well posed, contains a dense Gδ-subset of KG(X) (resp. K(X)), thus extending the recent results due to Blasi, Myjak and Papini and Li.
A type (4) space in (FR)-classification
Argyros, Spiros A; Pelczar-Barwacz, Anna
2012-01-01
We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.
Models of CT dose profiles in Banach space; with applications to CT Dosimetry
Weir, Victor J
2015-01-01
This paper consists of two parts.In the first part, the scatter components of computed tomograpahy dose profiles are modeled using various functions including the solution to Riccati's differential equation. These scatter functions are combined with primary components such as a trapezoidal function and a constructed function that uses the analytic continuation of Heaviside step function. A mathematical theory is developed in Banach space. The modeled function, which is the product of the scatter and primary functions, is used to accurately fit data from the O-arm cone beam imaging system. In a second part of the paper, an approach to dosimtery is developed that shows that the results obtained from the use of a pencil shaped ion chamber is equivalent to that from a farmer chamber. This result is verified by presenting some preliminary experimental data measured in a 64 slice Siemens Sensation scanner.
Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space
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Wei W
2007-01-01
Full Text Available A class of the linear impulsive periodic system with time-varying generating operators on Banach space is considered. By constructing the impulsive evolution operator, the existence of -periodic -mild solution for homogeneous linear impulsive periodic system with time-varying generating operators is reduced to the existence of fixed point for a suitable operator. Further the alternative results on -periodic -mild solution for nonhomogeneous linear impulsive periodic system with time-varying generating operators are established and the relationship between the boundness of solution and the existence of -periodic -mild solution is shown. The impulsive periodic motion controllers that are robust to parameter drift are designed for a given periodic motion. An example given for demonstration.
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
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Chen Rudong
2011-01-01
Full Text Available Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011 and Lu et al. (Nonlinear Anal, 71(3-4, 1032-1041, 2009. 2000 Mathematics subject classification 47H05; 47H09; 65J15
A Banach space-valued ergodic theorem for amenable groups and applications
Pogorzelski, Felix
2012-01-01
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of quasi tilings for these groups. In light of that, constructions of Ornstein and Weiss are extended by quantitative estimates for the covering properties of the corresponding decompositions. Afterwards, we apply the developed methods to obtain an abstract ergodic theorem for a class of functions mapping subsets of the group into some Banach space. Moreover, applications of this convergence result are studied: the uniform existence of the integrated density of states (IDS) for operators on amenable Cayley graphs; the uniform existence of the IDS for operators on discrete structures being quasi-isometric to some amenable group; the approximation of L2-Betti numbers on cellular CW-complexes; the existence of certain densities of clusters in a percolated Cayley graph.
International Nuclear Information System (INIS)
Suppose E is a real uniformly smooth Banach space and K is a nonempty closed convex and bounded subset of E, T:K → K is a Lipschitz pseudo-contraction. It is proved that the Picard iterates of a suitably defined operator converges strongly to the unique fixed point of T. Furthermore, this result also holds for the slightly larger class of Lipschitz strong hemi-contractions. Related results deal with strong convergence of the Picard iterates to the unique solution of operator equations involving Lipschitz strongly accretive maps. Apart from establishing strong convergence, our theorems give existence, uniqueness and convergence-rate which is at least as fast as a geometric progression. (author). 51 refs
Hybrid Approximate Proximal Point Algorithms for Variational Inequalities in Banach Spaces
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Yao JC
2009-01-01
Full Text Available Let be a nonempty closed convex subset of a Banach space with the dual , let be a continuous mapping, and let be a relatively nonexpansive mapping. In this paper, by employing the notion of generalized projection operator we study the variational inequality (for short, VI( : find such that for all , where is a given element. By combining the approximate proximal point scheme both with the modified Ishikawa iteration and with the modified Halpern iteration for relatively nonexpansive mappings, respectively, we propose two modified versions of the approximate proximal point scheme L. C. Ceng and J. C. Yao (2008 for finding approximate solutions of the VI( . Moreover, it is proven that these iterative algorithms converge strongly to the same solution of the VI( , which is also a fixed point of .
Improved bounds in the scaled Enflo type inequality for Banach spaces
Giladi, Ohad
2010-01-01
It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \\ge 1, then for every integer n there exists an even integer m X, \\Avg_{x,\\e}[||f(x+ m\\e/2)-f(x)}||_X^p] < C(p,X) m^p\\sum_{j=1}^n\\Avg_x[||f(x+e_j)-f(x)||_X^p], where the expectation is with respect to uniformly chosen x \\in Z_m^n and \\e \\in \\{-1,1\\}^n, and C(p,X) is a constant that depends on p and the Rademacher type constant of X. This improves a bound of m < Cn^{3-2/p} that was obtained in [Mendel, Naor 2007]. The proof is based on an augmentation of the "smoothing and approximation" scheme, which was implicit in [Mendel, Naor 2007].
Song, Guohui; Zhang, Haizhang
2011-01-01
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learn...
On the p-Asplund Space of a Banach Space%Banach空间的p-Asplund伴随空间
Institute of Scientific and Technical Information of China (English)
程立新
2001-01-01
我们称一个定义在Banach空间E上的连续凸函数f具有Frechet可微性质(FDP),如果E上的每个实值凸函数g≤f均在E的一个稠密的Gδ-子集上Frechet可微.本文主要证明了:对任何Banach空间E,均存在一个局部凸的相容拓扑p使得1)(E,p)是Hausdorff局部凸空间;2)E上的每个范数连续具有FDP的凸函数均是p-连续的;3)每个p-连续的凸函数均具有FDP;4)p等价某个范数拓扑当且仅当E是Asplund空间.%Recently, a sequence of articles studied the Frechet differentiability property of convex functions on general Banach spaces and even on topological linear spaces. Cheng et al introduced the notion of the FDP (Frechet differentiability property) of convex functions: an extended real valued proper convex function f on a Banach space E is said to have the FDP if every continuous convex function g with g≤f on E is Frechet differentiable on a dense Gδ subset of E. This paper mainly shows that all such continuous convex functions f on the space E are exactly all continuous convex functions on a locally convex space (E, τ) for some suitably locally convex topology τ, that the space (E, τ) is normable if and only if E is an Asplund space. It also presents a revised version of the main theorems of Cheng et al.
Perturbations of Bessel Sequences of Order p in a Banach Space%Banach空间中P阶Bessel列的扰动
Institute of Scientific and Technical Information of China (English)
王秋芬; 曹怀信; 武海辉
2011-01-01
应用算子论方法研究Banach空间X中p(1＜P＜∞)阶Bessel列的扰动问题,对X中的任一p阶Bessel列f={fi}i∈I,定义了有界线性算子Tf:X*→lp,建立了从全体p阶Bessel列组成的Banach空间BpX(Ⅰ)到算子空间B(X*,lp)上的等距线性同构α:f→Tf,并给出了p阶Bessel列的扰动定理.%With the aid of operator theory, some perturbations of Bessel sequences of order p in a Banach space X were discussed. For a Bessel sequence f = {fi} i∈I of order p in X, we defined a bounded linear operator Tf from X* into lp and established a linear isometry isomorphism a from the space BpX (I) of all the Bessel sequences of order p in a Banach space X into the operator space B(X*,lp) defined by α(f) = Tr. In the light of operator theory, some results on perturbations of Bessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.
Sokhuma, K.; A. Kaewkhao
2010-01-01
Let be a nonempty compact convex subset of a uniformly convex Banach space , and let and be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that and for all . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary by , , where and , are sequences of positive numbers satisfying , , converges strongly to a common fixed point of and ; that is, there exists such tha...
Institute of Scientific and Technical Information of China (English)
Wang Xiong-rui; Quan Jing; Ji You-qing
2015-01-01
The purpose of this article is to introduce a class of total quasi-ϕ-asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-ϕ-asymptotically nonexpan-sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this arti-cle extend and improve the corresponding results of many authors.
Institute of Scientific and Technical Information of China (English)
郭铁信
1996-01-01
A deep representation theorem of random conjugate spaces and its several important applications are given. As an application of the representation theorem, the following basic theorem is also proved: let B* be the conjugate space of a Banach space B, be a given probability space. Then every B*-valued w*-u-measurable function defined on is w*-equivalent to a B*-valued u-measurable function defined on if and only if B* has the Radon-Nikodym property with respect to
Directory of Open Access Journals (Sweden)
J. W. Kitchen
1994-01-01
Full Text Available We study bundles of Banach algebras π:A→X, where each fiber Ax=π−1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π:A→X relates to the standard adjunction of identities to the fibers.
Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces
Ramm, A G
2010-01-01
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\\|F'(u)-F'(v)\\|\\leq \\omega(\\|u-v\\|)$, where $\\omega\\in C([0,\\infty))$, $\\omega(0)=0$, $\\omega(r)>0$ if $r>0$, $\\omega(r)$ is strictly growing on $[0,\\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$ is the Fr\\'{e}chet derivative of $F$, and $A_a:=A+aI.$ Assume that (*) $\\|A^{-1}_a(u)\\|\\leq \\frac{c_1}{|a|^b}$, $|a|>0$, $b>0$, $a\\in L$. Here $a$ may be a complex number, and $L$ is a smooth path on the complex $a$-plane, joining the origin and some point on the complex $a-$plane, $00$ is a small fixed number, such that for any $a\\in L$ estimate (*) holds. It is proved that the DSM (Dynamical Systems Method) \\bee \\dot{u}(t)=-A^{-1}_{a(t)}(u(t))[F(u(t))+a(t)u(t)-f],\\quad u(0)=u_0,\\ \\dot{u}=\\frac{d u}{dt}, \\eee converges to $y$ as $t\\to +\\infty$, where $a(t)\\in L,$ $F(y)=f$, $r(t):=|a(t)|$, and $r(t)=c_4(t+c_2)^{-c_3}$, where $c_j>0$ are some suitably chosen constants, $j=2,3,4.$ Existence of a solution $y$ to the equation $F(u)=f$ is assumed. It is also assu...
Lp-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE
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A. KOSSEVA; S. KOSTADINOV; K. SCHNEIDER
2003-01-01
The notion of Lp-dichotomy for linear differential equations with possibly unbounded oper-ator is introduced. By help of Banach fixed point theorem sufficient conditions for the existenceof bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part areobtained.
Institute of Scientific and Technical Information of China (English)
Li Shan LIU
2001-01-01
In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234-240) is true for1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK ≠φ.This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractivemaps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations andimprovements of the recent results obtained by many authors.
Institute of Scientific and Technical Information of China (English)
Shisheng ZHANG; Lin WANG; Yunhe ZHAO
2013-01-01
The purpose of this article is first to introduce the concept of multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups,which contains many kinds of semigroups as its special cases,and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-φ-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces.The results presented in this article improve and extend the corresponding results announced by many authors recently.
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Plubtieng Somyot
2010-01-01
Full Text Available The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of a countable family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Moreover, we apply our result to the problem of finding a common element of an equilibrium problem and the problem of finding a zero of a maximal monotone operator. Our result improve and extend the corresponding results announced by Takahashi and Zembayashi (2008 and 2009, and many others.
Banach空间的不动点性质%Fixed Point Property in Banach Spaces
Institute of Scientific and Technical Information of China (English)
吴春雪
2007-01-01
Banach空间中的许多几何性质在不动点理论中起着很重要的作用,其中包括一致凸性,Banach-Saks性质和正规结构等等.文中引入了一个新的几何性质(Ag2)*,通过建立Banach空间X中(Ag2)*性质和Banach-Saks性质及UKK性质、一致Frechet可微的关系,得到的结论是:如果Banach空间X是可分的且其对偶空间X*具有(Ag2)*性质,则X及X*具有弱不动点性质.
RICCATI EQUATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS
Curtain, Ruth
2011-01-01
Conditions for the existence of a solution of a Riccati equation to be in some prescribed noncommutative involutive Banach algebras are given. The Banach algebras are inverse-closed subalgebras of the space of bounded linear operators on some Hilbert space, and the Riccati equation has an exponentia
Banach空间范数的 k-点态粗性和 k-粗性%k- pointwise roughness and k- roughness on Banach spaces
Institute of Scientific and Technical Information of China (English)
义德日胡; 苏雅拉图
2012-01-01
对 Banach 空间范数引入了 k-点态粗和 k-粗的概念，利用 Banach 空间理论的方法，给出了 x ∈ S(X)为范数的 k-粗糙点和 X 的范数是 k-粗的一些充分必要条件，证明了(k +1)-粗糙点是 k-粗糙点以及 k-粗糙点与 Fr´echet 可微性的一些结果。特别地，在 k =1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果% In this paper, the k- pointwise rough and k- rough norm on Banach space are introduced. By the method of Banach space theory, the some necessary and suﬃcient conditions of k- rough point of norm and k-rough norm of X are given respectively. We proved that (k + 1)- rough point is k- rough point and obtained some results related with k- rough point and Fr´echet differentiability. In particular, when k = 1 our results contains the results of about rough point of norm, pointwise rough norm and rough norm.
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Lu-Chuan Ceng
2013-01-01
Full Text Available We introduce and analyze hybrid implicit and explicit extragradient methods for finding a zero of an accretive operator and solving a general system of variational inequalities and a fixed point problem of an infinite family of nonexpansive self-mappings in a uniformly convex Banach space X which has a uniformly Gateaux differentiable norm. We establish some strong convergence theorems for hybrid implicit and explicit extra-gradient algorithms under suitable assumptions. Furthermore, we derive the strong convergence of hybrid implicit and explicit extragradient algorithms for finding a common element of the set of zeros of an accretive operator and the common fixed point set of an infinite family of nonexpansive self-mappings and a self-mapping whose complement is strictly pseudocontractive and strongly accretive in X. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.
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Bekkai Messirdi
2015-03-01
Full Text Available Let X and Y two complex Banach spaces and (A,B a pair of bounded linear operators acting on X with value on Y. This paper is concerned with spectral analysis ofthe pair (A;B: We establish some properties concerning the spectrum of the linear operator pencils (A-lambda B when B is not necessarily invertible and lambda is a complex number. Also, we use the functional calculus for the pair (A,B to prove the corresponding spectral mapping theorem for (A,B. In addition, we define the generalized Kato essential spectrum and the closed range spectra of the pair (A,B and we give some relationships between this spectrums. As application, we describe a spectral analysis of quotient operators.
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Boubakari Ibrahimou
2013-01-01
maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.
Normal Structure and Antipodal Points in Banach Spaces%Banach空间的正规结构与对径点
Institute of Scientific and Technical Information of China (English)
高继
2000-01-01
Let X be a Banach space and S(X)={x∈X, ‖x‖=1} be the unit sphere of X. Four new parameters Jε(X)=sup{βε(x), x∈S(X)}, jε(X)=inf{βε(x), x∈S(X)}, Gε(X)=sup{αε(x),x∈S(X)}, and gε(X)=inf{αε(x),x∈S(X)} where βε(x)=sup{min{‖x+εy‖, ‖x-εy‖, y∈S(X)}}, and αε(x)=inf{max{‖x+εy‖, ‖x-εy‖, y∈S(X)}} 0ε1 and x∈S(X), are introduced and studied. The main result is that a Banach space X with Jε(X)＜1+(ε)/(2), or gε(X)＞1+(ε)/(3) for some 0ε1 has uniform normal structure.%假设S(X)是Banach空间X的单位球面,作者引进了四个新的几何参数:Jε(X)=sup{βε(x), x∈S(X)}, jε(X)=inf{βε(x), x∈S(X)}, Gε(X)=sup{αε(x),x∈S(X)}, gε(X)=inf{αε(x),x∈S(X)}, 其中0ε1,βε(x)=sup{min{‖x+εy‖, ‖x-εy‖, y∈S(X)}}, αε(x)=inf{max{‖x+εy‖, ‖x-εy‖, y∈S(X)}}. 讨论了这些参数的性质. 本文主要结果是:如果有一个ε, 0ε1,使得Jε(X)＜1+(ε)/(2)或gε(X)＞1+(ε)/(3),那末X有一致正规结构.
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Jing Zhao
2012-01-01
Full Text Available We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-ϕ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.
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Anousheh Fatemeh
2015-10-01
Full Text Available Let A be a Banach algebra, E be a Banach A-bimodule and Δ E → A be a bounded Banach A-bimodule homomorphism. It is shown that under some mild conditions, the weakΔ''-amenability of E'' (as an A''-bimodule necessitates weak Δ-amenability of E (as an A-bimodule. Some examples of weak-amenable Banach modules are provided as well.
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
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Raja P
2008-01-01
Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
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J. F. Tan
2012-01-01
Full Text Available The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi--asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors.
CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES
Institute of Scientific and Technical Information of China (English)
HANDEGUANG
1996-01-01
This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that erevy linear derivation of a nest algebra algN is continuous provided that one of the following conditions is satisfied:(1)0+（包含）0.(2)X-（包含于）X.(3)there exists a non-trivial idempotnet p in algN such that the range of p belongs to N, It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional.
Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line
Institute of Scientific and Technical Information of China (English)
Mu Fa CHEN
2002-01-01
Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities,spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimatesfor the optimal constants in the inequalities are presented. As a typical application, the logarithmicSobolev constant is carefully examined.
New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph
Hussain, N.; S. Khaleghizadeh; P. Salimi; Akbar, F.
2013-01-01
We introduce the concept of an ${\\alpha }_{c}$ -admissible non-self-mappings with respect to ${\\eta }_{c}$ and establish the existence of PPF dependent fixed and coincidence point theorems for ${\\alpha }_{c}{\\eta }_{c}$ - $\\psi $ -contractive non-self-mappings in the Razumikhin class. As applications of our PPF dependent fixed point and coincidence point theorems, we derive some new fixed and coincidence point results for $\\psi $ -contractions whenever the range space is endowed with a graph ...
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Institute of Scientific and Technical Information of China (English)
魏利; 周海云
2008-01-01
A new projection scheme with errors for zero points of maximal monotone operators is introduced and is proved to be strongly convergent to zero points of maximal monotone operators in Banach space by using the techniques of Lyapunov functional and generalized projection operator,etc.
Institute of Scientific and Technical Information of China (English)
Sheng Fan ZHOU; Qiu Li JIA; Wei SHI
2007-01-01
We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov's ε-entropy of the global attractor for lattice systems.
Institute of Scientific and Technical Information of China (English)
娄健; 何欣枫; 何震
2009-01-01
In this paper,we introduce and study a new system of variational inclusions involving (H,η)-monotone operators in Banach space.Using the resolvent operator associated with (H,η)-monotone operators,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.
Institute of Scientific and Technical Information of China (English)
黄健; 戴正德
2004-01-01
在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.
Fréchet differential of a power series in Banach algebras
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Benedetto Silvestri
2010-01-01
Full Text Available We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \\(C(T : A \\mapsto [A,T]\\. Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.
Visual suppression of the vestibulo-ocular reflex during space flight
Uri, John J.; Thornton, William E.; Moore, Thomas P.; Pool, Sam L.
1989-01-01
Visual suppression of the vestibulo-ocular reflex was studied in 16 subjects on 4 Space Shuttle missions. Eye movements were recorded by electro-oculography while subjects fixated a head mounted target during active sinusoidal head oscillation at 0.3 Hz. Adequacy of suppression was evaluated by the number of nystagmus beats, the mean amplitude of each beat, and the cumulative amplitude of nystagmus during two head oscillation cycles. Vestibulo-ocular reflex suppression was unaffected by space flight. Subjects with space motion sickness during flight had significantly more nystagmus beats than unaffected individuals. These susceptible subjects also tended to have more nystagmus beats before flight.
A generalization of fixed point theorem in 2 -Banach space%2-Banach空间上不动点定理的一个推广
Institute of Scientific and Technical Information of China (English)
朴勇杰; 沈京虎
2011-01-01
The definition and the relative concepts of a 2 -linear norm are introduced on a linear space and the definition of a class Φ of 5 - dimensional functions on R 5+ is given. A convergent sequence { xn } on a 2 - Banach space is constructed by an involution map T satisfying a class Φ of 5 dimensional functions on R 5+, and then the limit of the sequence { xn } being the fixed point of T is proved. The main result generalizes and improves the corresponding result obtained by M S Hhan and M D Hkan.%介绍了线性空间上的2-线性赋范的定义和相关概念并给出了R5+上的5-元函数类Φ的定义.利用2-Banach空间上满足5-元函数类Φ中的对合映射T构造出一类收敛的序列,并证明了该序列的极限正是T的不动点.主要结果推广和改进了由M S Hhan和M D Hkan得到的相应结果.
Nonlinear potentials in function spaces
Rao, Murali; Vondraček, Zoran
2002-01-01
We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capa...
An inner product for a Banach-algebra
International Nuclear Information System (INIS)
An inner product is defined on a commutative Banach algebra with an essential involution and the resultant inner product space is shown to be a topological algebra. Several conditions for its completeness are established and moreover, a decomposition theorem is proved. It is shown that every commutative Banach algebra with an essential involution has an auxiliary norm which turns it into an A*-algebra. (author). 6 refs
A Generation Condition of Integrated Bisemigroup on Banach Space%Banach空间积分双半群的生成条件
Institute of Scientific and Technical Information of China (English)
许跟起; 邵琛
2002-01-01
研究Banach空间中积分双半群的生成条件. 利用算子A的豫解算子,给出了积分双半群T(t)的生成定理. 结果表明:如果对任意的x∈X,f∈X*,以及()|λ|≤δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t), t∈R,S(t)强连续且满足积分双半群的定义.%The generation condition of integrated bisemigroup in Banach space is studied in this paper. Using the resolvent of operator A, a generation theorem of integrated bisemigroup T(t) is proved. The result is showed that if ()|λ|≤δ,λ∈ρ(A), and satisfy 〈∈Lp(R), for all x∈X, f∈X*, then there exists a family operators S(t), t∈R, which is strongly continuous and satisfies the definition of integrated bisemigroup.
