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1

Q-Reflexive Banach spaces  

CERN Document Server

Let $E$ be a Banach space and, for any positive integer $n$, let ${\\cal P}(^nE)$ denote the Banach space of continuous $n$-homogeneous polynomials on $E$. Davie and Gamelin showed that the natural extension mapping from ${\\cal P}(^nE)$ to ${\\cal P}(^nE^{\\ast\\ast})$ is an isometry into the latter space. Here, we investigate when there is a natural isomorphism between ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$. Among other things, we show that if $E$ satisfies: \\break (a) no spreading model built on a normalised weakly null sequence has a lower $q$-estimate for any $q < \\infty,$ (b) $E^{\\ast}$ has RNP, and (c) $E^{\\ast}$ has the approximation property, then ${\\cal P}(^nE)$ has RNP for every $n$. Moreover, if $E$ satisfies (a) and is such that $E^{\\ast\\ast}$ has both the RNP and the approximation property, then ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal P}(^nE^{\\ast\\ast})$ are isomorphic for every $n$. We also exhibit a quasi-reflexive Banach space $E$ for which ${\\cal P}(^nE)^{\\ast\\ast}$ and ${\\cal...

Aron, R M; Aron, Richard M.; Dineen, Sean

1994-01-01

2

Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces  

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For each ordinal $\\alpha< \\omega_1$, we prove the existence of a separable, reflexive Banach space with a basis and Szlenk index $\\omega^{\\alpha+1}$ which is universal for the class of separable, reflexive Banach spaces $X$ such that the Szlenk indices $Sz(X), Sz(X^*)$ do not exceed $\\omega^\\alpha$.

Causey, Ryan

2013-01-01

3

Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.

Shin Min Kang

2003-01-01

4

Nonlinear variational inequalities on reflexive Banach spaces and topological vector spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The purpose of this paper is to introduce and study a class of nonlinear variational inequalities in reflexive Banach spaces and topological vector spaces. Based on the KKM technique, the solvability of this kind of nonlinear variational inequalities is presented. The obtained results extend, improve, and unify the results due to Browder, Carbone, Siddiqi, Ansari, Kazmi, Verma, and others.

Shin Min Kang; Jeong Sheok Ume; Zeqing Liu

2003-01-01

5

Ergodic Banach Spaces  

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We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space $X$ as a space such that $E_0$ Borel reduces to isomorphism on the set of subspaces of $X$, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis $ which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results; for example, in combina...

Ferenczi, Valentin; Rosendal, Christian

2003-01-01

6

Subprojective Banach spaces  

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A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.

Oikhberg, Timur; Spinu, Eugeniu

2014-01-01

7

Interpolating hereditarily indecomposable Banach spaces  

CERN Document Server

It is shown that every Banach space either contains $\\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\\lambda )$, $1Banach space.

Argyros, S A; Argyros, Spiros A.

1997-01-01

8

Multipliers of Banach valued weighted function spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We generalize Banach valued spaces to Banach valued weighted function spaces and study the multipliers space of these spaces. We also show the relationship between multipliers and tensor product of Banach valued weighted function spaces.

Serap ztop

2000-10-01

9

On unconditionally saturated Banach spaces  

CERN Document Server

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set $\\aaa$, in the Effros-Borel space of subspaces of $C[0,1]$, of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space $Y$, with a Schauder basis, that contains isomorphic copies of every space $X$ in the class $\\aaa$.

Dodos, Pandelis

2008-01-01

10

Weakly compact approximation in Banach spaces  

CERN Document Server

The Banach space $E$ has the weakly compact approximation property (W.A.P. for short) if there is a constant $C 0$ there is a weakly compact operator $V: E \\to E$ satisfying $\\sup_{x\\in D} || x - Vx || < \\epsilon$ and $|| V|| \\leq C$. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type spaces from a general class of quasi-reflexive spaces (which contains the classical James' space $J$) have the W.A.P, but that James' tree space $JT$ fails to have the W.A.P. It is also shown that the dual $J^*$ has the W.A.P. It follows that the Banach algebras $W(J)$ and $W(J^*)$, consisting of the weakly compact operators, have bounded left approximate identities. Among the other results we obtain a concrete Banach space $Y$ so that $Y$ fails to have the W.A.P., but $Y$ has this approximation property without the uniform bound $C$.

Odell, E; Odell, Edward; Tylli, Hans-Olav

2003-01-01

11

Banach spaces of universal disposition  

CERN Document Server

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.