Institute of Scientific and Technical Information of China (English)
Javad BALOOEE
2013-01-01
A new system of generalized nonlinear variational-like inclusions involving Amaximal m-relaxed η-accretive (so-called,(A,η)-accretive in [36]) mappings in q-uniformly smooth Banach spaces is introduced,and then,by using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings due to Lan et al.,the existence and uniqueness of a solution to the aforementioned system is established.Applying two nearly uniformly Lipschitzian mappings S1 and S2 and using the resolvent operator technique associated with A-maximal m-relaxed η-accretive mappings,we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q =(S1,S2) which is the unique solution of the aforesaid system.We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions.The results presented in this paper extend and improve some known results in the literature.
Some C∗-algebras which are coronas of non-C∗-Banach algebras
Voiculescu, Dan-Virgil
2016-07-01
We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.
Exploring the Gendering of Space by Using Memory Work as a Reflexive Research Method
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Lia Bryant
2007-09-01
Full Text Available How can memory work be used as a pathway to reflect on the situatedness of the researcher and field of inquiry? The key aim of this article is to contribute to knowledge about the gendering of space developed by feminist geographers by using memory work as a reflexive research method. The authors present a brief review of feminist literature that covers the local and global symbolic meanings of spaces and the power relations within which space is experienced. From the literature they interpret themes of the interconnections between space, place, and time; sexualization of public space; and the bodily praxis of using space. Memories of gendered bodies and landscapes, movement and restricted space, and the disrupting of space allow the exploration of conceptualizations within the literature as active, situated, fragmented, and contextualized.
Ayupov, Sh A
2011-01-01
In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which are strongly spectral and symmetric.
Fundamental aspects of vector-valued Banach limits
Garcia-Pacheco, F. J.; Perez-Fernandez, F. J.
2016-04-01
This paper is divided into four parts. In the first we study the existence of vector-valued Banach limits and show that a real Banach space with a monotone Schauder basis admits vector-valued Banach limits if and only if it is 1-complemented in its bidual. In the second we prove two vector-valued versions of Lorentz' intrinsic characterization of almost convergence. In the third we show that the unit sphere in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X) cannot be obtained via compositions of surjective linear isometries with vector-valued Banach limits. In the final part we show that if X enjoys the Krein-Milman property, then the set of vector-valued Banach limits is a face of the unit ball in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X).
Institute of Scientific and Technical Information of China (English)
2008-01-01
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (Ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A : there exists an element p in S such that Xp(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit ball S*(1) = {f ∈ S* : Xf* 1} of the random conjugate space (S*,X*) of (S,X) is compact under the random weak star topology on (S*,X*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {An : n ∈ N} of at most countably many μ-atoms from E∩A such that E =∪n∞=1 An and for each element F in E∩A, there is an H in the σ-algebra generated by {An : n ∈ N} satisfying μ(F △H) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding classical case. Further, Banach-Bourbaki-Kakutani-mulian (briefly, BBKS) theorem in a complete random normed module is established as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S : Xp 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E∩A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James theorem and
Institute of Scientific and Technical Information of China (English)
GUO TieXin
2008-01-01
Let(Ω,A,μ)be a probability space,K the scalar field R of real numbers or C of complex numbers,and(S,X)a random normed space over K with base(Ω,A,μ).Denote the support of(S,X)by E,namely E is the essentiaI supremum of the ser {A∈A:there exists an element p in S such that Xp(ω)＞0 for almost all ω in A}. In this paper,Banach-Alaoglu theorem in a random normed space is first established as follows:The random closed unit ball S*(1)={f∈S*:X*f≤1}of the random conjugate space(S*,x*)of(S,X)is compact under the random weak star topology on (S*,X*)iff E∩A=:{E∩A|A∈A}is essentially purely μ-atomic(namely,there exists a disjoint family{An:n∈N}of at most countably many μ-atoms from E∩A such that E=∪∞n=1 An and for each element F in E∩A,there is an H in the σ-algebra generated by{An:n∈N)satisfying μ(F△H)=0),whose proof forces us to provide a key topological skill,and thus is much more involved than the corresponding classical case.Further,Banach-Bourbaki-Kakutani-Smulian(briefly,BBKS)theorem in a complete random normed module is established as follows:If(S,X)is a complete random normed module,then the random closed unit ball S(1)={p∈S:Xp≤1}of(S,X)is compact under the random weak topology on(S,X)iff both(S,X)is random reflexive and E∩A is essentially purely μ-atomic.Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module,namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball,but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure,namely their supports are essentially purely μ-atomic.Combining the James theorem and BBKS theorem in complete random normed modules leads directly to an interesting
Institute of Scientific and Technical Information of China (English)
王雄瑞
2011-01-01
In this paper, the author gives some convergence theorems of the sufficient and necessary conditions in determining the convergence of Reich type mean iteration for asymptotically nonexpansive mapping in Banach spaces, such as Hilbert spaces, and some implicit conditions of recent relative papers are deleted.%利用粘性逼近法在Hilbert空间以及lp(1＜p≤2)等空间中给出了判定渐近非扩张非自射映象的Reich均值迭代强收敛的充要条件,并去掉了最近相关文献中的一些复杂条件.
Derivations into Duals of Ideals of Banach Algebras
Indian Academy of Sciences (India)
M E Gorgi; T Yazdanpanah
2004-11-01
We introduce two notions of amenability for a Banach algebra $\\mathcal{A}$. Let be a closed two-sided ideal in $\\mathcal{A}$, we say $\\mathcal{A}$ is -weakly amenable if the first cohomology group of $\\mathcal{A}$ with coefficients in the dual space * is zero; i.e., $H^1(\\mathcal{A},I^*) =\\{0\\}$, and, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the -weak amenability of a Banach algebra $\\mathcal{A}$ for some special closed two-sided ideal .
On the convexity and smoothness of Banach space and its application%Banach空间的凸性和光滑性及其应用
Institute of Scientific and Technical Information of China (English)
方习年
2001-01-01
简要概述国际和国内 Banach空间理论的研究状况 , 综述对 Banach空间的凸性和光滑性所做的工作 : 用线性泛函的函数值作元素构成的行列式、单位球的切片、一致凸定义的形式以及特征函数等形式 ,分别刻划及定义空间的 k- 严格凸、 (局部 )k- 致凸、 k- 强凸、 (局部 )近 - 致凸、近强凸等凸性以及 (局部 )k- 致光滑 , k- 强光滑 (局部 )近 - 致光滑等光滑性 , 并讨论以上空间的关系及性质 ; 给出弱 Banach- Saks性质的新特征 , 引入 B- NUC和 g- NUCε空间概念证明 : 具有 Banach- Saks性质的近 - 致凸空间等价于 B- NUC空间、具有 Banach- Saks性质的 NUCε空间等价于 g- NUCε空间举例说明非 k- NUC空间的 B- NUC空间的存在性 ; 研究近强凸、近非常凸空间的几何性质、拓朴性质 , 并得到 : 近强凸空间中的度量投影具有上半连续性 , 近非常凸空间中的度量投影具有弱上半连续性
Institute of Scientific and Technical Information of China (English)
张育梅; 程毅; 王靖华
2012-01-01
利用同伦方法证明了一类发展方程反周期解在Banach空间中的存在性和唯一性.先构造同伦方程,再对方程做先验估计.最后通过定义解算子,运用拓扑度方法,给出了发展方程反周期解存在的充分条件.%We proved the existence and uniqueness of a class of evolution equation in Banach space using homotopy methods. We constructed a homotopy equation and made α priori, estimate to this equation. Under the definition solution operator conditions, a sufficient condition of existence of solutions was obtained by means of topological degree method.
Institute of Scientific and Technical Information of China (English)
赵吕慧子; 孙经先
2011-01-01
The definition of a class of new operators, convex-power 1-set-contraction operators in Banach spaces is giv en , and the existence of fixed points of this class of operators is studied. By using methods of approximation by opera tors, the fixed point theorems of Rothe and Altman type convex-power 1-set-contraction operators is obtained, which generalize fixed point theorems of 1-set-contraction operators.%在Banach空间中给出了一类新算子——凸幂1集压缩算子的定义,研究了这类新算子不动点的存在性问题,利用算子逼近的方法,获得了Rothe及Altman型凸幂1集压缩算子的不动点定理,推广了1集压缩算子的不动点定理.
Stability of functional equations in Banach algebras
Cho, Yeol Je; Rassias, Themistocles M; Saadati, Reza
2015-01-01
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the l...
Institute of Scientific and Technical Information of China (English)
Abbas NAJATI
2009-01-01
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equation f(x+y/2+z)-g(x-y/2+z)=h(y).This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soe., 72, 297-300 (1978).
Wagon, Stan
1985-01-01
The Banach-Tarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explore
Institute of Scientific and Technical Information of China (English)
刘玉波; 张凤敏; 苟长义
2009-01-01
首先证明了取值于Banach空间上强连续的向量值函数是可积分的;然后用初等方法证明了向量值函数的柯西积分公式和高阶导数公式;最后讨论了取值于lp(p≥1)空间上的向量值函数解析、可积、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式,并且给出了有限维赋范线性空间上的向量值函数连续、解析、可积、柯西定理、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式.%The strongly continuous vector valued functions in Banach space are proved integrable. The Cauchy integral for-mula and higher.derivative formula of vector-valued functions are proved using the elementary method. The relationship be-tween vector valued functions in the space of lp (p≥1) and their componential functions about analyticity, integrability, the Cauchy integral formula and higher derivative formula are discussed. And the relationship between vector valued functions in finite dimensional normed linear space and their componential functions about continuity, analyticity, integrability, Cauchys theorem, the Cauchy integral formula and higher derivative formula are also given.
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) proposes to develop an advanced reflexive structure system to increase the survivability of aerostructures. This reflexive...
The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Fishman, Lior; Reams, Vanessa; Simmons, David
2015-01-01
We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.
Directory of Open Access Journals (Sweden)
Aileen Collier
2016-05-01
Full Text Available Background: There is international consensus of the need for improved palliative and end-of-life care in hospital settings. What is less clear is how such improvements might be realised in practice. Research and practice improvement methodologies need to acknowledge the relational, spiritual, moral and ethical as well as physical dimensions of death and dying if improvements in care are to be achieved. Aims and objectives: The aim of this article is to explore the potential of video-reflexive ethnography as a practice development methodology to improve care of people with a life-limiting illness in the hospital setting. Methods: The study used video-reflexive ethnography and was underpinned by an indigenous research ethical framework. Findings: Study findings highlight the potential of video-reflexive ethnography as a practice development methodology. The reach of video extended internally and externally beyond immediate practice research sites to make hospital dying tangible. The research acted as a disruptive innovation, foregrounding peoples’ (patients and families expertise as well as that of healthcare workers. For some patient and family participants, the research offered a visual legacy. Conclusions: The theories underpinning video-reflexive ethnography and practice development are closely aligned; the former has potential as a practice development methodology to promote person-centred palliative and end-of-life care. The underpinning philosophical, ethical and values framework through which it is applied, along with the skills and aptitude of facilitation, are critical if its potential is to be realised. Implications for practice development: The delivery of person-centred end-of-life care may be facilitated by: Healthcare workers seeing themselves and those they care for differently Healthcare organisations seeing their employees as well as patients and families differently Researchers also being prepared to see themselves differently
Banach function algebras and certain polynomially norm-preserving maps
Hosseini, Maliheh; Sady, Fereshteh
2012-01-01
Let $A$ and $B$ be Banach function algebras on compact Hausdorff spaces $X$ and $Y$, respectively. Given a non-zero scalar $\\alpha$and $s,t\\in \\Bbb N$ we characterize the general form of suitable powers of surjective maps $T, T': A \\longrightarrow B$ satisfying $\\|(Tf)^s (T'g)^t-\\alpha\\|_Y=\\|f^s g^t-\\alpha \\|_X$, for all $f,g \\in A$, where $\\|\\cdot \\|_X$ and $\\|\\cdot \\|_Y$ denote the supremum norms on $X$ and $Y$, respectively. A similar result is given for the case where $T...
Complemented Asymptotically Isometric Copies of c0 in Banach Spaces%Banach空间中的含c0的可补渐进等距copy
Institute of Scientific and Technical Information of China (English)
陈东阳
2005-01-01
Asymptotically isometric versions of Sobczyk's theorem is given, and complemented asymptoti-cally isometric copies of C0 in vector-valued function spaces is discussed.%给出了Sobczyk定理的渐近等距版本,同时也在向量值函数空间中讨论含C0的可补渐进等距copy.
Peterka, Robert J.
Recent studies by Diamond and Markham 1,2 have identified significant correlations between space motion sickness susceptibility and measures of disconjugate torsional eye movements recorded during parabolic flights. These results support an earlier proposal by von Baumgarten and Thümler 3 which hypothesized that an asymmetry of otolith function between the two ears is the cause of space motion sickness. It may be possible to devise experiments that can be performed in the 1 g environment on earth that could identify and quantify the presence of asymmetric otolith function. This paper summarizes the known physiological and anatomical properties of the otolith organs and the properties of the torsional vestibulo-ocular reflex which are relevant to the design of a stimulus to identify otolith asymmetries. A specific stimulus which takes advantage of these properties is proposed.
Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, less than 20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. One result of this study will be to characterize the variability (gain, asymmetry) in both otolith-ocular responses and motion perception during variable radius centrifugation, and measure the time course of post-flight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved
The vestibulo-ocular reflex and its possible roles in space motion sickness
Watt, Douglas G. D.
1987-01-01
Prolonged exposure to an inappropriate vestibulo-ocular reflex (VOR) will usually lead to motion sickness, and it has been predicted on theoretical grounds that VOR gain may be decreased in weightlessness. While experiments during parabolic flight in aircraft tend to confirm this prediction, experiments during orbital spaceflight have led to apparently contradictory results. It is suggested that VOR gain is reduced initially, but that rapid compensatory mechanisms restore it to normal within minutes of reaching weightlessness. However, even though this process may lead to the rapid return of functionally normal gaze stability, it may not protect against the development of motion sickness.
Eventually and asymptotically positive semigroups on Banach lattices
Daners, Daniel; Glück, Jochen; Kennedy, James B.
2016-09-01
We develop a theory of eventually positive C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on Lp-spaces, the Dirichlet-to-Neumann operator on L2 and the Laplacian with non-local boundary conditions on L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call "asymptotic positivity", where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t → ∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.
Spectral theory of linear operators and spectral systems in Banach algebras
Müller, Vladimir
2003-01-01
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...
On Riccati equations in Banach algebras
Curtain, Ruth F
2010-01-01
Let $R$ be a commutative complex Banach algebra with the involution $\\cdot ^\\star$ and suppose that $A\\in R^{n\\times n}$, $B\\in R^{n\\times m}$, $C\\in R^{p\\times n}$. The question of when the Riccati equation
Admissibility of Linear Systems in Banach Spaces
Institute of Scientific and Technical Information of China (English)
GUO Fa-ming
2005-01-01
In this paper, infinite-time p-admissibility of unbounded operators is introduced and the Co-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.
The Maslov index in symplectic Banach spaces
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Zhu, Chaofeng
index. As an application, we consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, we derive a desuspension spectral ow formula for varying well-posed boundary conditions on manifolds...... such decompositions we dene the Maslov index of the curve by symplectic reduction to the classical nite-dimensional case. We prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction, while recovering all the standard properties of the Maslov...
(2-1)-Ideal amenability of triangular banach algebras
Indian Academy of Sciences (India)
S Etemad; M Ettefagh
2015-05-01
Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital Banach algebras and let $\\mathcal{M}$ be an unital Banach $\\mathcal{A}$, $\\mathcal{B}$-module. Also, let $\\mathcal{T}=\\left[\\begin{smallmatrix} \\mathcal{A} & \\mathcal{M}\\\\ & \\mathcal{B}\\end{smallmatrix}\\right]$ be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435–1452) have studied the -weak amenability of triangular Banach algebras. In this paper, we investigate (2-1)-ideal amenability of $\\mathcal{T}$ for all ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2-1)-ideal amenability of $\\mathcal{T}$ depends on (2-1)-ideal amenability of Banach algebras $\\mathcal{A}$ and $\\mathcal{B}$.
The Reflexive Adaptations of School Principals in a "Local" South African Space
Fataar, Aslam
2009-01-01
This paper is an analysis of the work of three principals in an impoverished black township in post-apartheid South Africa. Based on qualitative approaches, it discusses the principals' entry into the township, and their navigation of their schools' surrounding social dynamics. It combines the lenses of "space" and "performance" to analyse the…
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
Indian Academy of Sciences (India)
S J Bhatt; P A Dabhi; H V Dedania
2011-11-01
Given a weighted discrete abelian semigroup $(S,)$, the semigroup $M_(S)$ of -bounded multipliers as well as the Rees quotient $M_(S)/S$ together with their respective weights $\\overline{}$ and $\\overline{}_q$ induced by are studied; for a large class of weights , the quotient $\\ell^1(M_(S),\\overline{})/\\ell^1(S,)$ is realized as a Beurling algebra on the quotient semigroup $M_(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
... area into the arm may be present (these nerves are called brachial plexus). A Moro reflex in an older infant, child, or adult is ... be done to examine the child's muscles and nerves. Diagnostic ... absent reflex, may include: Shoulder x-ray Tests for disorders ...
Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K
Directory of Open Access Journals (Sweden)
Malahayati Malahayati
2013-11-01
Full Text Available The first Baire class of bounded functions on separable metric spaces K denoted by B1(k. One of the most important subclass of B1(k is D(K, by D(K is denoted the class of all functions on K which are differences of bounded semicontinuous functions. In this paper we proved that D(K is abelian Banach algebra and identity element
A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román
2013-01-01
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears ...
Supersets for the spectrum of elements in extended Banach algebras
Directory of Open Access Journals (Sweden)
Morteza Seddighin
1989-01-01
Full Text Available If A is a Banach Algebra with or without an identity, A can be always extended to a Banach algebra A¯ with identity, where A¯ is simply the direct sum of A and C, the algebra of complex numbers. In this note we find supersets for the spectrum of elements of A¯.
Institute of Scientific and Technical Information of China (English)
马吉溥
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: U( x0) E—→F be C1 nonlinear map, where U (x0) is an open set containing point x0∈ E. With the locally fine property for Frechet derivatives f’ (x) and generalized rank theorem for f ’( x), a local conjugacy theorem, i. e. a characteristic condition for f being conjugate to f (x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Applications of locally fine property for operators are further developed. Let E and F be Banach spaces and f: be C1 nonlinear map, where U (x0) is an open set containing point x0∈E. With the locally fine property for Frechet derivatives f′(x) and generalized rank theorem for f′(x), a local conjugacy theorem, i.e. a characteristic condition for f being conjugate to f′(x0) near x0,is proved. This theorem gives a complete answer to the local conjugacy problem. Consequently, several rank theorems in advanced calculus are established, including a theorem for C1 Fredholm map which has been so far unknown. Also with this property the concept of regular value is extended, which gives rise to a generalized principle for constructing Banach submanifolds.
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
Directory of Open Access Journals (Sweden)
Hirasawa Go
2005-01-01
Full Text Available We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to .
Very Smooth Points of Spaces of Operators
Indian Academy of Sciences (India)
T S S R K Rao
2003-02-01
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an -ideal in the space of bounded operators, a very smooth operator attains its norm at a unique vector (up to a constant multiple) and ( ) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon–Nikodým property. We give an example of a smooth Banach space without any very smooth points.
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) will develop an advanced reflexive structure technology system to increase the survivability of future systems constructed of...
Ideal Amenability of Banach Algebras on Locally Compact Groups
Indian Academy of Sciences (India)
M Eshaghi Gordji; S A R Hosseiniun
2005-08-01
In this paper we study the ideal amenability of Banach algebras. Let $\\mathcal{A}$ be a Banach algebra and let be a closed two-sided ideal in $\\mathcal{A}, \\mathcal{A}$ is -weakly amenable if $H^1(\\mathcal{A},I^∗)=\\{0\\}$. Further, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.
Amenability and Contractibility Modulo an Ideal of Banach Algebras
Directory of Open Access Journals (Sweden)
Hamidreza Rahimi
2014-01-01
Full Text Available We investigate the concept of amenability modulo an ideal of Banach algebra, showing that amenability modulo an ideal can be characterized by the existence of virtual and approximate diagonal modulo an ideal. We also study the concept of contractible modulo an ideal of Banach algebra. As a consequence, we prove a version of Selivanov's theorem for a large class of semigroups, including E-inversive E-semigroup and eventually inverse semigroups.
Institute of Scientific and Technical Information of China (English)
向雪萍; 孟京华; 李红
2011-01-01
对具数列的渐近非扩张型映像T给出了修正的Ishikawa Reich-Takahashi迭代序列,讨论其对T的不动点的强收敛性.同时,给出了T有不动点且序列Sm(y)=(1-αm)x+αm Tm y强收敛到T的不动点的充分条件,其中x∈D,y∈D,D是Banach空间E中闭凸子集,αm∈[0.1],αm→1.改进和推广了近期一些文献的相关结果.%The modified lshikawa Reich-Takahashi Iterative sequances for asymptotically nonexpansive type mapping T with sequence of number were discussed, which had a strong convergence for the fixed point of T. The sufficient conditions of the existence of fixed point of T and some sequences Sm (y) = ( 1 - am ) x + am,Tmy converging to a fLxed point of T were derived, with D being an nonempty closed convex subset of a Banach space E,x,y ∈ D, am, ∈[ 0,1 ] and am→l. The outcome improved and extended some recent results.
Modern methods in topological vector spaces
Wilansky, Albert
2013-01-01
Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect
关于Banach共轭算子和Hilbert共轭算子的讨论%Discussion on Banach conjugate operator and Hilbert conjugate operator
Institute of Scientific and Technical Information of China (English)
杨纪华; 李艳秋
2014-01-01
Banach conjugate operator and Hilbert conjugate operator are two very important concepts in functional analysis. Hilbert space is a special Banach space,but the conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and thevast majority textbooks don′t explain the reasons for this definition.Described the reason why conjugate operator in Hilbert space does not follow the definition of conjugate operator in Banach space,and discussed the relationship between the two operators.%Banach共轭算子和Hilbert共轭算子是泛函分析中两个非常重要的概念．Hilbert 空间是特殊的Banach空间，但Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子的定义，并且绝大数教材都没有说明这样定义的原因．阐述了Hilbert空间上的共轭算子没有沿用Banach空间上共轭算子定义的原因，并讨论Hilbert空间中这两种算子的关系.
Mean ergodic operators and reflexive Fréchet lattices
Bonet, J.; De Pagter, B.; Ricker, W.J.
2011-01-01
Connections between (positive) mean ergodic operators acting in Banach lattices and properties of the underlying lattice itself are well understood (see the works of Emel'yanov, Wolff and Zaharopol). For Fréchet lattices (or more general locally convex solid Riesz spaces) there is virtually no infor
Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra
Directory of Open Access Journals (Sweden)
Yang-Hi Lee
2013-01-01
Full Text Available We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, <20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved with vibrotactile feedback of orientation.
Directory of Open Access Journals (Sweden)
M. Kanani Arpatapeh∗
2015-12-01
Full Text Available Let A and B be unital Banach algebras and M be a left A-module and right B-module. We consider generalized derivations associate with Hochschild 2-cocycles on triangular Banach algebra T (related to A, B and M. We characterize this new version of generalized derivations on triangular Banach algebras and we obtain some results for l 1 − direct summands of Banach algebras
Convexity and Banach-Saks Property%凸性和Banach-Saks性质
Institute of Scientific and Technical Information of China (English)
方习年; 王建华
2002-01-01
该文引入ω-NUC空间、(k,k+l)-UR空间,证明了:ω-NUC空间具有Banach-Saks性质(B.S.P),从而推广了[1]中的结果,且包含[2]中相应的结果;2)严格凸的ω-NUC空间是ωR空间;3)k-UR空间是(k,k+l)-UR空间,(k,k+l)-UR空间是(k+l)-NUC空间,这个结论改进和包含了文[2]中的一个结果.
Lackner, J. R.; Graybiel, A.
1981-01-01
Recordings of horizontal nystagmus were obtained on 16 male subjects exposed to repeated patterns of horizontal angular acceleration, constant velocity rotation, and sudden-stop deceleration in the laboratory and in the free-fall and high-force periods of parabolic flight. Nystagmus intensity was a clear function of gravitoinertial force level: slow phase velocity and beat frequency increased during exposure to high force levels and decreased in free-fall compared to values obtained at 1 G. These findings indicate that the gain of the vestibulo-ocular reflex decreases in free-fall. This fact likely accounts for the disorientation and dizziness sometimes experienced by astronauts when moving their heads in the early phases of orbital flight and again after splashdown. The implications of the present findings, both for the etiology and for the treatment of space motion sickness, are discussed.
Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales
Institute of Scientific and Technical Information of China (English)
MA Tao; LIU Peide
2006-01-01
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0 ＜ r≤ 1.Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY
Institute of Scientific and Technical Information of China (English)
TaoChangli; LuShijie; ChenPeixin
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
Vestibulo-spinal reflex mechanisms
Reschke, M. F.
1981-01-01
The specific objectives of experiments designed to investigate postural reflex behavior during sustained weightlessness are discussed. The first is to investigate, during prolonged weightlessness with Hoffmann response (H-reflex) measurement procedures, vestibulo-spinal reflexes associated with vestibular (otolith) responses evoked during an applied linear acceleration. This objective includes not only an evaluation of otolith-induced changes in a major postural muscle but also an investigation with this technique of the adaptive process of the vestibular system and spinal reflex mechanisms to this unique environment. The second objective is to relate space motion sickness to the results of this investigation. Finally, a return to the vestibulo-spinal and postural reflexes to normal values following the flight will be examined. The flight experiment involves activation of nerve tissue (tibial N) with electrical shock and the recording of resulting muscle activity (soleus) with surface electrodes. Soleus/spinal H-reflex testing procedures will be used in conjuction with linear acceleration through the subject's X-axis.
Portraying Reflexivity in Health Services Research.
Rae, John; Green, Bill
2016-09-01
A model is proposed for supporting reflexivity in qualitative health research, informed by arguments from Bourdieu and Finlay. Bourdieu refers to mastering the subjective relation to the object at three levels-the overall social space, the field of specialists, and the scholastic universe. The model overlays Bourdieu's levels of objectivation with Finlay's three stages of research (pre-research, data collection, and data analysis). The intersections of these two ways of considering reflexivity, displayed as cells of a matrix, pose questions and offer prompts to productively challenge health researchers' reflexivity. Portraiture is used to show how these challenges and prompts can facilitate such reflexivity, as illustrated in a research project. PMID:26935721
Portraying Reflexivity in Health Services Research.
Rae, John; Green, Bill
2016-09-01
A model is proposed for supporting reflexivity in qualitative health research, informed by arguments from Bourdieu and Finlay. Bourdieu refers to mastering the subjective relation to the object at three levels-the overall social space, the field of specialists, and the scholastic universe. The model overlays Bourdieu's levels of objectivation with Finlay's three stages of research (pre-research, data collection, and data analysis). The intersections of these two ways of considering reflexivity, displayed as cells of a matrix, pose questions and offer prompts to productively challenge health researchers' reflexivity. Portraiture is used to show how these challenges and prompts can facilitate such reflexivity, as illustrated in a research project.
The Classical Integral Operators in Weighted Lorentz Spaces with Variable Exponent.
D.M. Israfilov; N.P. Tuzkaya
2006-01-01
In this paper the Lorentz spaces with variable exponent are introduced. These Banach function spaces are defined on the base of variable Lebesgue spaces. Boundedness of classical integral operators are proved in variable Lorentz spaces.
Almost Lie structures on an anchored Banach bundle
Cabau, Patrick
2011-01-01
Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"
On Reflection: Is Reflexivity Necessarily Beneficial in Intercultural Education?
Blasco, Maribel
2012-01-01
This article explores how the concept of reflexivity is used in intercultural education. Reflexivity is often presented as a key learning goal in acquiring intercultural competence (ICC). Yet, reflexivity can be defined in different ways, and take different forms across time and space, depending on the concepts of selfhood that prevail and how…
Approximately Linear Mappings in Banach Modules over a C*-algebra
Institute of Scientific and Technical Information of China (English)
Choonkil PARK; Jian Lian CUI
2007-01-01
Let X and Y be vector spaces. The authors show that a mapping f: X → Y satisfies the functional equation 2df(∑2dj=1(-1)j+1xj/2d)=∑2dj=1(-1)j+1f(xj) with f(0) = 0 if and only if the mapping f: X → Y is Cauchy additive, and prove the stability of the functional equation (++) in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, the authors show that every almost homomorphism h: A → B of A into B is a homomorphism when h((2d-1)nuy) = h((2d-1)nu)h(y) or h((2d-1)nuoy) = h((2d-1)nu)oh(y) for all unitaries u ∈ A, all y ∈ A, n= 0, 1, 2,....Moreover, the authors prove the stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
The smooth Banach submanifold B*(E,F) in B(E,F)
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for B*(E,F)={T ∈ B+(E,F):dimN(T)=codimR(T)= ∞} without the characteristic numbers,dimN(A) ,codimR(A) ,index(A) and Rank(A) of the equivalent classes above,it is very diffcult to find which class of operators in B*(E,E) forms a smooth submanifold of B(E,F) . Fortunately,we find that B*(E,F) is just a smooth submanifold of B(E,F) with the tangent space TAB*(E,F)={T ∈ B(E,F) :T N(A) -R(A) } for each A ∈ B*(E,F) . Thus the geometric construction of B+(E,F) is obtained,i.e.,B+(E,F) is a smooth Banach submanifold of B(E,F) ,which is the union of the previous smooth submanifolds disjoint from each other. Meanwhile we give a smooth submanifold S(A) of B(E,F) ,modeled on a fixed Banach space and containing A for any A ∈ B+(E,F) . To end these,results on the generalized inverse perturbation analysis are generalized. Specially,in the case E=F=Rn,it is obtained that the set Σr of all n × n matrices A with Rank(A)=r < n is an arcwise connected and smooth hypersurface(submanifold) in B(Rn) with dimΣr=2nr-r2. Then a new geometrical construction of B(Rn) ,analogous to B+(E,F) ,is given besides its analysis and algebra constructions known well.
Functional Inequalities in Non-Archimedean Normed Spaces
Institute of Scientific and Technical Information of China (English)
Choonkil PARK
2015-01-01
In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in Ba-nach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in non-Archimedean Banach spaces.
The Socle and Finite Dimensionality of some Banach Algebras
Indian Academy of Sciences (India)
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
de Jeu, Marcel
2012-01-01
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points.
On the Banach $*$-algebra crossed product associated with a topological dynamical system
Svensson, Christian
2009-01-01
Given an arbitrary topological dynamical system $\\Sigma = (X, \\sigma)$, where $X$ is a compact Hausdorff space and $\\sigma$ a homeomorphism of $X$, we introduce and analyze the associated Banach $*$-algebra crossed product $\\ell^1 (\\Sigma)$. The $C^*$-envelope of this algebra is the usual $C^*$-crossed product of $C(X)$ by the integers under the automorphism of $C(X)$ induced by $\\sigma$. While the connections between the structure of this $C^*$-algebra and the properties of $\\Sigma$ are well-studied, such considerations concerning $\\ell^1 (\\Sigma)$ are new. We derive equivalences between topological dynamical properties of $\\Sigma$ and structural properties of $\\ell^1 (\\Sigma)$ that have well-known analogues in the $C^*$-algebra context, but also obtain a result on this so-called interplay whose counterpart in the case of $C^* (\\Sigma)$ is false.
Lectures given at the Banach Center and C.I.M.E. Joint Summer School
Lachowicz, Mirosław
2008-01-01
The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.
DEFF Research Database (Denmark)
Ratner, Helene
What Danish school managers can teach STS researchers about epistemological ideals and pragmatic morals. Reflexivity has an ambivalent status in both anthropology and Science and Technology Studies. On the one hand, the critique of representation at the heart of the reflexivity debates of the 1980s......” and “navel gazing” become practical problems which school managers need to deal with. Moreover, they find that the emancipatory hopes of reflexivity (cf. Schön 1991) produces new problems in terms of failing to meet teachers’ practical concerns or even excluding teachers who do not master the vocabulary...... of reflexivity, using managerial strategies as a commentary on social science reflexivity debates....
Tools for analysis of Dirac structures on banach spaces
Iftime, Orest V.; Sandovici, Adrian; Golo, Goran
2005-01-01
Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework
Stochastic antiderivational equations on non-Archimedean Banach spaces
Directory of Open Access Journals (Sweden)
S. V. Ludkovsky
2003-01-01
non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.
SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD ∑r OF B(E,F) AND A DIMENSION FORMULA IN B(IRn,IRm)
Institute of Scientific and Technical Information of China (English)
Jipu Ma
2008-01-01
Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear oper-ators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑#r the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submani-fold in B(E, F) with given expression of its tangent space at each A ∈∑r. In this paper, the equality ∑#r = 1 is proved. Consequently, the following theorem is obtained: for any non-negative integer r, ∑r is a smooth and path connected Banach submanifold in B(E, F) with the tangent space TA∑r={B∈B(E,F): BN(A) R(A)} at each A∈∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = IRn and F = IRm, then ∑r is a smooth and path connected submanifold of B(IRn,IRm) and its dimension is dim ∑r = (m + n)r- r2 for each r, 0 ≤ r < min{n,m}.
Emotionally Colorful Reflexive Games
Tarasenko, Sergey
2011-01-01
This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The major advantages of RGT are its ability to predict human behavior and unfold the entire spectra of reflexion in the human mind. On the other hand, PAD provides ultimate approach to model emotions. It is illustrated that emotions are reflexive processes and, consequently, RGT fused with PAD model is natural solution to model emotional interactions between people. The fusion of RGT and PAD, called Emotional Reflexive Games (ERG), inherits the key features of both components. Using ERG, we show how reflexive control can be successfully applied to model human emotional states. Up to date, EGR is a unique methodology capable of modeling human reflexive processes and emotional aspects simultaneously.
Reflexive intensification in Spanish: Toward a complex reflexive?
DEFF Research Database (Denmark)
Pedersen, Johan
2005-01-01
Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo......Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo...
Vestibular reflexes of otolith origin
Wilson, Victor J.
1988-01-01
The vestibular system and its role in the maintenance of posture and in motion sickness is investigated using cats as experimental subjects. The assumption is that better understanding of the physiology of vestibular pathways is not only of intrinsic value, but will help to explain and eventually alleviate the disturbances caused by vestibular malfunction, or by exposure to an unusual environment such as space. The first project deals with the influence on the spinal cord of stimulation of the vestibular labyrinth, particularly the otoliths. A second was concerned with the properties and neural basis of the tonic neck reflex. These two projects are related, because vestibulospinal and tonic neck reflexes interact in the maintenance of normal posture. The third project began with an interest in mechanisms of motion sickness, and eventually shifted to a study of central control of respiratory muscles involved in vomiting.
Convolution and Involution on Function Spaces of Homogeneous Spaces
Farashahi, Arash Ghaani
2012-01-01
Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\\mu)$ such that the Banach space $L^1(G/H,\\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$.
Directory of Open Access Journals (Sweden)
Mario Cardano
2014-01-01
Full Text Available This essay deals with a relevant and controversial topic – objectivity in ethnographic research. More specifically, I would like to examine how reflexive procedures, more precisely “reflexive account”, can increase the robustness of results gained through an ethnographic research. The essay is organized in five parts. I will start by giving a preliminary definition of the two key concepts which are at the center of the analysis – objectivity and reflexivity. I will then give a brief description of the epistemological framework in which the proposed conceptions of objectivity and reflexivity are located. Thirdly, I move on to consider the epistemic status of ethnographic research, and will emphasize that ethnographies are not just “theory-laden”, as many writers have stated, but also “praxis” or “procedure laden”. In other words, I will stress that it is not only theories which are inevitably embedded in research, influencing how observations can be made; much the same can also be said of the concrete research practices which contribute to determine the experience of the ethnographer and its representation in a text. Fourthly, I will discuss why it is useful to employ reflexive practices, and then immediately afterwards will illustrate the ways in which reflexive descriptions can contribute to greater objectivity of ethnographic accounts. In conclusion, I will discuss a number of objections which have been raised against this use of reflexivity.
Vela Velupillai, K.
2014-01-01
The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...
Institute of Scientific and Technical Information of China (English)
CHENG LIXIN; TENG YANMEI
2005-01-01
This paper presents a type of variational principles for real valued w* lower semicon tinuous functions on certain subsets in duals of locally convex spaces, and resolve a problem concerning differentiability of convex functions on general Banach spaces. They are done through discussing differentiability of convex functions on nonlinear topological spaces and convexification of nonconvex functions on topological linear spaces.
Geometry of Müntz spaces and related questions
Gurariy, Vladimir
2005-01-01
Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Remark on Regularity of Continuous Operators on AL-Spaces
Institute of Scientific and Technical Information of China (English)
冯勋省; 陈滋利
2004-01-01
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
Moduli of Reflexive Sheaves on Smooth Projective 3-folds
Vermeire, Peter
2005-01-01
We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth projective threefolds; this class includes Fano and Calabi-Yau threefolds. We also explore both local and global relationships between moduli spaces of reflexive rank 2 sheaves and the Hilbert scheme of curves.
Approximately
Karimi T; Kaboli Gharetapeh S; Gordji MEshaghi
2009-01-01
Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresp...
DEFF Research Database (Denmark)
Krogsgaard, Michael R; Dyhre-Poulsen, Poul; Fischer-Rasmussen, Torsten
2002-01-01
the anterior cruciate ligament (ACL) was pulled, and tension in the ligament caused activity of the gamma motor neurones of the muscles around the knee. Impulses from the sensory nerves in ACL were activated during motion of the knee, in particular overstretching and combined extension and rotation. In humans......The idea of muscular reflexes elicited from sensory nerves of the cruciate ligaments is more than 100 years old, but the existence of such reflexes has not been proven until the recent two decades. First in animal experiments, a muscular excitation could be elicited in the hamstrings when...
-Metric Space: A Generalization
Directory of Open Access Journals (Sweden)
Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
Sweeney, Mary M.; Urcuioli, Peter J.
2010-01-01
A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was…
Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras
Directory of Open Access Journals (Sweden)
Madjid Eshaghi Gordji
2012-01-01
Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.
Functional calculus and *-regularity of a class of Banach algebras II
Leung, Chi-Wai; Ng, Chi-Keung
2006-10-01
In this article, we define a natural Banach *-algebra for a C*-dynamical system (A,G,[alpha]) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is *-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and *-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press].
Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces
Directory of Open Access Journals (Sweden)
Sahar M. Ali
2007-01-01
Full Text Available We proved the existence of fixed points of non-expansive operators defined on weakly Cauchy spaces in which parallelogram law holds, the given normed space is not necessarily be uniformly convex Banach space or Hilbert space, we reduced the completeness and the uniform convexity assumptions which imposed on the given normed space.
The Intuitionistic Fuzzy Normed Space of Coefficients
Bilalov, B. T.; S. M. Farahani; Guliyeva, F. A.
2012-01-01
Intuitionistic fuzzy normed space is defined using concepts of $t$ -norm and $t$ -conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.
Perceptual rivalry: reflexes reveal the gradual nature of visual awareness.
Naber, Marnix; Frässle, Stefan; Einhäuser, Wolfgang
2011-01-01
Rivalry is a common tool to probe visual awareness: a constant physical stimulus evokes multiple, distinct perceptual interpretations ("percepts") that alternate over time. Percepts are typically described as mutually exclusive, suggesting that a discrete (all-or-none) process underlies changes in visual awareness. Here we follow two strategies to address whether rivalry is an all-or-none process: first, we introduce two reflexes as objective measures of rivalry, pupil dilation and optokinetic nystagmus (OKN); second, we use a continuous input device (analog joystick) to allow observers a gradual subjective report. We find that the "reflexes" reflect the percept rather than the physical stimulus. Both reflexes show a gradual dependence on the time relative to perceptual transitions. Similarly, observers' joystick deflections, which are highly correlated with the reflex measures, indicate gradual transitions. Physically simulating wave-like transitions between percepts suggest piece-meal rivalry (i.e., different regions of space belonging to distinct percepts) as one possible explanation for the gradual transitions. Furthermore, the reflexes show that dominance durations depend on whether or not the percept is actively reported. In addition, reflexes respond to transitions with shorter latencies than the subjective report and show an abundance of short dominance durations. This failure to report fast changes in dominance may result from limited access of introspection to rivalry dynamics. In sum, reflexes reveal that rivalry is a gradual process, rivalry's dynamics is modulated by the required action (response mode), and that rapid transitions in perceptual dominance can slip away from awareness. PMID:21677786
Perceptual rivalry: reflexes reveal the gradual nature of visual awareness.
Directory of Open Access Journals (Sweden)
Marnix Naber
Full Text Available Rivalry is a common tool to probe visual awareness: a constant physical stimulus evokes multiple, distinct perceptual interpretations ("percepts" that alternate over time. Percepts are typically described as mutually exclusive, suggesting that a discrete (all-or-none process underlies changes in visual awareness. Here we follow two strategies to address whether rivalry is an all-or-none process: first, we introduce two reflexes as objective measures of rivalry, pupil dilation and optokinetic nystagmus (OKN; second, we use a continuous input device (analog joystick to allow observers a gradual subjective report. We find that the "reflexes" reflect the percept rather than the physical stimulus. Both reflexes show a gradual dependence on the time relative to perceptual transitions. Similarly, observers' joystick deflections, which are highly correlated with the reflex measures, indicate gradual transitions. Physically simulating wave-like transitions between percepts suggest piece-meal rivalry (i.e., different regions of space belonging to distinct percepts as one possible explanation for the gradual transitions. Furthermore, the reflexes show that dominance durations depend on whether or not the percept is actively reported. In addition, reflexes respond to transitions with shorter latencies than the subjective report and show an abundance of short dominance durations. This failure to report fast changes in dominance may result from limited access of introspection to rivalry dynamics. In sum, reflexes reveal that rivalry is a gradual process, rivalry's dynamics is modulated by the required action (response mode, and that rapid transitions in perceptual dominance can slip away from awareness.
Solvability of the $H^\\infty$ algebraic Riccati equation in Banach algebras
Sasane, Amol
2011-01-01
Let $R$ be a commutative complex unital semisimple Banach algebra with the involution $\\cdot ^\\star$. Sufficient conditions are given for the existence of a stabilizing solution to the $H^\\infty$ Riccati equation when the matricial data has entries from $R$. Applications to spatially distributed systems are discussed.
Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
Directory of Open Access Journals (Sweden)
Won-Gil Park
2012-01-01
Full Text Available We solve the bi-additive functional equation f(x+y,z−w+f(x−y,z+w=2f(x,z−2f(y,w and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
绝对平均有界数列空间Aab(K)%Absolutely Average Bounded Number Sequence Space Aab(K)
Institute of Scientific and Technical Information of China (English)
马凤红; 罗成; 孙凤龙
2011-01-01
Based on the absolutely average convergence of a number sequence,the concept of absolutely average bounded number sequence is given.Space Aab (K) is defined as absolutely average bounded number sequences over the real or complex scalar field K ,which is a space between space 1∞ of bounded number sequences and space Ab (K) of approxmatively bounded number sequences.Moreover,that an equivalent condition of a number sequence is absolutely average bounded is given,and space Aab(K) is a non-separable , non-reflexive Banach space which has neither the Krern-Mil 'man property nor Radon-Nikodym property are proved.%提出了绝对平均有界数列的概念,并由此定义了实(或复)数域K上绝对平均有界的数列空间Aab(K),这是一个介于有界数列空间l∞和近似有界数列空间Ab(K)之间的空间.给出了数列绝对平均有界性的等价条件,证明了空间Aab(K)是不可分的、不自反的、不具有Kre(r)n-Mil'man性质和Radon-Nikod(y)m性质的Banach空间.
Survey on nonlocal games and operator space theory
International Nuclear Information System (INIS)
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states
Survey on nonlocal games and operator space theory
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Survey on nonlocal games and operator space theory
Energy Technology Data Exchange (ETDEWEB)
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
A unified theory of cone metric spaces and its applications to the fixed point theory
Proinov, Petko D
2011-01-01
In this paper we develop a unified theory for cone metric spaces over a solid vector space. As an application of the new theory we present full statements of the iterated contraction principle and the Banach contraction principle in cone metric spaces over a solid vector space.
2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
Ayupov, Shavkat; Kudaybergenov, Karimbergen
2016-03-01
The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.
Proprioceptive reflexes and neurological disorders
Schouten, A.C.
2004-01-01
Proprioceptive reflexes play an important role during the control of movement and posture. Disturbed modulation of proprioceptive reflexes is often suggested as the cause for the motoric features present in neurological disorders. In this thesis methods are developed and evaluated to quantify propri
Acoustic reflex and general anaesthesia.
Farkas, Z
1983-01-01
Infant and small children are not always able to cooperate in impedance measurements. For this reason it was decided, -in special cases, -to perform acoustic reflex examination under general anaesthesia. The first report on stapedius reflex and general anaesthesia was published by Mink et al. in 1981. Under the effect of Tiobutabarbital, Propanidid and Diazepam there is no reflex response. Acoustic reflex can be elicited with Ketamin-hydrochlorid and Alphaxalone-alphadolone acetate narcosis. The reflex threshold remains unchanged and the amplitude of muscle contraction is somewhat increased. The method was used: 1. to assess the type and degree of hearing loss in children with cleft palate and/or lip prior to surgery. 2. to exclude neuromuscular disorders with indication of pharyngoplasties. 3. to quantify hearing level in children--mostly multiply handicapped--with retarded speech development. The results of Behavioral Observation and Impedance Audiometry are discussed and evaluated.
[Reflex seizures, cinema and television].
Olivares-Romero, Jesús
2015-12-16
In movies and television series are few references to seizures or reflex epilepsy even though in real life are an important subgroup of total epileptic syndromes. It has performed a search on the topic, identified 25 films in which they appear reflex seizures. Most seizures observed are tonic-clonic and visual stimuli are the most numerous, corresponding all with flashing lights. The emotions are the main stimuli in higher level processes. In most cases it is not possible to know if a character suffers a reflex epilepsy or suffer reflex seizures in the context of another epileptic syndrome. The main conclusion is that, in the movies, the reflex seizures are merely a visual reinforcing and anecdotal element without significant influence on the plot. PMID:26662874
[Reflex seizures, cinema and television].
Olivares-Romero, Jesús
2015-12-16
In movies and television series are few references to seizures or reflex epilepsy even though in real life are an important subgroup of total epileptic syndromes. It has performed a search on the topic, identified 25 films in which they appear reflex seizures. Most seizures observed are tonic-clonic and visual stimuli are the most numerous, corresponding all with flashing lights. The emotions are the main stimuli in higher level processes. In most cases it is not possible to know if a character suffers a reflex epilepsy or suffer reflex seizures in the context of another epileptic syndrome. The main conclusion is that, in the movies, the reflex seizures are merely a visual reinforcing and anecdotal element without significant influence on the plot.
Studies of the horizontal vestibulo-ocular reflex in spaceflight
Thornton, William E.; Uri, John J.; Moore, Tom; Pool, Sam
1989-01-01
Changes in the vestibulo-ocular reflex (VOR) during space flight have been suspected of contributing to space motion sickness. The horizontal VOR was studied in nine subjects on two space shuttle missions. Active unpaced head oscillation at 0.3 Hz was used as the stimulus to examine the gain and phase of the VOR with and without visual input, as well as the visual suppression of the reflex. No statistically significant changes were noted inflight in the gains or phase shifts of the VOR during any test condition, or between space motion sickness susceptible and nonsusceptible populations. Although VOR suppression was unaffected by spaceflight, the space motion sickness-susceptible group tended to exhibit greater error in the suppression than the nonsusceptible group. It is concluded that at this stimulus frequency, VOR gain is unaffected by space-flight, and any minor individual changes do not seem to contribute to space motion sickness.
ON TOPOLOGICAL LINEAR CONTRACTIONS ON NORMED SPACES AND APPLICATION
Institute of Scientific and Technical Information of China (English)
SHIHMAU-HSIAN; TAMPING-KWAN; TANKOK-KEONG
1999-01-01
Shlnultaneous contractificttions, simultaneous proper contractification8 and scxnlgroup(countable family or finite family) of commuting operators and of non-commuting operatorsare first given. Characterizations are given for single bounded llner operator being a topo-logical proper contraction. By using complexification of a real Banach space and by applying afixed point theorem of Edelstein, it is shown that every compact topological strict contractionon a Banach space is a topological proper contraction. Finally, results on simultaneous propercontractification are applied to study the stability of a common fixed point of maps which areFr6chet differentiable at that point.
On Fixed-point theorems in Intuitionistic Fuzzy metric Space
Samanta, T K; Jebril, Iqbal H
2010-01-01
In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.
Certain Fixed Point Theorems and Application to the Fractal Space
Institute of Scientific and Technical Information of China (English)
Ji You-qing; Ri Song-il
2015-01-01
In this paper, we present some important generalizations of the Banach contraction principle, in which the Lipschitz constant k is replaced by some real-valued control function. For the applications to the fractal space, we obtain the fixed point theorem of the some generalized contraction in the space of fractals.
On the injective tensor product of M-embedded spaces
Directory of Open Access Journals (Sweden)
T. S. S. R. K. Rao
1993-05-01
Full Text Available We exhibit classes of Banach spaces X which are M-embedded i.e., when X is canonically embedded in X**. X is an M-ideal in X**, for which the injective tensor product is again an M-embedded space.
Star product realizations of kappa-Minkowski space
DEFF Research Database (Denmark)
Durhuus, Bergfinnur; Sitarz, Andrzej
2013-01-01
We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products...
A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
2012-01-01
Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g x) =g x for everyg Î L¥, f Î E(X), x Î X, x* Î X*.
Institute of Scientific and Technical Information of China (English)
方习年
2001-01-01
本文通过引入B-NUC Banach空间及WB性质,进一步研究Banach-Saks性质(BSP)与近一致凸及紧完全凸性之间的关系.得到以下主要结果: 1)Banach空间X具有WB性质当且仅当X具有WBanach-Saks性质(WBSP); 2)X是B-NUC空间当且仅当X是具BSP的NUC空间; 3)若X具BSP及(H)性质,则X是CωR空间(紧完全ω-凸空间).
Dentocardiac Reflex: an Allegedly New Subform of the Trigeminocardiac Reflex
Amr Abdulazim; Ashkan Rashad; Behnam Bohluli; Bernhard Schaller; Fatemeh Momen-Heravi; Pooyan Sadr-Eshkevari
2011-01-01
Trigeminocardiac reflex (TCR) is currently defined as a sudden bradycardia and decrease in mean arterial blood pressure by 20% during the manipulation of the branches of trigeminal nerve. TCR, especially during the last decade has been mostly studied in the course of neurosurgical procedures which are supposed to elicit the central subtype of TCR. Previously the well-known oculocardiac reflex was also considered as a subtype of TCR. Recently, surgeons dealing with the other branches of the fi...
Soleus stretch reflex during cycling
DEFF Research Database (Denmark)
Grey, Michael James; Pierce, C. W.; Milner, T. E.;
2001-01-01
The modulation and strength of the human soleus short latency stretch reflex was investigated by mechanically perturbing the ankle during an unconstrained pedaling task. Eight subjects pedaled at 60 rpm against a preload of 10 Nm. A torque pulse was applied to the crank at various positions during...... the crank cycle, producing ankle dorsiflexion perturbations of similar trajectory. The stretch reflex was greatest during the power phase of the crank cycle and was decreased to the level of background EMG during recovery. Matched perturbations were induced under static conditions at the same crank angle...... and background soleus EMG as recorded during the power phase of active pedaling. The magnitude of the stretch reflex was not statistically different from that during the static condition throughout the power phase of the movement. The results of this study indicate that the stretch reflex is not depressed during...
The isometric extension of “into” mappings on unit spheres of AL-spaces
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.
SYSTEM REFLEXIVE STRATEGIC MARKETING MANAGEMENT
Directory of Open Access Journals (Sweden)
A. Dligach
2013-10-01
Full Text Available This article reviews the System Reflexive paradigm of strategic marketing management, being based on the alignment of strategic economic interests of stakeholders, specifically, enterprise owners and hired managers, and consumers. The essence of marketing concept of management comes under review, along with the strategic management approaches to business, buildup and alignment of economic interests of business stakeholders. A roadmap for resolving the problems of modern marketing is proposed through the adoption of System Reflexive marketing theory.
Reflex Sympathetic Dystrophy in Children
Adnan Ayvaz
2013-01-01
Reflex sympathetic dystrophy (chronic regional pain syndrome) isn’t frequently encountered in practical pediatrics and childhood. Reflex sympathetic dystrophy syndrome (RSD) is a disorder characterized by widespread localized pain, often along with swelling, discoloration, trophic changes and autonomic abnormalities such as vasomotor disorders. Its etio-pathogenesis hasn’t been completely determined.The disease can form in an area innerved by a partially damaged nerve...
Practical Reflexivity and Political Science
DEFF Research Database (Denmark)
Berling, Trine Villumsen; Bueger, Christian
2013-01-01
The simplistic but still influential, idea of a clear-cut boundary between science and politics does not capture the complexities of the ongoing “dialogue between science and politics”. Perhaps it never did. Critical Social Science from Mannheim to Kratochwil has made this painstakingly clear. Wi...... on practical reflexivity: The reflexivity about the social and practical positioning or ‘situatedness’ of researchers in their concrete interactions with the world of (policy) practice in which they juggle these pertinent dilemmas....
[Reflex sympathetic dystrophy].
Oliveira, Marta; Manuela, Manuela; Cantinho, Guilhermina
2011-01-01
Reflex Sympathetic Dystrophy is rare in pediatrics. It is a complex regional pain syndrome, of unknown etiology, usually post-traumatic, characterized by dysfunctions of the musculoskeletal, vascular and skin systems: severe persistent pain of a limb, sensory and vascular alterations, associated disability and psychosocial dysfunction. The diagnosis is based in high clinical suspection. In children and adolescents there are aspects that are different from the adult ones. Excessive tests may result in worsening of the clinical symptoms. Bone scintigraphy can help. Pain treatment is difficult, not specific. Physical therapies and relaxation technics give some relief. Depression must be treated. This syndrome includes fibromyalgia and complex regional pain syndrome type I. We present a clinical report of an adolescent girl, referred for pain, cold temperature, pallor and functional disability of an inferior limb, all signals disclosed by a minor trauma. She had been diagnosed depression the year before. The bone scintigraphy was a decisive test. The treatment with gabapentin, C vitamin, physiotherapy and pshycotherapy has been effective. PMID:22713207
Dentocardiac Reflex: an Allegedly New Subform of the Trigeminocardiac Reflex
Directory of Open Access Journals (Sweden)
Amr Abdulazim
2011-05-01
Full Text Available Trigeminocardiac reflex (TCR is currently defined as a sudden bradycardia and decrease in mean arterial blood pressure by 20% during the manipulation of the branches of trigeminal nerve. TCR, especially during the last decade has been mostly studied in the course of neurosurgical procedures which are supposed to elicit the central subtype of TCR. Previously the well-known oculocardiac reflex was also considered as a subtype of TCR. Recently, surgeons dealing with the other branches of the fifth cranial nerve have become more interested in this reflex. Some noteworthy points have been published discussing new aspects of the trigeminocardiac reflex (TCR in simple oral surgical procedures. Arakeri et al. have reviewed the similarities and differences between TCR, vasovagal response (VVR, and syncope. They have also explained a new possible pathway for the reflex during the simple extraction of upper first molars. The present paper aims to briefly discuss these recently presented points. Although the discussed concepts are noteworthy and consistent our preliminary results of our yet to be published studies, it seemed timely for us to discuss some possible shortcomings that may affect the results of such assessments.
Nieto-Lopez theorems in ordered metric spaces
Turinici, Mihai
2011-01-01
The comparison type version of the fixed point result in ordered metric spaces established by Nieto and Rodriguez-Lopez [Acta Math. Sinica (English Series), 23 (2007), 2205-2212] is nothing but a particular case of the classical Banach's contraction principle [Fund. Math., 3 (1922), 133-181].
Random fixed points of non-self maps and random approximations
Directory of Open Access Journals (Sweden)
Ismat Beg
1997-01-01
Full Text Available In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.
THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES
Institute of Scientific and Technical Information of China (English)
LIU SHANGPING; LI BINGREN
2005-01-01
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
Directory of Open Access Journals (Sweden)
Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
On prime and semiprime rings with generalized derivations and non-commutative Banach algebras
Indian Academy of Sciences (India)
MOHD ARIF RAZA; NADEEM UR REHMAN
2016-08-01
Let $R$ be a prime ring of characteristic different from 2 and $m$ a fixed positive integer. If $R$ admits a generalized derivation associated with a nonzero deviation $d$ such that $[F(x), d(y)]_m = [x, y]$ for all $x$, $y$ in some appropriate subset of $R$, then $R$ is commutative. Moreover, we also examine the case $R$ is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer--Werner theorem.
Reflexivity in the research process: psychoanalytic observations
Brown, J. C.
2006-01-01
This paper highlights what psychoanalysis can add to discussions of reflexivity, by specifically describing how reflexivity is conceptualized and fostered on psychoanalytic observation methods courses at the Tavistock Clinic, London. It is demonstrated that this psychological form of reflexivity is relevant to empirical and conceptual work and shown that it shares interesting parallels with debates about reflexivity in social research methods, while also being able to contribute to discussion...
ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS
Institute of Scientific and Technical Information of China (English)
ZHANG Shi-sheng
2006-01-01
The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions,it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.
Educating the Reflexive Practitioner
Directory of Open Access Journals (Sweden)
Marc J. Neveu
2012-09-01
wearing any clothes.Notwithstanding such issues, I do believe the studio holds the potentialto be an empowering learning experience. The intention of this article is to question the mode of instruction in an architectural studio. I’ve structured the paper in three parts. First, I will briefly describe the findingsof the study made by the Carnegie Foundation for the Advancementof Teaching known as the Boyer Report.2 To develop and support the findings of the Boyer Report, I introduce the work of the educator Donald Schön. Though I see much merit in the Boyer Report, and Schön’sproposals, I argue that a more nuanced approach is required. I will recommend, therefore, in the second section of this paper that a meansof architectural education as based on the Socratic method may be amore productive approach. My reading of the Socratic method is basedprimarily on early Socratic dialogues and I will specifically use Charmidesto illustrate the issues that I believe are relevant to studio pedagogy.3 From my analysis of Charmides I will, in the third section of the essay,describe how the Socratic method is beneficial to studio pedagogy threeways: reflexive, non-propositional, and finally how Socrates’ approachmay indeed be practical. This last section will be illustrated with a studentproject. It is my conjecture that the Socratic method offers insight intocurrent discussions of educational theory, namely student-centered,project-based learning.
TRANSIENT RELEASE REFLEXES IN CATONIC SCHIZOPHRENIA
Damodaran, Saji S.; Sinha, Vinod K.
1994-01-01
This case report describes the presence of grasp reflex and palmomental reflex as a state dependant phenomenon in a 23 year old patient with catatonic schizophrenia. A transitory disturbance of frontal lobe function is proposed as the probable mechanism. The need to study the release reflexes as an effort to delineate a neurological “sub group” of schizophrenia is suggested.
Reflexive fatherhood in everyday life
DEFF Research Database (Denmark)
Westerling, Allan
2015-01-01
This article looks at fathering practices in Denmark, using the findings from a research project on everyday family life in Denmark. It takes a social psychological perspective and employs discursive psychology and theories about reflexive modernisation. It shows how fathers orient towards intimacy...
Reflexivity in Narratives on Practice
DEFF Research Database (Denmark)
Jakobsen, Helle Nordentoft; Olesen, Lektor Birgitte Ravn
Previous research has shown how reflexivity is a precondition for knowledge co-production through productive dialogue in organisational contexts because it entails a re-ordering, re-arranging and re-designing of what one knows and therefore creates new angles of vision. In this paper, we draw on...
The reflexive case study method
DEFF Research Database (Denmark)
Rittenhofer, Iris
2015-01-01
This paper extends the international business research on small to medium-sized enterprises (SME) at the nexus of globalization. Based on a conceptual synthesis across disciplines and theoretical perspectives, it offers management research a reflexive method for case study research of postnational...
On the Hahn-Banach theorem for Hilbert C*-modules
Frank, M
1996-01-01
We show that for a given C*-algebra A and for any pair of Hilbert A-modules {{M, }, N subset of M} every bounded A-linear mapping r: N --> A can be continued to a bounded A-linear mapping r': M --> A so that (i) ||r||=||r'||, (ii) r' restricted to N equals r, and (iii) the extended mappings of N' form a Banach $A$-submodule of M' wherein the extensions {r'_n : n in N} of the standardly embedded mappings {r_n = : n in N} subset of M' coincide with the latter, if and only if the multiplier C*-algebra M(A) of A is monotone complete, if and only if the multiplier C*-algebra M(A) of A is additively complete. In this case the restrictions of the extended mappings r' \\in M' to the orthogonal complement of N with respect to M equal zero automatically. This generalized Hahn-Banach theorem is valid for a particular pair {M, N subset of M} of Hilbert A-modules over arbitrary C*-algebras A if and only if the bi-orthogonal complement N^{\\bot\\bot} of the Hilbert A-submodule N taken with respect to the A-bidual Hilbert A-m...
Institute of Scientific and Technical Information of China (English)
M. Eshaghi Gordji; A. Najati; A. Ebadian
2011-01-01
Using fixed point methods,we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms),and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equationrf(x+g/r)+rf(x-g/r)=2f(x)where r is a fixed positive real number in (1,∞).
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
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Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
Lipschitz spaces and bounded mean oscillation of harmonic mappings
Chen, Sh; Vuorinen, M; Wang, X
2012-01-01
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.
Sunder, V S
2016-01-01
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE
Institute of Scientific and Technical Information of China (English)
宋光兴
2003-01-01
By using partial order method, the existence, uniqueness and iterative ap-proximation of solutions for a class of systems of nonlinear operator equations in Banachspace are discussed. The results obtained in this paper extend and improve recent results.
On the mild solutions of higher-order differential equations in Banach spaces
Directory of Open Access Journals (Sweden)
Nguyen Thanh Lan
2003-01-01
Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
CONCEPTS OF DICHOTOMY FOR SKEW-EVOLUTION SEMIFLOWS IN BANACH SPACES
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Mihail Megan
2011-01-01
Full Text Available In this paper we investigate some dichotomy concepts for skew-evolution semiflows in Banachspaces.Our main objective is to estab-lish relations between these concepts.We motivate our approach byillustrative examples.
k-接近一致光滑Bananch空间%k-Nearly Uniformly Smooth Banach Spaces
Institute of Scientific and Technical Information of China (English)
王翠玲; 魏文展; 周玲丽
2006-01-01
定义k-接近一致光滑模,利用其给出k-接近一致光滑(k-NUS)空间的概念,证明k-接近一致光滑空间与k-接近一致凸空间是对偶概念,同时引入具有w*k性质的空间,给出k-接近一致光滑空间的一个特征刻画,并讨论(k+1)-接近一致光滑空间与接近一致光滑和k-一致光滑(kUS)空间的关系.
NEW FIXED POINT THEOREMS FOR P1-COMPACT MAPPINGS IN BANACH SPACES
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
F.E. Browder and W. V. Petryshyn[1] defined the topological degree for Aproper mappings and then W. V. Petryshyn[2] studied a class of A-proper mappings, namely,P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn[2], we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem,Petryshyn's theorem, etc.
Institute of Scientific and Technical Information of China (English)
徐西安
2004-01-01
In this paper, we first obtain some New results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
Institute of Scientific and Technical Information of China (English)
LIU WeiDong; FU KeAng; ZHANG LiXin
2008-01-01
In this paper, we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables. As an interesting application, we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
Indian Academy of Sciences (India)
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Directory of Open Access Journals (Sweden)
Zhiqun Xue
2008-03-01
Full Text Available The purpose of this paper is to compare convergence speed of the Picard and Mann iterations on one hand, Krasnoselskij and Ishikawa iterations on the other hand, for the class of Zamfirescu operators. The results improve corresponding results of (Berinde 2004 and (Babu and Vara Prasad 2006.
An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces
Directory of Open Access Journals (Sweden)
Cabada Alberto
2009-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness.