Aviles, Antonio; Castillo, Jesus M F; Gonzalez, Manuel; Moreno, Yolanda

2011-01-01

12

Variational calculus on Banach spaces  

International Nuclear Information System (INIS)

The problem of variational calculus is considered in a (variable) subdomain of a Banach space. Analogues of the basic principles of the finite-dimensional theory are derived: the main formula for variations of a functional, necessary conditions of an extremum, Noether's theorem. All the results obtained are dimension-invariant and become the classical ones in the finite-dimensional setting. The main tool of the analysis is the theory of surface integration in Banach spaces

13

A pythagorean approach in Banach spaces  

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Full Text Available 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.

Gao Ji

2006-01-01

14

Existence of zeros for operators taking their values in the dual of a Banach space  

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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.

Ricceri Biagio

2004-01-01

15

On dual of Banach sequence spaces  

Directory of Open Access Journals (Sweden)

Full Text Available J. Hagler and P. Azimi have introduced a class of Banach sequence spaces, the X?,1 spaces as a class of hereditarily $ell_1$ Banach spaces. In this paper, (i We show that X*?, 1, the dual of Banach space X?,1 contains asymptotically isometric copies of $ell_infty$. (ii With two methods, we show that X*?,1 is nonseparable although X?,1 is a separable Banach space. Also, we showX?,1 is not hereditarily indecomposable.

A. A. Ledari

2013-09-01

16

Smooth analysis in Banach spaces  

CERN Document Server

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

Hjek, Petr

2014-01-01

17

Analytic sheaves in Banach spaces  

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We introduce a class of analytic sheaves in a Banach space X, that we call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan's Theorems A and B for cohesive sheaves over pseudoconvex open subsets of X, provided X has an unconditional basis.

Lempert, Laszlo

2005-01-01

18

Sesquilinear quantum stochastic analysis in Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A theory of quantum stochastic processes in Banach space is initiated. The processes considered here consist of Banach space valued sesquilinear maps. We establish an existence and uniqueness theorem for quantum stochastic differential equations in Banach modules, show that solutions in unital Banach algebras yield stochastic cocycles, give sufficient conditions for a stochastic cocycle to satisfy such an equation, and prove a stochastic LieTrotter product formula. The theory is used to ex...

Lindsay, Martin; Das, Bata Krishna; Tripak, Orawan

2014-01-01

19

Frchet spaces with no infinite-dimensional Banach quotients  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We exhibit examples of Frchet Montel spaces E which have a non-reflexive Frchet quotient but such that every Banach quotient is finite-dimensional. The construction uses a method developed by Albanese and Moscatelli and requires new ingredients. Some of the main steps in the proof are presented in Section 2. They are of independent interest and show for example that the canonical inclusion between James spaces JpJq, 1 pJq has no infinite-dimensional Banach quotients. Plichko and Maslyuc...

Bonet Solves, Jose? Antonio; Albanese, A.

2012-01-01

20

Dynamical entropy in Banach spaces  

CERN Document Server

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometrically and topologically. This leads to various applications; for example, we obtain a geometric description of the topological Pinsker factor and show that a C*-algebra is type I if and only if every multiplier inner *-automorphism has zero CA entropy. We also examine the behaviour of CA entropy under various product constructions and determine its value in many examples, including isometric automorphisms of l_p spaces and noncommutative tensor product shifts.

Kerr, D; Kerr, David; Li, Hanfeng

2004-01-01

 
 
 
 
21

The Banach space mp(X, for 1 ? p <8 has the Banach-Saks Property  

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Full Text Available Problem statement: In the theory of Banach spaces one of the problems which describes geometric property of Banach spaces is Banach-Saks Property. In this context we were known many Banach spaces which had this property such as Lp[0, 1] for 1 Approach: Following the sequential structure of the Banach sequence space mp(X, for 1 ? p Results: In this note we showed that Banach spaces mp(X, for 1 ? p Conclusion/Recommendations: Based in present approach, we recommend using our method to study the weak Banach-Saks property in sequential Banach spaces.

Naim L. Braha

2009-01-01

22

Isometries on Banach spaces function spaces  

CERN Document Server

Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one.Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras.This treatment p...

Fleming, Richard J

2002-01-01

23

Convex optimization on Banach Spaces  

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Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space $X$. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the smoothness of the objective function and the sparsity or compressibility (with respect to a given dictionary) of a point in $X$ where the minimu...

Devore, R. A.; Temlyakov, V. N.

2014-01-01

24

A Banach space dichotomy for quotients of subspaces  

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A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable (QHI) property if $X/Y$ is hereditarily indecomposable (HI) for any infinite codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. A reflexive space with the restricted QHI property is in particular HI, has HI dual, and is saturated with subspaces which are HI and have HI dual. The following dichotomy theorem is proved...

Ferenczi, Valentin

2006-01-01

25

Regularization methods in Banach spaces  

CERN Document Server

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

Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S

2012-01-01

26

Compactness in Banach space theory - selected problems  

CERN Document Server

We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\\'{y}m compacta.