The fixed point theorems of 1-set-contractive operators in Banach space
Directory of Open Access Journals (Sweden)
Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
Directory of Open Access Journals (Sweden)
Chang Shih-sen
2008-01-01
Full Text Available Abstract In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007, Liu (1996, Osilike (2004, Su and Li (2006, Gu (2007, Xu and Ori (2001.
Proper Splitting for the Generalized Inverse AT,S(2 and Its Application on Banach Spaces
Directory of Open Access Journals (Sweden)
Xiaoji Liu
2012-01-01
Full Text Available A possible type of the operator splitting is studied. Using this operator splitting, we introduce some properties and representations of generalized inverses as well as iterative method for computing various solutions of the restricted linear operator system Ax=b, x∈T, where A∈ℒ(X,Y and T is an arbitrary but fixed subspace of X.
Dinda, Bivas; Jebril, Iqbal H
2011-01-01
In this paper intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are introduced. Intuitionistic fuzzy Banach contraction theorem for M-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Elelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are proved.
Integrating Reflexivity in Livelihoods Research
DEFF Research Database (Denmark)
Prowse, Martin
2010-01-01
Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods researc...... that overcomes the unproductive social science dualism of positivism and social constructivism. The approach is linked to a conceptual framework and a menu of research methods that can be sequenced and iterated in light of research questions.......Much poverty and development research is not explicit about its methodology or philosophical foundations. Based on the extended case method of Burawoy and the epistemological standpoint of critical realism, this paper discusses a methodological approach for reflexive inductive livelihoods research...
Ferro, Leonardo
2013-01-01
El objetivo principal de esta disertación es el estudio de la teoría de las álgebras de Lie–Jordan Banach y su papel en el marco de la mecánica clásica y cuántica y sus aplicaciones en diferentes ámbitos de las matemáticas. La investigación algebraica de los fundamentos de la física surgió de la búsqueda de una formulación “excepcional” para la mecánica cuántica, que finalmente culminó en la formulación de las álgebras de Jordan y las posteriores C∗–álgebras.............
The trigeminocardiac reflex – a comparison with the diving reflex in humans
Lemaitre, Frederic; Chowdhury, Tumul; Schaller, Bernhard
2015-01-01
The trigeminocardiac reflex (TCR) has previously been described in the literature as a reflexive response of bradycardia, hypotension, and gastric hypermotility seen upon mechanical stimulation in the distribution of the trigeminal nerve. The diving reflex (DR) in humans is characterized by breath-holding, slowing of the heart rate, reduction of limb blood flow and a gradual rise in the mean arterial blood pressure. Although the two reflexes share many similarities, their relationship and esp...
Arakeri′s Reflex: an Alternative Pathway for Dento-Cardiac Reflex Mediated Syncope
Veena Arali; Shailaja Reddy; C G Raghuram; Gururaj Arakeri
2010-01-01
Introduction: Dentocardiac reflex, a variant of trigeminocardiac reflex elicited specifically during tooth extraction procedures in den-tal/maxillofacial surgery and is believed to cause syncope with an afferent link mediated by posterior superior alveolar nerve. Another variant of trigeminocardiac reflex which is also of interest to the oral and maxillofacial surgeon is oculocardiac reflex which can be triggered by direct or indirect manipulation of eye globe or muscles around it.The hypothe...
Snakes and articulated arms in an Hilbert space
Pelletier, Fernand
2011-01-01
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [Pe] and [LaPe]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [Ha], [Ro] and proved for a finite dimensional Hilbert space
Two ways to support reflexivity
DEFF Research Database (Denmark)
Adriansen, Hanne Kirstine; Knudsen, Hanne
2013-01-01
’. This requires participants to conduct experiments in their own organization, to reflect on and analyse their experiences with concepts from the curriculum. While the new language and the experimental teaching format are difficult, the participants learn a reflexive practice that can enable them to life up...... Management (MEM). MEM provides the participating managers with a new language that can give them a critical distance to the overload of expectations they meet at work and MEM teaches the participants to translate this new language into practice. The pedagogy used for this is labelled ‘experimental management...
Reflexive choice in Dutch and German
Hendriks, Petra; Hoeks, John C. J.; Spenader, Jennifer
2014-01-01
Standard Dutch and German have two reflexive forms: a weak form ('zich' in Dutch and 'sich' in German) and a strong form ('zichzelf' in Dutch and 'sich selbst' in German). The choice between the two reflexive forms in Dutch has been explained by the selectional restrictions of the verb, distinguishi
Axon reflexes in human cold exposed fingers
Daanen, H.A.M.; Ducharme, M.B.
2000-01-01
Exposure of fingers to severe cold induces cold induced vasodilation (CIVD). The mechanism of CIVD is still debated. The original theory states that an axon reflex causes CIVD. To test this hypothesis, axon reflexes were evoked by electrical stimulation of the middle fingers of hands immersed in wat
Reflexivity in Teams: A Measure and Correlates
M.C. Schippers (Michaéla); D.N. den Hartog (Deanne); P.L. Koopman (Paul)
2005-01-01
textabstractReflexivity -the extent to which teams reflect upon and modify their functioning- has been identified as a possible key factor in the effectiveness of work teams. The aim of the present study was to develop a questionnaire to measure (aspects of) reflexivity, with a focus on team reflect
[Non-reflex activity of the CNS].
Brozek, G
1995-06-01
Recent studies of biological rhythms have modified Sherrington's concept of nervous system as exclusively reflexive to include the fact that some neural activity is also endogenously rhythmic. Reflexes are undoubtedly the most important components of animal's and human behavior. But are reflexes the basic units of all complex movements and acts? Rhythmical movements such as respiration, walking and running and other forms of locomotion, as well as rhythmical alimentary processes such as respiration, walking and running and other forms of locomotion, as well as rhythmical alimentary processes such as licking, mastication, and the peristaltic propulsion of nutrients and waste are examples of acts controlled by intrinsic oscillators, so called central pattern generators. Information from the periphery is, however, essential for controlling the extent and rate of movements. Between reflex and non-reflex activity it is possible to place complex species-specific responses called by ethologists fixed-action patterns. Recent investigators have shown that many complex sequences of behavior like speech or piano playing are determined by an internal plan, rather than being generated by a "chain" of reflexes. Non-reflexive activity appears earlier in ontogeny, and is probably phylogenetically older than reflexes.
Reflexive Learning through Visual Methods
DEFF Research Database (Denmark)
Frølunde, Lisbeth
2014-01-01
recommendations on four aspects that can develop facilitation: being attentive to situatedness, differences, challenges, and nurturing reflexivity. Theoretical perspectives on facilitating with visual methods are discussed using pragmatic and dialogic approaches. A summary of facilitation stages is presented......What. This chapter concerns how visual methods and visual materials can support visually oriented, collaborative, and creative learning processes in education. The focus is on facilitation (guiding, teaching) with visual methods in learning processes that are designerly or involve design. Visual...... or professional, to facilitate with visual methods in a critical, reflective, and experimental way. The chapter offers recommendations for facilitating with visual methods to support playful, emergent designerly processes. The chapter also has a critical, situated perspective. Where. This chapter offers case...
Reflexive Learning through Visual Methods
DEFF Research Database (Denmark)
Frølunde, Lisbeth
2014-01-01
methods are exemplified through two university classroom cases about collaborative idea generation processes. The visual methods and materials in the cases are photo elicitation using photo cards, and modeling with LEGO Serious Play sets. Why. The goal is to encourage the reader, whether student or...... professional, to facilitate with visual methods in a critical, reflective, and experimental way. The chapter offers recommendations for facilitating with visual methods to support playful, emergent designerly processes. The chapter also has a critical, situated perspective. Where. This chapter offers case...... vignettes that refer to design-oriented workshops where student groups generate ideas, such as for a campaign. The cases are set at Roskilde University. How. There are recommendations on how to facilitate workshops and develop your own practice as a reflexive facilitator. Some of the typical facilitation...
The Spaces of Functions of Two Variables of Bounded κΦ-Variation in the Sense of Schramm-Korenblum
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A. Azócar
2015-01-01
Full Text Available The purpose of this paper is twofold. Firstly, we introduce the concept of bounded κΦ-variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of R2. Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra.
[Urinary urgency and reflex incontinence].
Madersbacher, H
1991-07-01
Urge and reflex incontinence are caused by detrusor dysfunction:urgency may be due to hyperactivity or hypersensitivity of the bladder. Neurogenic hyperactivity of the detrusor is called detrusor hyperreflexia: the neurogenic uninhibited bladder is caused by incomplete, and the so-called reflex bladder by complete, suprasacral lesions. The pathophysiology of symptomatic and idiopathic detrusor hyperactivity and the therapeutic armentarium are described. Bladder drill together with biofeedback and pharmacotherapy with spasmolytic drugs - several potent spasmolytic drugs with different modes of action are available - are the basis of treatment for hyperactivity and hypersensitivity of the detrusor. An alternative is electrostimulation: stimulation of the afferents of the pudendal nerve, via the pelvic floor (anal, vaginal), percutaneously (dorsal nerve of the penis, clitoric nerve) or by the implantation of electrodes results in inhibition of the detrusor. Most (80-90%) patients can be treated successfully by conservative means. Operative measurements comprise bladder denervation and bladder augmentation. The results of bladder denervation by transtrigonal phenolization of the pelvic plexus are highly controversial. In patients with uncontrollable hyperactivity of the detrusor, augmentation of the bladder (e.g. clam ileocystoplasty) is the method of choice, while for those with uncontrollable hypersensitivity of the detrusor, cystectomy followed by bladder substitution should be performed as a last resort. Treatment for urinary incontinence due to detrusor hyperreflexia must be selected bearing in mind that bladder emptying is inadequate, in most cases because of dyssynergia between detrusor and external sphincter. Therapy is basically aimed at transforming hyperreflexia of the detrusor into hyporeflexia, primarily by potent spasmolytic drugs.(ABSTRACT TRUNCATED AT 250 WORDS)
Reflexivity and technology in adult learning
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Neil Selwyn
2005-03-01
Full Text Available It is argued by influential commentators such as Ulrich Beck and Scott Lash that we now live in a ‘reflexively modern' age. People are seen to now be free of the structures of modern society and driven instead by individualised opportunities to reflexively engage with their fast-changing social worlds and identities. Taking the notion of reflexive modernisation as its starting point, this paper explores the roles that information technologies (ITs may play in supporting adults' reflexive judgements about, and reflexive engagements with, education and learning. Through an analysis of interview data with 100 adults in the UK the paper finds that whilst a minority of interviewees were using ITs to support and inform reflexive engagementwith learning, the majority of individuals relayed little sign of technology-supported reflexivity when it came to their (nonengagement with education. For most people ITs were found, at best, to reinforce pre-established tendencies to ‘drift' through the formal education system. The paper concludes by considering the implications of these findings for ongoing efforts in developed countries to establish technology-supported ‘learning societies'.
A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES
Institute of Scientific and Technical Information of China (English)
Peyman SALIMI; Pasquale VETRO
2014-01-01
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.
△'-Reflexive Modules and Cogen(P)-Linear Compactness
Institute of Scientific and Technical Information of China (English)
Lin Xin
2005-01-01
In this paper, we introduce the notion of △'-reflexive modules. We investigate the reflexive modules with respect to a partial cotilting (bi)module and obtain a connection between △'-reflexive modules and Cogen(P)-linearly compact modules. The main results generalize the results on reflexive modules with respect to a cotilting bimodule.
Functional Contractive Maps in Triangular Symmetric Spaces
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Mihai Turinici
2013-01-01
Full Text Available Some fixed point results are given for a class of functional contractions acting on (reflexive triangular symmetric spaces. Technical connections with the corresponding theories over (standard metric and partial metric spaces are also being established.
Latencies of Reflex Discharges in Some Oro-facial Reflexes of the Frog
NOMURA, HIROMICHI; Suzuki, Hirokazu
1987-01-01
Unitary reflex discharges were recorded from the branches of the trigeminal nerve innervating the submental and masseter muscles following electrical stimulation of the lingual branch of the glossopharyngeal nerve, the maxillary branch of the trigeminal nerve and the mandibular branch of the facial nerve. Reflex discharges were effectively elicited by repetitive electrical stimulation of afferent nerves, but the number of reflex impulses as well as the latencies varied from discharge to disch...
Studies of the vestibulo-ocular reflex on STS 4, 5 and 6
Thornton, William E.; Pool, Sam L.; Moore, Thomas P.; Uri, John J.
1988-01-01
The vestibulo-ocular reflex (VOR) may be altered by weightlessness. Since this reflex plays a large role in visual stabilization, it was important to document any changes caused by space flight. This is a report on findings on STS-4 through 6 and is part of a larger study of neurosensory adaptation done on STS-4 through 8. Voluntary horizontal head oscillations at 1/3 Hz with amplitude of 30 deg right and left of center were recorded by a potentiometer and compared to eye position recorded by electroculography under the following conditions: eyes open, head fixed, tracking horizontal targets switched 0, 15, and 30 degrees right and left (optokinetic reflex - OKR - and calibration); eyes open and fixed on static external target with oscillation, (vestibulo ocular reflex, eyes closed - VOR EC); eyes open and wearing opaque goggles with target fixed in imagination (vestibulo-ocular reflex, eyes shaded - VOR ES); and eyes open and fixed on a head synchronized target with head oscillation (VOR suppression). No significant changes were found in voluntary head oscillation frequency or amplitude in those with (n=5), and without (n=3), space motion sickness (SMS), with phase of flight or test condition. Variations in head oscillation were too small to have produced detectable changes in test results.
Sampling and Galerkin reconstruction in reproducing kernel spaces
Cheng, Cheng; Jiang, Yingchun; Sun, Qiyu
2014-01-01
In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin met...
The legacy of care as reflexive learning
García, Marta Rodríguez; Moya, Jose Luis Medina
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through constant comparisons of the categories. Results: the results demonstrate that the tutors' use of reflexive strategies such as didactic questioning, didactic empathy and pedagogical silence contributes to encourage the students' reflection and significant learning. Conclusions: reflexive practice is key to tutors' training and students' learning. PMID:27305180
Entrepreneurship Teaching Conducted as Strategic Reflexive Conversation
DEFF Research Database (Denmark)
Kristiansson, Michael
The paper intends exploring and ascertaining whether the concept of strategic reflexive conversation can profitably be applied to entrepreneurship. As a start, a process of conceptualisation is undertaken, which is instrumental in placing the notion of strategic reflexive conversation...... into a knowledge management perspective. Strategic reflexive conversation is presented in an enhanced and updated version, which is contrasted to entrepreneurship through reflection. The findings indicate and it can be concluded that, with some important reservations, strategic reflexive conversation can...... advantageously, and on a pilot basis, be applied to entrepreneurship in practical environments and within the framework of entrepreneurship-centred teaching. The present theoretical investigation is solely of an introductory nature and steps are considered that can lead to the planning of additional exploratory...
The legacy of care as reflexive learning
García, Marta Rodríguez; Moya, Jose Luis Medina
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through const...
The legacy of care as reflexive learning
Marta Rodríguez García; Jose Luis Medina Moya
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through c...
Demanding Reflexivity: Lazy Ozzie and Other Stories.
McCormack, David
2007-01-01
One of the orthodoxies of supervising research within the framework of a radical approach to adult education is that you 'demand' a reflexive approach. That is, you ask that the researcher adopt a paradigm of research that does not pretend scientific validity, one that recognises that the researcher's own assumptions, experiences and subjectivity constitute the major source of colour in the canvas he or she is painting. Reflexivity in research involves developing 'critical literacy' by not...
The passive of reflexive verbs in Icelandic
Directory of Open Access Journals (Sweden)
Hlíf Árnadóttir
2011-10-01
Full Text Available The Reflexive Passive in Icelandic is reminiscent of the so-called New Passive (or New Impersonal in that the oblique case of a passivized object NP is preserved. As is shown by recent surveys, however, speakers who accept the Reflexive Passive do not necessarily accept the New Passive, whereas conversely, speakers who accept the New Passive do also accept the Reflexive Passive. Based on these results we suggest that there is a hierarchy in the acceptance of passive sentences in Icelandic, termed the Passive Acceptability Hierarchy. The validity of this hierarchy is confirmed by our diachronic corpus study of open access digital library texts from Icelandic journals and newspapers dating from the 19th and 20th centuries (tímarit.is. Finally, we sketch an analysis of the Reflexive Passive, proposing that the different acceptability rates of the Reflexive and New Passives lie in the argument status of the object. Simplex reflexive pronouns are semantically dependent on the verbs which select them, and should therefore be analyzed as syntactic arguments only, and not as semantic arguments of these verbs.
Brauer-Thrall for totally reflexive modules
Christensen, Lars Winther; Rahmati, Hamidreza; Striuli, Janet; Wiegand, Roger
2010-01-01
Let R be a commutative noetherian local ring that is not Gorenstein. It was recently discovered that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R,m) with m^3=0 are commonly regarded as the structurally simplest rings to admit diverse categorical and homological characteristics. For such rings we obtain conclusive results about the category of totally reflexive modules, modeled on the Brauer-Thrall conjectures. Starting from a non-free cyclic totally reflexive module, we construct a family of indecomposable totally reflexive R-modules that contains, for every n in N, a module that is minimally generated by n elements. Moreover, if the residue field R/m is algebraically closed, then we construct for every n in N an infinite family of indecomposable and pairwise non-isomorphic totally reflexive R-mo...
复指数函数系在Lpα空间中的完备性%Completeness of Complex Exponential System in Space
Institute of Scientific and Technical Information of China (English)
闫峰; 邓冠铁
2008-01-01
A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space Lpα = {f : f∞-∞ |f(t)e-α(t)|pdt ∞}, where 1 ≤ p + ∞and α(t) is a nonnegative continuous function on R.
On weakly Radon-Nikod\\'ym compact spaces
Martínez-Cervantes, Gonzalo
2015-01-01
A compact space is said to be weakly Radon-Nikod\\'ym if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of $\\ell_1$. In this work we provide an example of a continuous image of a Radon-Nikod\\'ym compact space which is not weakly Radon-Nikod\\'ym. Moreover, we define a superclass of the continuous images of weakly Radon-Nikod\\'ym compact spaces and study its relation with Corson compacta and weakly Radon-Nikod\\'ym compacta.
Perenboom, M.J.L.; Ruit, van de M.; Groot, de J.H.; Schouten, A.C.; Meskers, C.G.M.
2015-01-01
Adaptation of reflexes to environment and task at hand is a key mechanism in optimal motor control, possibly regulated by the cortex. In order to locate the corticospinal integration, i.e. spinal or supraspinal, and to study the critical temporal window of reflex adaptation, we combined transcranial
RELIABLE ASSESSMENT OF THE HUMAN NOCICEPTIVE WITHDRAWAL REFLEX AND REFLEX RECEPTIVE FIELDS
DEFF Research Database (Denmark)
Jensen, Michael Brun
The nociceptive withdrawal reflex (NWR) is considered a reliable and objective tool in pain assessment. It is often assessed by estimation of a single NWR threshold (NWR-T) but spatial assessment is possible by quantification of the reflex receptive field (RRF). Both methods are sufficiently...
Bastiaanse, Catharina Maria
2003-01-01
This thesis describes six studies on the influence of active movements and body loading on reflex responses. To measure those influences healthy subjects were asked to walk with different loadings (e.g. a backpack) or with different active movements (e.g. arm swing) while different reflex responses
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Laowang W; Panyanak B
2010-01-01
Suppose that is a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto . Let be a nonexpansive nonself mapping with . Suppose that is generated iteratively by , , , where and are real sequences in for some . Then -converges to some point in . This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.
Integral type operators from normal weighted Bloch spaces to QT,S spaces
Directory of Open Access Journals (Sweden)
Yongyi GU
2016-08-01
Full Text Available Operator theory is an important research content of the analytic function space theory. The discussion of simultaneous operator and function space is an effective way to study operator and function space. Assuming that is an analytic self map on the unit disk Δ, and the normal weighted bloch space μ-B is a Banach space on the unit disk Δ, defining a composition operator C∶C(f=f on μ-B for all f∈μ-B, integral type operator JhC and CJh are generalized by integral operator and composition operator. The boundeness and compactness of the integral type operator JhC acting from normal weighted Bloch spaces to QT,S spaces are discussed, as well as the boundeness of the integral type operators CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.
Variable Lebesgue spaces and hyperbolic systems
2014-01-01
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some mor...
The effect of elbow position on biceps tendon reflex
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Keles Isik
2004-07-01
Full Text Available Background: Testing of tendon (T reflex is the basic method used in the diagnostic procedure of clinical neurology. Measurement of T reflexes precisely can be a valuable adjunct to clinical examination. Quantification of T reflexes may provide more accurate results. Aims: To analyze the effect of elbow position on biceps T reflex. Settings and Design: A self-controlled clinical trial of biceps T reflex testing at the Electrophysiology Unit of the Department of Physical Medicine and Rehabilitation. Methods and Materials: Biceps T reflex was obtained utilizing a hand-held electronic reflex hammer in 50 extremities of 25 healthy volunteers and the effect of elbow position (at 90°, 120° and 150° on reflex response was evaluated. Statistical Analysis: Repeated-measures analysis of variance by the General Linear Model and Pearson correlation test procedures. Results: Onset latency was significantly shorter at 120° of elbow position. The maximum amplitude value of biceps T reflex was obtained at 90° of elbow position. Onset latency of the reflex correlated significantly with the height and arm length but not with age. Conclusions: The electrophysiological measurement of T reflexes is an easy and useful method in the quantification of reflexes, supplying more objective data. However, when performing T reflex studies, the position of the extremity should be taken into consideration to achieve more reliable results.
Directory of Open Access Journals (Sweden)
Maziar Nekovee
2010-01-01
Full Text Available Cognitive radio is being intensively researched as the enabling technology for license-exempt access to the so-called TV White Spaces (TVWS, large portions of spectrum in the UHF/VHF bands which become available on a geographical basis after digital switchover. Both in the US, and more recently, in the UK the regulators have given conditional endorsement to this new mode of access. This paper reviews the state-of-the-art in technology, regulation, and standardisation of cognitive access to TVWS. It examines the spectrum opportunity and commercial use cases associated with this form of secondary access.
Reflexive structures an introduction to computability theory
Sanchis, Luis E
1988-01-01
Reflexive Structures: An Introduction to Computability Theory is concerned with the foundations of the theory of recursive functions. The approach taken presents the fundamental structures in a fairly general setting, but avoiding the introduction of abstract axiomatic domains. Natural numbers and numerical functions are considered exclusively, which results in a concrete theory conceptually organized around Church's thesis. The book develops the important structures in recursive function theory: closure properties, reflexivity, enumeration, and hyperenumeration. Of particular interest is the treatment of recursion, which is considered from two different points of view: via the minimal fixed point theory of continuous transformations, and via the well known stack algorithm. Reflexive Structures is intended as an introduction to the general theory of computability. It can be used as a text or reference in senior undergraduate and first year graduate level classes in computer science or mathematics.
A reflex resonance model of vocal vibrato
Titze, Ingo R.; Story, Brad; Smith, Marshall; Long, Russel
2002-05-01
A reflex mechanism with a long latency (>40 ms) is implicated as a plausible cause of vocal vibrato. At least one pair of agonist-antagonist muscles that can change vocal-fold length is needed, such as the cricothyroid muscle paired with the thyroarytenoid muscle, or the cricothyroid muscle paired with the lateral cricoarytenoid muscle or a strap muscle. Such an agonist-antagonist muscle pair can produce negative feedback instability in vocal-fold length with this long reflex latency, producing oscillations on the order of 5-7 Hz. It is shown that singers appear to increase the gain in the reflex loop to cultivate the vibrato, which grows out of a spectrum of 0-15-Hz physiologic tremors in raw form.
Reflexive Planning as Design and Work
DEFF Research Database (Denmark)
Lissandrello, Enza; Grin, John
2011-01-01
In recent years, planning theorists have advanced various interpretations of the notion of reflexivity, inspired by American pragmatism, complexity theory, hermeneutics, discursive and collaborative planning. Scholars agree that “reflexivity” has a strong temporal dimension: it not only aims...... to solve present planning problems, but to imagine and understand alternative trajectories for future action. This article explores the practical utility of reflexivity for planners, through a case study that focuses on a project to promote sustainable development in the Port of Amsterdam. Reflexivity...... in planning emerges as a new tool for generating critical knowledge and dialogue that can synthesise the perspectives of multiple actors in a common understanding, existing structural constraints and a collective imagination of alternative future possibilities. Such research highlights the potential...
Visual reflex seizures induced by complex stimuli.
Zifkin, Benjamin G; Inoue, Yushi
2004-01-01
Visual reflex seizures induced by complex stimuli may be triggered by patterned and flashing displays that are now ubiquitous. The seizures may be clinically generalized, but unilateral and bilateral myoclonic attacks also may be triggered, especially in patients with juvenile myoclonic epilepsy, and recently, clearly focal reflex occipital lobe seizures have been described. Some seizure-triggering properties of video displays can be identified, such as perceived brightness, pattern, flicker frequency, and color. Knowledge of these is useful in planning individual treatment and in designing regulations for screen content of television broadcasts or for other video displays. Some subjects will also be sensitive to cognitive or action-programming activation, especially when playing video games, and this can increase the chance of seizure triggering. Nonspecific factors such as sleep deprivation, prolonged exposure, and drug or alcohol use also may play a role in reflex seizure occurrence. PMID:14706042
Directory of Open Access Journals (Sweden)
Francesca Pistone
2014-11-01
Full Text Available In its historical parabola from safeguard to control, from hospitals to their surroundings, from institutions to facilities, from diseases to actual human people, the function of health facilities in Italy has progressively become that of decrypting the complex social context in which they act. In accordance with this historical development, the author debates on how disability questions the whole political and social space of health services and interprets the demand for care and the need for socialization within a more general relational system. The questioning of human bodies as cultural and political predicates, the regard for the subjectivity of citizens and for a consequent socio-cultural calibration of health services, are the main anthropological goals in which the care of disability can be involved. The ethnographic case study of a “A.s.l.” in Rome is presented and discussed by the author as an example of such a turning from a “public” to a “communal” institution where narrative and autoreflexivity can be used as a project shift toward a destination culture of institutions where anthropology (its gaze and even its expographic writing can be involved in a multidisciplinary équipe.
Anatomy and neuro-pathophysiology of the cough reflex arc
Polverino Mario; Polverino Francesca; Fasolino Marco; Andò Filippo; Alfieri Antonio; De Blasio Francesco
2012-01-01
Abstract Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the...
Brainstem reflexes and brainstem auditory evoked responses in Huntington's chorea.
Bollen, E; Arts, R.J.; Roos, R A; van der Velde, E A; Buruma, O J
1986-01-01
Blink reflex, corneal reflex, jaw reflex, exteroceptive suppression in masseter muscles and brainstem auditory evoked potentials were measured in 20 patients with Huntington's chorea and 12 controls. A significantly increased latency of the second component of the homolateral and heterolateral blink reflex was found in the patient group as compared with the controls. The other investigations revealed no significant differences between patients and controls except for some facilitation of the ...
Elements of mathematics topological vector spaces
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).
Vestibulospinal control of reflex and voluntary head movement
Boyle, R.; Peterson, B. W. (Principal Investigator)
2001-01-01
Secondary canal-related vestibulospinal neurons respond to an externally applied movement of the head in the form of a firing rate modulation that encodes the angular velocity of the movement, and reflects in large part the input "head velocity in space" signal carried by the semicircular canal afferents. In addition to the head velocity signal, the vestibulospinal neurons can carry a more processed signal that includes eye position or eye velocity, or both (see Boyle on ref. list). To understand the control signals used by the central vestibular pathways in the generation of reflex head stabilization, such as the vestibulocollic reflex (VCR), and the maintenance of head posture, it is essential to record directly from identified vestibulospinal neurons projecting to the cervical spinal segments in the alert animal. The present report discusses two key features of the primate vestibulospinal system. First, the termination morphology of vestibulospinal axons in the cervical segments of the spinal cord is described to lay the structural basis of vestibulospinal control of head/neck posture and movement. And second, the head movement signal content carried by the same class of secondary vestibulospinal neurons during the actual execution of the VCR and during self-generated, or active, rapid head movements is presented.
Madonna as a symbol of reflexive modernisation
M. van den Berg; C.L. ter Hoeven
2013-01-01
The communication of social and cultural tensions embodied in the symbol Madonna explain the unparalleled public and scientific fascination for this cultural phenomenon. These tensions can be seen as communications of reflexive modernisation, in which modernisation has produced its own counterforce.
Dilemmas and Deliberations in Reflexive Ethnographic Research
Robinson, Janean Valerie
2014-01-01
This paper traces insights into the challenges and dilemmas experienced whilst researching students' interpretations and understandings of the Behaviour Management in Schools policy in Western Australia. Journal records, supported by student transcripts, are woven together in a reflexive ethnographic journey--from the beginning phase of…
Reflectivity, Reflexivity and Situated Reflective Practice
Malthouse, Richard; Roffey-Barentsen, Jodi; Watts, Mike
2014-01-01
This paper describes an aspect of reflective practice referred to as situated reflective practice. The overarching theory is derived from social theories of structuration and reflexivity. In particular, from Giddens' theory of structuration, which sees social life as an interplay of agency and structure. Discussion of the research reported…
The reflexive self and culture: a critique.
Adams, Matthew
2003-06-01
This article attempts to engage with a tendency in the theorization of social change and self-identity, evident in the work of a number of contemporary social theorists, to place an extended process of reflexivity at the heart of modern identity. As symptomatic of 'neo-modern' accounts of selfhood, critical readings of Giddens, Beck, Castells and some aspects of social theory more generally, and their account of modern reflexivity's relationship to culture, are assessed. In light of these criticisms, ways in which culture might still play an important part in the shaping of identity are considered. The relationship between language, culture and reflexivity, drawing from philosophy, sociology and G. H. Mead's own brand of social psychology, are all utilized in establishing a critique of the role Giddens and others designate for culture in the constitution of the contemporary self. By potentially repositioning self-identity in its connection to culture, the overall bearing of reflexivity upon the processes of self-identity is thus questioned. It is argued that a culturally-situated, yet fluid and multifarious account of self-identity is a necessary analytical and normative alternative. PMID:12945868
A Reflexive Model for Teaching Instructional Design.
Shambaugh, Neal; Magliaro, Susan
2001-01-01
Documents a five-year study of two instructors who collaborated on formally studying their teaching of a master's level instructional design course. Outlines their views on learning, teaching, and instructional design (ID), describes the ID course, and explains the reflexive instructional model used, in which the teachers examined their teaching…
Directory of Open Access Journals (Sweden)
Mathieu Beraneck
Full Text Available The vestibular organs consist of complementary sensors: the semicircular canals detect rotations while the otoliths detect linear accelerations, including the constant pull of gravity. Several fundamental questions remain on how the vestibular system would develop and/or adapt to prolonged changes in gravity such as during long-term space journey. How do vestibular reflexes develop if the appropriate assembly of otoliths and semi-circular canals is perturbed? The aim of present work was to evaluate the role of gravity sensing during ontogeny of the vestibular system. In otoconia-deficient mice (ied, gravity cannot be sensed and therefore maculo-ocular reflexes (MOR were absent. While canals-related reflexes were present, the ied deficit also led to the abnormal spatial tuning of the horizontal angular canal-related VOR. To identify putative otolith-related critical periods, normal C57Bl/6J mice were subjected to 2G hypergravity by chronic centrifugation during different periods of development or adulthood (Adult-HG and compared to non-centrifuged (control C57Bl/6J mice. Mice exposed to hypergravity during development had completely normal vestibulo-ocular reflexes 6 months after end of centrifugation. Adult-HG mice all displayed major abnormalities in maculo-ocular reflexe one month after return to normal gravity. During the next 5 months, adaptation to normal gravity occurred in half of the individuals. In summary, genetic suppression of gravity sensing indicated that otolith-related signals might be necessary to ensure proper functioning of canal-related vestibular reflexes. On the other hand, exposure to hypergravity during development was not sufficient to modify durably motor behaviour. Hence, 2G centrifugation during development revealed no otolith-specific critical period.
Beraneck, Mathieu; Bojados, Mickael; Le Séac'h, Anne; Jamon, Marc; Vidal, Pierre-Paul
2012-01-01
The vestibular organs consist of complementary sensors: the semicircular canals detect rotations while the otoliths detect linear accelerations, including the constant pull of gravity. Several fundamental questions remain on how the vestibular system would develop and/or adapt to prolonged changes in gravity such as during long-term space journey. How do vestibular reflexes develop if the appropriate assembly of otoliths and semi-circular canals is perturbed? The aim of present work was to evaluate the role of gravity sensing during ontogeny of the vestibular system. In otoconia-deficient mice (ied), gravity cannot be sensed and therefore maculo-ocular reflexes (MOR) were absent. While canals-related reflexes were present, the ied deficit also led to the abnormal spatial tuning of the horizontal angular canal-related VOR. To identify putative otolith-related critical periods, normal C57Bl/6J mice were subjected to 2G hypergravity by chronic centrifugation during different periods of development or adulthood (Adult-HG) and compared to non-centrifuged (control) C57Bl/6J mice. Mice exposed to hypergravity during development had completely normal vestibulo-ocular reflexes 6 months after end of centrifugation. Adult-HG mice all displayed major abnormalities in maculo-ocular reflexe one month after return to normal gravity. During the next 5 months, adaptation to normal gravity occurred in half of the individuals. In summary, genetic suppression of gravity sensing indicated that otolith-related signals might be necessary to ensure proper functioning of canal-related vestibular reflexes. On the other hand, exposure to hypergravity during development was not sufficient to modify durably motor behaviour. Hence, 2G centrifugation during development revealed no otolith-specific critical period. PMID:22808156
New Molecular Knowledge Towards the Trigemino-Cardiac Reflex as a Cerebral Oxygen-Conserving Reflex
Directory of Open Access Journals (Sweden)
N. Sandu
2010-01-01
Full Text Available The trigemino-cardiac reflex (TCR represents the most powerful of the autonomous reflexes and is a subphenomenon in the group of the so-called “oxygen-conserving reflexes”. Within seconds after the initiation of such a reflex, there is a powerful and differentiated activation of the sympathetic system with subsequent elevation in regional cerebral blood flow (CBF, with no changes in the cerebral metabolic rate of oxygen (CMRO2 or in the cerebral metabolic rate of glucose (CMRglc. Such an increase in regional CBF without a change of CMRO2 or CMRglc provides the brain with oxygen rapidly and efficiently. Features of the reflex have been discovered during skull base surgery, mediating reflex protection projects via currently undefined pathways from the rostral ventrolateral medulla oblongata to the upper brainstem and/or thalamus, which finally engage a small population of neurons in the cortex. This cortical center appears to be dedicated to transduce a neuronal signal reflexively into cerebral vasodilatation and synchronization of electrocortical activity; a fact that seems to be unique among autonomous reflexes. Sympathetic excitation is mediated by cortical-spinal projection to spinal preganglionic sympathetic neurons, whereas bradycardia is mediated via projections to cardiovagal motor medullary neurons. The integrated reflex response serves to redistribute blood from viscera to the brain in response to a challenge to cerebral metabolism, but seems also to initiate a preconditioning mechanism. Previous studies showed a great variability in the human TCR response, in special to external stimuli and individual factors. The TCR gives, therefore, not only new insights into novel therapeutic options for a range of disorders characterized by neuronal death, but also into the cortical and molecular organization of the brain.
Voluntary and reflex cough and the expiration reflex; implications for aspiration after stroke
Widdicombe, J G; Addington, W.R.; Fontana, G.A.; Stephens, R.E.
2011-01-01
Abstract Aspiration is a common result of stroke, and may lead to lung infections and pneumonia. Cough may prevent this aspiration and thus prevent the pneumonia. We review the four types of cough usually used to assess aspiration risk: voluntary cough (VC), reflex cough (RC), the laryngeal expiration reflex (LER), and cough on swallow (CoS). VC is easy to test but starts with an inspiration that may cause aspiration, and is controlled by cortico-brainstem pathways that may not be ...
Nice Surjections on Spaces of Operators
Indian Academy of Sciences (India)
T S S R K Rao
2006-11-01
A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on $\\mathcal{K}(X, Y)$ for Banach spaces , . We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for $\\mathcal{L}(X, Y)$ thereby proving an analogue of the result from [9] for $L^p(1 < p ≠ 2 < ∞)$ spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from [8].
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Directory of Open Access Journals (Sweden)
Kalabušić S
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Directory of Open Access Journals (Sweden)
Dž. Burgić
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation zn+1=F(zn,zn−1, n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.
Infinite System of Differential Equations in Some Spaces
Directory of Open Access Journals (Sweden)
M. Mursaleen
2012-01-01
Full Text Available The first measure of noncompactness was defined by Kuratowski in 1930 and later the Hausdorff measure of noncompactness was introduced in 1957 by Goldenštein et al. These measures of noncompactness have various applications in several areas of analysis, for example, in operator theory, fixed point theory, and in differential and integral equations. In particular, the Hausdorff measure of noncompactness has been extensively used in the characterizations of compact operators between the infinite-dimensional Banach spaces. In this paper, we present a brief survey on the applications of measures of noncompactness to the theory of infinite system of differential equations in some spaces and .
Institute of Scientific and Technical Information of China (English)
Yekini SHEHU
2014-01-01
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.
Reflexive regulation of CSR to promote sustainability
DEFF Research Database (Denmark)
Buhmann, Karin
2011-01-01
and the EU CSR Alliance. Focusing on human rights based in international law, it analyses the patterns of negotiation in the MSF and the background for the launch of the CSR Alliance. It shows that analysing public-private regulation of CSR from the perspective of reflexive law theory assists us...... in understanding the mechanisms by which public authorities seek to influence firm’s behaviour through CSR in order to promote public policy objectives. The analysis indicates that to be effective, reflexive regulatory approaches to public-private regulation should pay careful attention to procedural design...... in order to balance power disparities among participants. Finally, the analysis suggests that a juridification of CSR is taking place. This development is welcome because legal theory and scholarship’s insight into institutionalisation of norms of conduct has much to offer to society’s interests...
Reflexive regulation of CSR to promote sustainablility
DEFF Research Database (Denmark)
Buhmann, Karin
and the EU CSR Alliance. Focusing on human rights based in international law, it analyses the patterns of negotiation in the MSF and the background for the launch of the CSR Alliance. It shows that analysing public-private regulation of CSR from the perspective of reflexive law theory assists us...... in understanding the mechanisms by which public authorities seek to influence firm’s behaviour through CSR in order to promote public policy objectives. The analysis indicates that to be effective, reflexive regulatory approaches to public-private regulation should pay careful attention to procedural design...... in order to balance power disparities among participants. Finally, the analysis suggests that a juridification of CSR is taking place. This development is welcome because legal theory and scholarship’s insight into institutionalisation of norms of conduct has much to offer to society’s interests...
ABNORMAL CARDIOVASCULAR REFLEXES IN PATIENTS WITH ACHALASIA
Institute of Scientific and Technical Information of China (English)
戈峰; 李泽坚; 柯美云
1994-01-01
Using 3 non-invasive tests,abnormalities of cardiovascular reflex function were found in 7 of 15 patients with achalasia.Abnormalities of heart rate responses to the Valsalva maneuver,deep breathing ,and standing were moted in patients with autonomic neuropathy defect.The findings are consistent with the hypothesis that an abnormality of vagal function may contribute to the pathogenesis of achalasia.
Reflectivity, reflexivity and situated reflective practice
Malthouse, R; Roffey-Barentsen, J; Watts, DM
2014-01-01
This paper describes an aspect of reflective practice referred to as ‘Situated Reflective Practice’ (SRP). The overarching theory is derived from social theories of structuration and reflexivity. In particular, from Giddens’s (1984) theory of structuration, this sees social life as interplay of agency and structure. Discussion of the research reported here centres on the nature of such situated reflection, considers related literature and presents the data collected in a recent small-scale st...
Axially evoked postural reflexes: influence of task
Govender, Sendhil; Dennis, Danielle L.; Colebatch, James G.
2014-01-01
Postural reflexes were recorded in healthy subjects (n = 17) using brief axial accelerations and tap stimuli applied at the vertebra prominens (C7) and manubrium sterni. Short latency (SL) responses were recorded from the soleus, hamstrings and tibialis anterior muscles and expressed as a percentage of the background EMG prior to stimulus onset. In the majority of postural conditions tested, subjects were recorded standing erect and leaning forward with their feet together. The SL response wa...
Banach空间中的∞阶Bessel序列%Bessel sequence of order ∞ in a Banach space
Institute of Scientific and Technical Information of China (English)
虞志坚; 曹怀信
2001-01-01
在Banach空间中引入了∞阶Bessel序列与 Bessel算子的概念,研究了它们的一系列重要性质,并给出了一个序列成为∞阶Bessel序列的若干充分必要条件,证明了全体∞阶Bessel序列之集构成一个Banach空间.
Bessel sequences of order 1 in a Banach space%Banach空间中的1阶Bessel序列
Institute of Scientific and Technical Information of China (English)
虞志坚; 曹怀信
2005-01-01
在Banach空间X中引入了1阶Bessel序列与Bessel算子的概念,证明了X上的全体1阶Bessel序列构成一个Banach空间;对X上的任意1阶Bessel序列f={fn}n∈∧,引入了算子Tf:X*→l1,给出一个序列成为1阶Bessel序列的若干充分必要条件;引入(1,∞)阶对偶对的概念,证明了(f,g*)成为X×X*中的(1,∞)阶对偶对当且仅当Tf*Tg*|x=IX.
International Nuclear Information System (INIS)
The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs
Widder-Arendt theorem and integrated semigroups in locally convex space
Institute of Scientific and Technical Information of China (English)
肖体俊; 梁进
1996-01-01
A well-known result established by Arendt in 1987 with regard to the Laplace transforms in Banach spaces is developed. A Widder-Arendt theorem in the setting of sequentially complete locally convex spaces is set up (Theorem 1.1). Moreover, integrated semigroups in such spaces are introduced and generation theorems and some basic properties for semigroups of this type are obtained. As examples, elliptic differential operators on certain classes of function spaces with locally convex topology are shown to be the generators of integrated semigroups under some conditions.
The swallowing reflex and its significance as an airway defensive reflex
Directory of Open Access Journals (Sweden)
Takashi eNishino
2013-01-01
Full Text Available Swallowing function, in humans, is very complex. Swallowing plays, not only an important role in food digestion, but also a major role in preventing the entrance of food and/or other materials into the lower respiratory tract. To achieve this, precise coordination is necessary between breathing and swallowing since the pharynx serves as a common pathway for both respiration and digestion. The swallowing reflex consists of afferent pathways, central integration, and efferent pathways. Any defect or disorder along reflex arc can cause a potential delay or impairment in swallow function. The swallowing reflex can be modulated not only by pathological factors but also by physiological factors. Among these, timing of swallows in relation to the phase of respiration may be the most important factor that determines the occurrence of pulmonary aspiration, since phases of inspiration and the expiration-inspiration transition are the most vulnerable for pulmonary aspiration.
An experimental study of artificial murine bladder reflex arc established by abdominal reflex
Institute of Scientific and Technical Information of China (English)
WANG Jin-wu; ZHAO Yu-wu; HOU Chun-lin; NI Wei-feng; RUI Bi-yu; GUO Shang-chun; ZHENG Xian-you; DAI Ke-rong
2011-01-01
Background The neurogenic bladder dysfunction caused by spinal cord injury is difficult to treat clinically. The aim of this research was to establish an artificial bladder reflex arc in rats through abdominal reflex pathway above the level of spinal cord injury, reinnervate the neurogenic bladder and restore bladder micturition.Methods The outcome was achieved by intradural microanastomosis of the right T13 ventral root to S2 ventral root with autogenous nerve grafting, leaving the right T13 dorsal root intact. Long-term function of the reflex arc was assessed from nerve electrophysiological data and intravesical pressure tests during 8 months postoperation. Horseradish peroxidase (HRP) tracing was performed to observe the effectiveness of the artificial reflex.Results Single stimulus (3 mA, 0.3 ms pulses, 20 Hz, 5-second duration) on the right T13 dorsal root resulted in evoked action potentials, raised intravesical pressures and bladder smooth muscle, compound action potential recorded from the right vesical plexus before and after the spinal cord transaction injury between L5 and S4 segmental in 12 Sprague-Dawley rats. There were HRP labelled cells in T13 ventral horn on the experimental side and in the intermediolateral nucleus on both sides of the L6-S4 segments after HRP injection. There was no HRP labelled cell in T13 ventral horn on the control side.Conclusion Using the surviving somatic reflex above the level of spinal cord injury to reconstruct the bladder autonomous reflex arc by intradural microanastomosis of ventral root with a segment of autologous nerve grafting is practical in rats and may have clinical applications for humans.
Cholesteric Liquid Crystal Based Reflex Color Reflective Displays
Khan, Asad
2012-02-01
Bistable color cholesteric liquid crystal displays are unique LCDs that exhibit high reflectivity, good contrast, extremely low power operation, and are amenable to versatile roll-to-roll manufacturing. The display technology, now branded as Reflex has been in commercialized products since 1996. It has been the subject of extensive research and development globally by a variety of parties in both academic and industrial settings. Today, the display technology is in volume production for applications such as dedicated eWriters (Boogie Board), full color electronic skins (eSkin), and displays for smart cards. The flexibility comes from polymerization induced phase separation using unique materials unparalleled in any other display technology. The blend of monomers, polymers, cross linkers, and other components along with nematic liquid crystals and chiral dopants is created and processed in such ways so as to enable highly efficient manufactrable displays using ultra thin plastic substrates -- often as thin as 50μm. Other significant aspects include full color by stacking or spatial separation, night vision capability, ultra high resolution, as well as active matrix capabilities. Of particular note is the stacking approach of Reflex based displays to show full color. This approach for reflective color displays is unique to this technology. Owing to high transparency in wavelength bands outside the selective reflection band, three primarily color layers can be stacked on top of each other and reflect without interfering with other layers. This highly surprising architecture enables the highest reflectivity of any other reflective electronic color display technology. The optics, architecture, electro-topics, and process techniques will be discussed. This presentation will focus on the physics of the core technology and color, it's evolution from rigid glass based displays to flexible displays, development of products from the paradigm shifting concepts to consumer
Skew polynomial rings over abelian and idempotent reflexive rings
Louzari, Mohamed
2015-01-01
Let $R$ be a ring and $\\sigma$ an endomorphism of $R$. In this note, we study skew polynomial rings and skew power series rings over idempotent reflexive rings and abelian rings. Also, we introduce the concept of right (resp., left) $\\sigma$-idempotent reflexive rings which generalizes right (resp., left) idempotent reflexive rings and $\\sigma$-abelian rings. Certain results are obtained as corollaries from our results.
Can Treadmill Perturbations Evoke Stretch Reflexes in the Calf Muscles?
Sloot, Lizeth H.; van den Noort, Josien C; van der Krogt, Marjolein M.; Bruijn, Sjoerd M.; Jaap Harlaar
2015-01-01
Disinhibition of reflexes is a problem amongst spastic patients, for it limits a smooth and efficient execution of motor functions during gait. Treadmill belt accelerations may potentially be used to measure reflexes during walking, i.e. by dorsal flexing the ankle and stretching the calf muscles, while decelerations show the modulation of reflexes during a reduction of sensory feedback. The aim of the current study was to examine if belt accelerations and decelerations of different intensiti...
The Role of Transformational Leadership in Enhancing Team Reflexivity
Schippers, M.C.; Hartog, den, JI Jerry; Koopman, P.L.; Knippenberg, van, D.
2007-01-01
textabstractTeam reflexivity, or the extent to which teams reflect upon and modify their functioning, has been identified as a key factor in the effectiveness of work teams. As yet, however, little is known about the factors that play a role in enhancing team reflexivity, and it is thus important to develop theorizing around the determinants of reflexivity. From an applied perspective, leadership is a very relevant factor. The current study is a first step in the development of such a theory,...
Electrophysiological observations on the human pudendo-anal reflex.
Varma, J S; Smith, A N; McInnes, A
1986-01-01
A reproducible electrophysiological technique is described to determine the latency of reflex contraction of the external anal sphincter in response to stimulation of the dorsal genital nerve: the pudendo-anal reflex. This was studied in 38 asymptomatic control subjects and 20 women with neurogenic faecal incontinence, supplemented by determination of the mean motor unit potential duration (MUPD) of the external anal sphincter and anorectal manometry. The reflex latency in the control group w...
Characteristics of Glottic Closure Reflex in a Canine Model
Kim, Young-Ho; Kang, Ju Wan; Kim, Kwang-Moon
2009-01-01
Purpose The most important function of the larynx is airway protection which is provided through a polysynaptic reflex closure triggered by the receptors in the glottic and supraglottic mucosa, evoking the reflex contraction of the laryngeal muscles especially by strong adduction of vocal cords. Based on the hypotheses that central facilitation is essential for this bilateral adductor reflex and that its disturbance can result in weakened laryngeal closure, we designed this study to elucidate...
Cardiovascular regulation by skeletal muscle reflexes in health and disease
Murphy, Megan N.; Mizuno, Masaki; Mitchell, Jere H.; Smith, Scott A
2011-01-01
Heart rate and blood pressure are elevated at the onset and throughout the duration of dynamic or static exercise. These neurally mediated cardiovascular adjustments to physical activity are regulated, in part, by a peripheral reflex originating in contracting skeletal muscle termed the exercise pressor reflex. Mechanically sensitive and metabolically sensitive receptors activating the exercise pressor reflex are located on the unencapsulated nerve terminals of group III and group IV afferent...
Sympathetic reflex control of blood flow in human peripheral tissues
DEFF Research Database (Denmark)
Henriksen, O
1991-01-01
Sympathetic vasoconstrictor reflexes are essential for the maintenance of arterial blood pressure in upright position. It has been generally believed that supraspinal sympathetic vasoconstrictor reflexes elicited by changes in baroreceptor activity play an important role. Recent studies on human ...... to collision of normodromically and antidromically conducted impulses in efferent sympathetic vasoconstrictor fibers. The evidence obtained suggests that sympathetic vasoconstrictor reflexes to postural changes are complex and highly differentiated....
Cortical control of hering-breuer reflexes in anesthetized rats
Aleksandrov VG; Mercuriev VA; Ivanova TG; Tarasievich AA; Aleksandrova NP
2009-01-01
Abstract It had been hypothesized that the regions of prefrontal cortex which are involved in respiratory control can modulate Hering-Breuer reflexes evoked by vagal input from pulmonary stretch receptors. In the present study, experiments were performed on urethane anesthetized spontaneously breathing Wistar rats. The expiratory-promoting reflex was evaluated from changes in expiratory time immediately after airway occlusion at the end of inspiration. The inspiratory-inhibitory reflex was es...
Anatomy and neuro-pathophysiology of the cough reflex arc
Directory of Open Access Journals (Sweden)
Polverino Mario
2012-06-01
Full Text Available Abstract Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the complex and multiple etiologies of cough.
Energy Technology Data Exchange (ETDEWEB)
Kumar, Deepak, E-mail: deepak.kumar@eli-beams.eu; Englesbe, Alexander; Parman, Matthew; Stutman, Dan; Finkenthal, Michael [Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218 (United States)
2015-11-15
Tabletop reflex discharges in a Penning geometry have many applications including ion sources and eXtreme Ultra-Violet (XUV) sources. The presence of primary electrons accelerated across the cathode sheaths is responsible for the distribution of ion charge states and of the unusually high XUV brightness of these plasmas. Absolutely calibrated space resolved XUV spectra from a table top reflex discharge operating with Al cathodes and Ne gas are presented. The spectra are analyzed with a new and complete model for ion charge distribution in similar reflex discharges. The plasma in the discharge was found to have a density of ∼10{sup 18 }m{sup −3} with a significant fraction >0.01 of fast primary electrons. The implications of the new model on the ion states achievable in a tabletop reflex plasma discharge are also discussed.
Directory of Open Access Journals (Sweden)
E.C. Vasquez
1997-04-01
Full Text Available The maintenance of arterial pressure at levels adequate to perfuse the tissues is a basic requirement for the constancy of the internal environment and survival. The objective of the present review was to provide information about the basic reflex mechanisms that are responsible for the moment-to-moment regulation of the cardiovascular system. We demonstrate that this control is largely provided by the action of arterial and non-arterial reflexes that detect and correct changes in arterial pressure (baroreflex, blood volume or chemical composition (mechano- and chemosensitive cardiopulmonary reflexes, and changes in blood-gas composition (chemoreceptor reflex. The importance of the integration of these cardiovascular reflexes is well understood and it is clear that processing mainly occurs in the nucleus tractus solitarii, although the mechanism is poorly understood. There are several indications that the interactions of baroreflex, chemoreflex and Bezold-Jarisch reflex inputs, and the central nervous system control the activity of autonomic preganglionic neurons through parallel afferent and efferent pathways to achieve cardiovascular homeostasis. It is surprising that so little appears in the literature about the integration of these neural reflexes in cardiovascular function. Thus, our purpose was to review the interplay between peripheral neural reflex mechanisms of arterial blood pressure and blood volume regulation in physiological and pathophysiological states. Special emphasis is placed on the experimental model of arterial hypertension induced by N-nitro-L-arginine methyl ester (L-NAME in which the interplay of these three reflexes is demonstrable
Olyaei G; Akbari M; Esfandiarpoor F
2000-01-01
The purpose of the this study was to investigate the effect of direct current on montoneuron reflex exitability. Thirty six subjects (18 males, 18 females) 19.36 years of age ( x= 24.06, SD= 3.63) participated in this study. The reflex excitability of soleus motoneruons was assessed by measuring the amount of change in the peak to peak ampitude of the H-reflex before and after direct current was applied to the skin over the sural nerve. Reflex recordings were taken before and after direct cur...
Khinchin's Inequality, Dunford-Pettis and Compact Operators on the Space ([0, 1], )
Indian Academy of Sciences (India)
Dumitru Popa
2007-02-01
We prove that if , are Banach spaces, a compact Hausdorff space and :(,) → is a bounded linear operator, and if is a Dunford–Pettis operator the range of the representing measure $G()\\subseteq D P(X, Y)$ is an uniformly Dunford–Pettis family of operators and $\\|G\\|$ is continuous at $\\emptyset$. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space $C([0,1],X)$ with values in $c_0$ or $l_p,(1≤ p < ∞)$ be Dunford–Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.
Gorini, C.; Jameson, H. S.; Mendelowitz, D.
2009-01-01
Stimulation of the trigeminal nerve evokes a dramatic decrease in heart rate and blood pressure, and this reflex has generally been termed the trigeminocardiac reflex. A subset of the trigeminocardiac reflex is the diving reflex in which the nasal mucosa is stimulated with water or air-borne chemical irritants. Activation of the diving reflex evokes a pronounced bradycardia, mediated by increased parasympathetic cardiac activity, and is the most powerful autonomic reflex. However, exaggeratio...
Metabolic syndrome and the hepatorenal reflex
Wider, Michael D.
2016-01-01
Insufficient hepatic O2 in animal and human studies has been shown to elicit a hepatorenal reflex in response to increased hepatic adenosine, resulting in stimulation of renal as well as muscle sympathetic nerve activity and activating the renin angiotensin system. Low hepatic ATP, hyperuricemia, and hepatic lipid accumulation reported in metabolic syndrome (MetS) patients may reflect insufficient hepatic O2 delivery, potentially accounting for the sympathetic overdrive associated with MetS. This theoretical concept is supported by experimental results in animals fed a high fructose diet to induce MetS. Hepatic fructose metabolism rapidly consumes ATP resulting in increased adenosine production and hyperuricemia as well as elevated renin release and sympathetic activity. This review makes the case for the hepatorenal reflex causing sympathetic overdrive and metabolic syndrome in response to exaggerated splanchnic oxygen consumption from excessive eating. This is strongly reinforced by the fact that MetS is cured in a matter of days in a significant percentage of patients by diet, bariatric surgery, or endoluminal sleeve, all of which would decrease splanchnic oxygen demand by limiting nutrient contact with the mucosa and reducing the nutrient load due to the loss of appetite or dietary restriction.
Reflex sympathetic dystrophy: Early treatment and psychological aspects
Geertzen, J.H.B.; De Bruijn, H.; De Bruijn-Kofman, A.T.; Arendzen, J.H.
1994-01-01
We report the results of two prospective studies of early treatment and psychological aspects in a series of 26 patients with sympathetic reflex dystrophy of the hand in which treatment was started within 3 months after diagnosis. Ismelin blocks is an often used therapy in sympathetic reflex dystrop
Ultimate concerns in late modernity: Archer, Bourdieu and reflexivity.
Farrugia, David; Woodman, Dan
2015-12-01
Through a critique of Margaret Archer's theory of reflexivity, this paper explores the theoretical contribution of a Bourdieusian sociology of the subject for understanding social change. Archer's theory of reflexivity holds that conscious 'internal conversations' are the motor of society, central both to human subjectivity and to the 'reflexive imperative' of late modernity. This is established through critiques of Bourdieu, who is held to erase creativity and meaningful personal investments from subjectivity, and late modernity is depicted as a time when a 'situational logic of opportunity' renders embodied dispositions and the reproduction of symbolic advantages obsolete. Maintaining Archer's focus on 'ultimate concerns' in a context of social change, this paper argues that her theory of reflexivity is established through a narrow misreading and rejection of Bourdieu's work, which ultimately creates problems for her own approach. Archer's rejection of any pre-reflexive dimensions to subjectivity and social action leaves her unable to sociologically explain the genesis of 'ultimate concerns', and creates an empirically dubious narrative of the consequences of social change. Through a focus on Archer's concept of 'fractured reflexivity', the paper explores the theoretical necessity of habitus and illusio for understanding the social changes that Archer is grappling with. In late modernity, reflexivity is valorized just as the conditions for its successful operation are increasingly foreclosed, creating 'fractured reflexivity' emblematic of the complex contemporary interaction between habitus, illusio, and accelerating social change.
Normal values of patellar and ankle tendon reflex latencies
Frijns, CJM; Laman, DM; vanDuijn, MAJ; vanDuijn, H
1997-01-01
The clinical value of latency measurement of tendon reflexes in neurological patients has been reported by several authors. However, normal values are not readily comparable. In the present study, latencies and amplitudes of patellar (PTR) and ankle tendon reflexes (ATR) were measured at rest and af
The feasibility of reflexive control in transfemoral prostheses
Wentink, E.C.; Rietman, J.S.; Veltink, P.H.
2009-01-01
The feasibility of reflexive control in transfemoral prosthesis is assessed using a model of the lower extremity. The artificial triggering of reflexes, the processing of the central nervous system, the EMG detection and the control input to the prosthetic knee all take time. A model was used to ass
[The development of I. P. Pavlov's conditioned reflex theory].
Kim, O J
1992-01-01
This paper deals with the theory of Ivan Petrovich Pavlov (1849-1936), a Russian physiologist who presented for the first time the systematic theory of the function of the brain that controls the whole behavior of animals, i.e. higher nervous activity through experimental studies. This paper, principally based on Lectures on Conditioned Reflexes (1928), investigates the development of conditioned reflex theory from its beginning by dividing it into three periods. First, during the period from 1898 to 1906, the fundamental concept of conditioned reflex was established and the study of conditioned reflex became an independent discipline. From 1907 to 1916, the second period, Pavlov theorized on higher nervous activity on the basis of extensive data from his laboratory experiments of conditioned reflex. And Pavlov complemented conditioned reflex theory, during the third period from 1916 to 1928, and extended the boundaries of it through applications of conditioned reflex theory to psychopathology and typology. The study contributes to the understanding that conditioned reflex theory was historically developed, and not presented as a complete form from the beginning, and that Pavlov intended to study the higher nervous activity through the method of neurophysiology.
The role of transformational leadership in enhancing team reflexivity
M.C. Schippers; D.N. den Hartog; P.L. Koopman; D. van Knippenberg
2008-01-01
Team reflexivity, or the extent to which teams reflect upon and modify their functioning, has been identified as a key factor in the effectiveness of work teams. As yet, however, little is known about the factors that play a role in enhancing team reflexivity, and it is thus important to develop the
The Role of Transformational Leadership in Enhancing Team Reflexivity
M.C. Schippers (Michaéla); D.N. den Hartog (Deanne); P.L. Koopman (Paul); D.L. van Knippenberg (Daan)
2007-01-01
textabstractTeam reflexivity, or the extent to which teams reflect upon and modify their functioning, has been identified as a key factor in the effectiveness of work teams. As yet, however, little is known about the factors that play a role in enhancing team reflexivity, and it is thus important to
Reflexivity in Teams: A Review and New Perspectives.
Konradt, Udo; Otte, Kai-Philip; Schippers, Michaéla C; Steenfatt, Corinna
2016-01-01
Team reflexivity posits that the extent to which teams reflect upon and adapt their functioning is positively related to team performance. While remarkable progress has been made to provide evidence of this relationship, the underlying framework is missing elements of current theoretical streams for analyzing and describing teamwork, leaving the diversity of effects of team reflexivity often untouched. In this article, we present an update for this framework, by reviewing previous research on reflexivity, addressing gaps in the literature, and revising the original model by integrating feedback and dynamic team effectiveness frameworks for describing temporal developments of reflexivity. We furthermore propose a new dimensional structure for reflexivity, relying on prior work conceptualizing teams as information-processing systems that learn and advance through social-cognitive elements. Our model is therefore not only suitable for explaining the diverse set of relationships between team reflexivity on outcomes, but also provides valuable directions for viewing reflexivity as process that takes place during both transition and action phases of teamwork. We conclude with implications for managers, identify limitations, and propose an agenda for further research into this area. This article contributes an extended perspective relevant for further theory development and for effectively managing reflexivity in teams.
Reflexivity in Teams: A Review and New Perspectives.
Konradt, Udo; Otte, Kai-Philip; Schippers, Michaéla C; Steenfatt, Corinna
2016-01-01
Team reflexivity posits that the extent to which teams reflect upon and adapt their functioning is positively related to team performance. While remarkable progress has been made to provide evidence of this relationship, the underlying framework is missing elements of current theoretical streams for analyzing and describing teamwork, leaving the diversity of effects of team reflexivity often untouched. In this article, we present an update for this framework, by reviewing previous research on reflexivity, addressing gaps in the literature, and revising the original model by integrating feedback and dynamic team effectiveness frameworks for describing temporal developments of reflexivity. We furthermore propose a new dimensional structure for reflexivity, relying on prior work conceptualizing teams as information-processing systems that learn and advance through social-cognitive elements. Our model is therefore not only suitable for explaining the diverse set of relationships between team reflexivity on outcomes, but also provides valuable directions for viewing reflexivity as process that takes place during both transition and action phases of teamwork. We conclude with implications for managers, identify limitations, and propose an agenda for further research into this area. This article contributes an extended perspective relevant for further theory development and for effectively managing reflexivity in teams. PMID:26457836
Ultimate concerns in late modernity: Archer, Bourdieu and reflexivity.
Farrugia, David; Woodman, Dan
2015-12-01
Through a critique of Margaret Archer's theory of reflexivity, this paper explores the theoretical contribution of a Bourdieusian sociology of the subject for understanding social change. Archer's theory of reflexivity holds that conscious 'internal conversations' are the motor of society, central both to human subjectivity and to the 'reflexive imperative' of late modernity. This is established through critiques of Bourdieu, who is held to erase creativity and meaningful personal investments from subjectivity, and late modernity is depicted as a time when a 'situational logic of opportunity' renders embodied dispositions and the reproduction of symbolic advantages obsolete. Maintaining Archer's focus on 'ultimate concerns' in a context of social change, this paper argues that her theory of reflexivity is established through a narrow misreading and rejection of Bourdieu's work, which ultimately creates problems for her own approach. Archer's rejection of any pre-reflexive dimensions to subjectivity and social action leaves her unable to sociologically explain the genesis of 'ultimate concerns', and creates an empirically dubious narrative of the consequences of social change. Through a focus on Archer's concept of 'fractured reflexivity', the paper explores the theoretical necessity of habitus and illusio for understanding the social changes that Archer is grappling with. In late modernity, reflexivity is valorized just as the conditions for its successful operation are increasingly foreclosed, creating 'fractured reflexivity' emblematic of the complex contemporary interaction between habitus, illusio, and accelerating social change. PMID:26434655
Bourdieu and Science Studies: Toward a Reflexive Sociology
Hess, David J.
2011-01-01
Two of Bourdieu's fundamental contributions to science studies--the reflexive analysis of the social and human sciences and the concept of an intellectual field--are used to frame a reflexive study of the history and social studies of science and technology as an intellectual field in the United States. The universe of large, Ph.D.-granting…
Stretch reflex regulation in healthy subjects and patients with spasticity
DEFF Research Database (Denmark)
Nielsen, Jens Bo; Petersen, Nicolas; Crone, Clarissa;
2005-01-01
In recent years, part of the muscle resistance in spastic patients has been explained by changes in the elastic properties of muscles. However, the adaptive spinal mechanisms responsible for the exaggeration of stretch reflex activity also contribute to muscle stiffness. The available data suggest...... of the spastic symptoms. A recent finding also shows no sign of exaggerated stretch reflexes in muscles voluntarily activated by the spastic patient in general. This is easily explained by the control of stretch reflex activity in healthy subjects. In healthy subjects, the stretch reflex activity is increased...... movements, antagonist muscles should remain silent and maximally relaxed. This is ensured by increasing transmission in several spinal inhibitory pathways. In spastic patients, this control is inadequate, and therefore stretch reflexes in antagonist muscles are easily evoked at the beginning of voluntary...
Prevalence of family history in patients with reflex syncope
DEFF Research Database (Denmark)
Holmegard, Haya N; Benn, Marianne; Kaijer, Michelle Nymann;
2013-01-01
Reflex syncope is defined by a rapid transient loss of consciousness caused by global cerebral hypoperfusion resulting from vasodilatation and/or bradycardia attributable to inappropriate cardiovascular reflexes. A hereditary component has been suggested, but prevalence of family history may differ...... among subtypes of reflex syncope, as these have different autonomic responses and pathogeneses may be diverse. The present study aimed to assess the prevalence of a positive family history of syncope and cardiovascular characteristics in patients with cardioinhibitory and vasodepressor reflex syncope....... Patients (n=74) were classified into subtypes of reflex syncope - cardioinhibition/asystole (Vasovagal Syncope International Study subtypes II-B [VASIS II-B], n=38) or vasodepressor (VASIS III, n=36) - using the head-up tilt test. Family history was obtained by questionnaires supplemented by interview...
Voluntary Control of the Near Reflex: A Case Report
Directory of Open Access Journals (Sweden)
Serpil Akar
2014-03-01
Full Text Available Spasm of the near reflex is a rare disorder that involves intermittent and variable episodes of esotropia, pseudomyopia, and pupillary myosis. It is usually functional in origin and is seen mainly in young patients. Treatment options for spasm of the near reflex have had variable success. In instances where the etiology of spasm of the near reflex was suspected to be hysteria, psychotherapy has proven beneficial. We report the case of an 11-year-old girl who had functional spasm of the near reflex. The symptoms persisted for two years. Symptomatic relief was achieved by cycloplegia and spectacle correction (added plus lenses at near. The patient also underwent psychological counseling. In our case, the functional spasm of the near reflex spontaneously resolved after 2 years. (Turk J Ophthalmol 2014; 44: 161-3
Effects of Bed Rest on Conduction Velocity of the Triceps Surae Stretch Reflex and Postural Control
Reschke, M. F.; Wood, S. J.; Cerisano, J. M.; Kofman, I. S.; Fisher, E. A.; Esteves, J. T.; Taylor, L. C.; DeDios, Y. E.; Harm, D. L.
2011-01-01
Despite rigorous exercise and nutritional management during space missions, astronauts returning from microgravity exhibit neuromuscular deficits and a significant loss in muscle mass in the postural muscles of the lower leg. Similar changes in the postural muscles occur in subjects participating in long-duration bed rest studies. These adaptive muscle changes manifest as a reduction in reflex conduction velocity during head-down bed rest. Because the stretch reflex encompasses both the peripheral (muscle spindle and nerve axon) and central (spinal synapse) components involved in adaptation to calf muscle unloading, it may be used to provide feedback on the general condition of neuromuscular function, and might be used to evaluate the effectiveness of countermeasures aimed at preserving muscle mass and function during periods of unloading. Stretch reflexes were measured on 18 control subjects who spent 60 to 90 days in continuous 6 deg head-down bed rest. Using a motorized system capable of rotating the foot around the ankle joint (dorsiflexion) through an angle of 10 degrees at a peak velocity of about 250 deg/sec, a stretch reflex was recorded from the subject's left triceps surae muscle group. Using surface electromyography, about 300 reflex responses were obtained and ensemble-averaged on 3 separate days before bed rest, 3 to 4 times in bed, and 3 times after bed rest. The averaged responses for each test day were examined for reflex latency and conduction velocity (CV) across gender. Computerized posturography was also conducted on these same subjects before and after bed rest as part of the standard measures. Peak-to-peak sway was measured during Sensory Organization Tests (SOTs) to evaluate changes in the ability to effectively use or suppress visual, vestibular, and proprioceptive information for postural control. Although no gender differences were found, a significant increase in reflex latency and a significant decrease in CV were observed during the bed
Fuzzy Closure Spaces vs. Fuzzy Rough Sets
S. P. Tiwari; Shambhu Sharan; Yadav, Vijay K.
2014-01-01
This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a cer...
International Nuclear Information System (INIS)
The main purpose of this paper is the theoretical study and the development of a technique for designing. A low power Reflex-Klystron, in order to construct it in the graduated section laboratories of the Instituto Politecnico Nacional. It is pretended to attain a power of 15-45 m W in frequencies of 8-10 GHz with low acceleration potentials (300-400 V) and electric current of 15-25 m A; the device will be mechanically tuned and will have a fine tuning through the potential of the reflector (150-180 V negative with respect to the resonator). The International System of Units is used in this thesis. (Author)
The Chinchilla's vestibulo-ocular reflex
Merwin, W. H., Jr.; Wall, Conrad, III; Tomko, D. L.
1989-01-01
The horizontal vestibulo-ocular reflex (VOR) was measured and characterized in seven adult chinchillas using 0.01 to 1.0 Hz angular velocity sinusoids. Gains were less than compensatory, and were variable from day to day, but phases were highly repeatable both within and between animals. The best fitting transfer function to the average data of all animals had a dominant time constant of 7.5 sec, and an adaptation operator with a time constant of 24.0 sec. There were certain nonlinearities in the horizontal VOR of this animal, and it was difficult to elicit a robust optokinetic response. Results are discussed in relation to similar measurements in other species.
Reflexivity and vulnerability in collaborative knowledge production
DEFF Research Database (Denmark)
Jakobsen, Helle Nordentoft; Olesen, Birgitte Ravn
Previous research argues that reflexive investigations into situations in which you become `struck´ cognitively and/or physiologically and/or emotionally have potential to instigate organisational knowledge production (Cunliffe, 2002). However, this research focuses mainly on participants’ self...... in the field of study. The purpose of this paper is to investigate the synergy between ‘how’ these incidents unfold in collaborative knowledge production processes – i.e. how potential discomforts arise and how power relations seem to affect the ‘what’; i.e. the knowledge co-produced in the situated context...... this discourse relevant in-interaction. A micro-sociological approach avoids theorized accounts, common sense conceptions and generalizations of power relations in order not to obscure local orders (Olesen and Nordentoft, 2013; Nielsen, 2007). The ’order of interaction’ comprises specific interactional rights...
McDaniel-Bacon, L; Fulton, R T; Laskowski, R P
1980-01-01
An ABAB functional analysis, conditioning and generalization, design was used in 3 experiments (2 were formal studies and 1 was empirical in nature) to investigate the conditionability of the middle ear reflex. The conditioned stimuli were subreflex threshold pure tones of various frequencies and intensities. The unconditioned stimulus (UCS) was an auricular air jet to the contralateral ear in the first experiment and cutaneous electrical stimulation to the ipsolateral, probe ear in the last 2 experiments. Reflexes were monitored by an otoadmittance meter, storage oscilloscope, and strip chart recorder. In the first experiment (air jet UCS), no subjects met the conditioning criterion within the maximum presentation of 400 paired trials, despite pilot evidence which indicated conditioning was feasible. In the second experiment (electrical stimulation UCS), 2 subjects met conditioning criterion; however, only one subject reconditioned and demonstrated partial generalization to other conditioned stimuli. In the third experiment (electrical stimulation UCS), one of 3 subjects who had previously been unconditionable with the air jet UCS met conditioning and reconditioning criterion and demonstrated partial generalization. Results indicate that the middle ear reflex can be conditioned to be elicited by subreflex threshold pure tones, however, results are limited.
Directory of Open Access Journals (Sweden)
Schüermann HW
2010-01-01
Full Text Available Abstract A method based on the Banach fixed-point theorem is proposed for obtaining certain solutions (TE-polarized electromagnetic waves of the Helmholtz equation describing the reflection and transmission of a plane monochromatic wave at a nonlinear lossy dielectric film situated between two lossless linear semiinfinite media. All three media are assumed to be nonmagnetic and isotropic. The permittivity of the film is modelled by a continuously differentiable function of the transverse coordinate with a saturating Kerr nonlinearity. It is shown that the solution of the Helmholtz equation exists in form of a uniformly convergent sequence of iterations of the equivalent Volterra integral equation. Numerical results are presented.
Directory of Open Access Journals (Sweden)
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.
Trembach, Vera
2014-01-01
Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.
Cardiorespiratory parameters and respiratory reflexes in rabbits during hyperthermia.
Javorka, K; Calkovská, A; Petrásková, M; Gecelovská, V
1996-01-01
The effects of different body temperature (BT) on the respiratory and cardiovascular parameters and respiratory reflexes were studied in 33 anaesthetized adult rabbits. Hyperthermia elicited panting with mean panting respiratory rate 199 +/- 14 x min-1 in all anaesthetized rabbits. Significant correlations between BT and frequency of breathing (positive), heart rate (positive) or tidal volume (negative) were found. Cooling was accompanied by considerable arterial hypotension. Duration of the Hering-Breuer reflex (HB) was reduced by the rise of BT. Intensity of the reflex (assessed as the ratio of the apnoeic pause to the mean duration of the previous 5 breaths) was unchanged up to the body temperature eliciting panting (41.15 +/- 0.08 degrees C) when it was greatly diminished. Defensive airway reflexes were also changed in hyperthermia. The duration as well as the intensity of nasal apnoea (Kratschmer's reflex) and laryngeal chemoreflex apnoea were decreased. The intensities of respiratory efforts in sneezing and laryngeal coughing were reduced. The expulsive reactions evoked by mechanical stimulation of the larynx were replaced by very shortlasting inhibition of breathing during panting. The results indicate that reflex control of breathing via the Hering-Breuer reflex and the ability to eliminate irritants from the airways are diminished during hyperthermia and panting in anaesthetized rabbits. PMID:9085374
Tendon reflex is suppressed during whole-body vibration.
Karacan, Ilhan; Cidem, Muharrem; Yilmaz, Gizem; Sebik, Oguz; Cakar, Halil Ibrahim; Türker, Kemal Sıtkı
2016-10-01
In this study we have investigated the effect of whole body vibration (WBV) on the tendon reflex (T-reflex) amplitude. Fifteen young adult healthy volunteer males were included in this study. Records of surface EMG of the right soleus muscle and accelerometer taped onto the right Achilles tendon were obtained while participant stood upright with the knees in extension, on the vibration platform. Tendon reflex was elicited before and during WBV. Subjects completed a set of WBV. Each WBV set consisted of six vibration sessions using different frequencies (25, 30, 35, 40, 45, 50Hz) applied randomly. In each WBV session the Achilles tendon was tapped five times with a custom-made reflex hammer. The mean peak-to-peak (PP) amplitude of T-reflex was 1139.11±498.99µV before vibration. It decreased significantly during WBV (ptapping between before and during vibration sessions. This study showed that T-reflex is suppressed during WBV. T-reflex suppression indicates that the spindle primary afferents must have been pre-synaptically inhibited during WBV similar to the findings in high frequency tendon vibration studies. PMID:27485766
Ternary numbers and algebras. Reflexive numbers and Berger graphs
Dubrovskiy, A
2007-01-01
The Calabi-Yau spaces with SU(n) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the $n$-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras, ${\\mathbb R}$, ${\\mathbb C}$, ${\\mathbb H}$, ${\\mathbb O}$, which helped to discover the most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case $n=3$, which gives the ternary generalization of quaternions and octonions, $3^n$, $n=2,3$, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra and group which are related to the natural extensions of the binary $su(3)$ algebra and SU(3) group. Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.
极大单调映象的满射定理及其应用%Some Surjectivity Theorems for Maximal Monotone Operators and Its Application
Institute of Scientific and Technical Information of China (English)
武跃祥; 王拉娣
2008-01-01
The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory.We prove some new surjectivity theorems under some conditions and give its application in differential equation.
On a minimax problem of ricceri
Cordaro Giuseppe
2001-01-01
Let be a real separable and reflexive Banach space, weakly closed and unbounded, and two non-constant weakly sequentially lower sernicontinuous functionals defined on , such that is coercive for each . In this setting, if for every , then, one has for every concave function .
Almost Chebyshev set with respect to bounded subsets
Institute of Scientific and Technical Information of China (English)
李冲; 王兴华
1997-01-01
The uniqueness and existence of restricted Chebyshev center with respect to arbitrary subset are investigated. The concept of almost Chebyshev sets with respect to bounded subsets is introduced. It is proved that each closed subset in a reflexive locally uniformly convex (uniformly convex, respectively) Banach space is an almost Chebyshev subset with respect to compact convex subsets (bounded convex subsets and bounded subsets, respectively).
On the calculation of the polar cone of the solution set of a differential inclusion
Polovinkin, E. S.
2012-01-01
A general form of the polar cone is obtained for the solution set of an arbitrary differential inclusion such that the graph of its right-hand side is a convex closed cone and the solutions take values in a reflexive Banach space.
Directory of Open Access Journals (Sweden)
Razani A
2010-01-01
Full Text Available Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence , where (0, 1, is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence is proved.
Strong Convergence Theorems for a Family of Quasi-φ-Asymptotically Nonexpansive Mappings
Institute of Scientific and Technical Information of China (English)
Xing Hui GAO; Hai Yun ZHOU
2011-01-01
The purpose of this article is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-φ-asymptotically nonexpansive mappings. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property(K). The results of this paper improve and extend recent some relative results.
Plasticity of the cervico-ocular reflex in health and Disease
W.P.A. Kelders (Willem)
2006-01-01
textabstractThe cervico-ocular reflex (COR) is an ocular stabilization reflex that is elicited by rotation of the neck. It works in conjunction with the vestibulo-ocular reflex (VOR) and the optokinetic reflex (OKR) in order to prevent visual slip over the retina due to self motion. The VOR
Compensatory increase of the cervico-ocular reflex with age in healthy humans.
W.P.A. Kelders (Willem); G.J. Kleinrensink (Gert Jan); J.N. van der Geest (Jos); L. Feenstra (Louw); C.I. de Zeeuw (Chris); M.A. Frens (Maarten)
2003-01-01
textabstractThe cervico-ocular reflex (COR) is an ocular stabilization reflex that is elicited by rotation of the neck. It works in conjunction with the vestibulo-ocular reflex (VOR) and the optokinetic reflex (OKR) in order to prevent visual slip over the retina due to self-motion
A task dependent change in the medium latency component of the soleus stretch reflex
DEFF Research Database (Denmark)
Grey, Michael James; Larsen, Birgit; Sinkjær, Thomas
2002-01-01
mediated H-reflex or the short latency stretch reflex. In the present study the medium latency component of a mechanically evoked stretch reflex is investigated during walking, pedalling, and sitting. Stretch reflexes were evoked in the soleus muscle using dorsiflexion perturbations generated...
The Approximation Theorem of Convolution Operator in △p Set-valued Function Space
Institute of Scientific and Technical Information of China (English)
Pei-xin Ye
2002-01-01
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space,
Short-duration spaceflight impairs human carotid baroreceptor-cardiac reflex responses
Fritsch, Janice M.; Charles, John B.; Bennett, Barbara S.; Jones, Michele M.; Eckberg, Dwain L.
1992-01-01
The effect of a spaceflight on the vagally mediated baroreceptor-cardiac reflex responses of humans were investigated by measuring the responses (provoked by neck pressure changes) in supine position and the heart rate and blood pressure in the supine and standing positions in 16 astronauts before and after 4- to 5-day long Space Shuttle missions. The results showed that exposures to spaceflight resulted in reduced baseline levels of the vagal-cardiac outflow and the vagally mediated responses to changes of the arterial baroreceptor input and that these changes contribute to postflight reductions of astronauts' ability to maintain standing arterial pressures.
Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces
Institute of Scientific and Technical Information of China (English)
Veli B. SHAKHMUROV
2006-01-01
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators Dα from this space to Eα -valued Lp,γ spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.
Soleus H-reflex excitability during pedaling post-stroke
DEFF Research Database (Denmark)
Schindler-Ivens, Sheila; Brown, David A.; Lewis, Gwyn N.;
2008-01-01
A major contributor to impaired locomotion post-stroke is abnormal phasing of paretic muscle activity, but the mechanisms remain unclear. Previous studies have shown that, in the paretic limb of people post-stroke, Group Ia reflexes are abnormally elevated and fail to decrease in amplitude during...... locomotion. Hence, we hypothesized that inappropriate muscle phasing may be associated with enhanced transmission in the monosynaptic Group Ia afferent pathway. Soleus (SO) H-reflexes were used to examine transmission in the Group Ia afferent pathway to SO motor neurons during pedaling, a locomotor task...... in the pedaling cycle and during tonic plantar flexion at comparable limb positions and levels of SO EMG. In both groups, SO H-reflexes were smaller during pedaling as compared to matched tonic plantar flexion. In the NI group, but not the paretic group, SO H-reflex amplitude was significantly modulated across...
Reconsidering reflexivity: introducing the case for intellectual entrepreneurship.
Cutcliffe, John R
2003-01-01
In this article, the author reconsiders reflexivity and attempts to examine some unresolved issues by drawing particular attention to the relationship between reflexivity and certain related phenomena/processes: the researcher's a priori knowledge, values, beliefs; empathy within qualitative research; the presence and influence of the researcher's tacit knowledge, and May's "magic" in method. Given the limitations of some reflexive activity identified in this article, the author introduces the case for greater intellectual entrepreneurship within the context of qualitative research. He suggests that excessive emphasis on reflexive activity might inhibit intellectual entrepreneurship. Wherein intellectual entrepreneurship implies a conscious and deliberate attempt on the part of academics to explore the world of ideas boldly; to take more risks in theory development and to move away from being timid researchers. PMID:12564268
On the gastrocecal inhibitory reflex in the rat.
Directory of Open Access Journals (Sweden)
Lee,Zai-Liu
1981-11-01
Full Text Available In rats anesthetized with urethane, the effects of distention of the stomach upon cecal motility and neural mechanisms which generate this effect were studied. Cecal motility was inhibited which generate this effect were studied. Cecal motility was inhibited when the pars glandularis of the stomach was distended by pressure ranging from 25 to 30 cm H2O. This inhibitory reflex was not affected by bilateral cervical vagotomy, but completely abolished following bilateral severance of the greater splanchnic nerves or after intravenous administration of guanethidine. After transection of the spinal cord at the level of the 5th thoracic segment the inhibitory reflex remained intact, but was abolished following pithing of the 6th thoracic segment and below. It may be concluded that the afferent and efferent path of the gastrocecal inhibitory reflex mainly pass through the greater splanchnic nerves and the reflex center is located in thoracic segments caudal to the 6th thoracic segment.
Interindividual differences in H reflex modulation during normal walking
DEFF Research Database (Denmark)
Simonsen, Erik B; Dyhre-Poulsen, Poul; Alkjaer, T;
2002-01-01
Based on previous studies, at least two different types of soleus Hoffmann (H) reflex modulation were likely to be found during normal human walking. Accordingly, the aim of the present study was to identify different patterns of modulation of the soleus H reflex and to examine whether...... or not subjects with different H reflex modulation would exhibit different walking mechanics and different EMG activity. Fifteen subjects walked across two force platforms at 4.5 km/h (+/-10%) while the movements were recorded on video. The soleus H reflex and EMG activity were recorded separately during...... treadmill walking at 4.5 km/h. Using a two-dimensional analysis joint angles, angular velocities, accelerations, linear velocities and accelerations were calculated, and net joint moments about the ankle, knee and hip joint were computed by inverse dynamics from the video and force plate data. Six subjects...
Nasal reflexes: implications for exercise, breathing, and sex.
Baraniuk, James N; Merck, Samantha J
2008-04-01
Nasal patency, with both congestion and decongestion, is affected in a wide variety of reflexes. Stimuli leading to nasal reflexes include exercise; alterations of body position, pressure, and temperature; neurologic syndromes; and dentistry. As anticipated, the vagal and trigeminal systems are closely integrated through nasobronchial and bronchonasal reflexes. However, perhaps of greater pathophysiologic importance are the naso-hypopharyngeal-laryngeal reflexes that become aggravated during sinusitis. None other than Sigmund Freud saw deeply beyond the facial adornment and recognized the deeper sexual tensions that can regulate nasal functions and psychoanalytical status. Wine, women, and song are linked with airflow through the nose-the nose, which by any other name would still smell as sweetly. PMID:18417057
Rudrashish Haldar; Jasleen Kaur; Sukhminder Jit Singh Bajwa
2015-01-01
Nasocardiac reflex is a relatively less discussed variant of trigeminovagal reflex where the afferent arc of the reflex is represented by any of the branches of the trigeminal nerves, and the efferent arc is via the vagus nerve. Elicitation of this reflex is commonly seen during surgical manipulation and is manifested as bradycardia or even asystole. We report a case where nasocardiac reflex was unusually observed in a patient when aspiration and injection were done through a nasogastric tube.