Avils, Antonio

2010-01-01

27

Characterizing R-duality in Banach spaces  

DEFF Research Database (Denmark)

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.

Christensen, Ole; Xiao, Xiang Chun

2013-01-01

28

Nonreflexive Banach SSD spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper, we unify the theory of SSD spaces, part of the theory of strongly representable multifunctions, and the theory of the equivalence of various classes of maximally monotone multifunctions.

Simons, Stephen

2008-01-01

29

Topics in Banach space integration  

CERN Document Server

The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.

Schwabik, tefan

2005-01-01

30

Infinitely divisible cylindrical measures on Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the result on the classification enables ...

Riedle, Markus

2011-01-01

31

On Uniformly finitely extensible Banach spaces  

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We continue the study of Uniformly Finitely Extensible Banach spaces (in short, UFO) initiated in Moreno-Plichko, \\emph{On automorphic Banach spaces}, Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \\emph{Banach spaces in various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they have the Uniform Approximation Property of Pe\\l czy\\'nski and Rosenthal and are compactly extensible. We will also consider their connection with the automorphic space probl...

Castillo, Jesu?s M. F.; Ferenczi, Valentin; Moreno, Yolanda

2013-01-01

32

Mean inequalities in certain Banach function spaces  

Science.gov (United States)

Boundedness of the Hardy operator and its adjoint is characterized between Banach function spaces Xq and Lp. By applying a limiting procedure, corresponding boundedness of the geometric mean operator is also derived.

Jain, Pankaj; Gupta, Babita; Verma, Daulti

2007-10-01

33

VARIOUS SPACES FOR BANACH SPACE VALUED POTENTIAL HANKEL TRANSFORM  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Different testing function spaces are defined for Banach space valued Potential Hankel transform by using Gelfand-Shilov technique of S? spaces, some properties of the spaces are also proved. At the end generalized Banach space valued Potential Hankel transform is defined.

Sahu, Nanda D.

2011-01-01

34

VARIOUS SPACES FOR BANACH SPACE VALUED POTENTIAL HANKEL TRANSFORM  

Directory of Open Access Journals (Sweden)

Full Text Available Different testing function spaces are defined for Banach space valued Potential Hankel transform by using Gelfand-Shilov technique of S? spaces, some properties of the spaces are also proved. At the end generalized Banach space valued Potential Hankel transform is defined.

NANDA D. SAHU

2011-12-01

35

Interpolation of quasi-Banach spaces  

International Nuclear Information System (INIS)

This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces

36

Spaces Of Lipschitz Functions On Banach Spaces  

CERN Document Server

A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C \\subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* \\in X^*$ attains its supremum on $C$; then $C$ is a weakly compact set. Actually, this result is significantly stronger than this statement; indeed, the proof can be used to obtain other surprising results. For example, suppose that $X$ is a separable Banach space and $S$ is a norm separable subset of the unit ball of $X^*$ such that for each $x \\in X$ there exists $x^* \\in S$ such that $x^*(x) = \\|x\\|$ then $X^*$ is itself norm separable . If we call $S$ a support set, in this case, with respect to the entire space $X$, one can ask questions about the size and structure of a support set, a support set not only with respect to $X$ itself but perhaps with respect to some other subset of $X$@. We analyze one particular case of this as well as give some applications.

Stegall, C P

1993-01-01

37

On ?-Type Duality of Frames in Banach Spaces  

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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 ?-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.

Renu Chugh

2013-11-01

38

A Gaussian Average Property for Banach Spaces  

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In this paper we investigate a Gaussian average property of Banach spaces. This property is weaker than the Gordon Lewis property but closely related to this and other unconditional structures. It is also shown that this property implies that certain Hilbert space valued operators defined on subspaces of the given space can be extended.

Casazza, Peter G.; Nielsen, Niels Jorgen

1996-01-01

39

On Sharp Triangle Inequalities in Banach Spaces II  

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Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al. (2007). In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.

Saito Kichi-Suke; Mitani Ken-Ichi

2010-01-01

40

On Sharp Triangle Inequalities in Banach Spaces II  

Directory of Open Access Journals (Sweden)

Full Text Available Sharp triangle inequality and its reverse in Banach spaces were recently showed by Mitani et al. (2007. In this paper, we present equality attainedness for these inequalities in strictly convex Banach spaces.

Saito Kichi-Suke

2010-01-01

 
 
 
 
41

Analytic cohomology in a Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Among other things, we show that the ideal sheaf of a complex Hilbert submanifold of a pseudoconvex open subset of Hilbert space is acyclic over the ambient pseudoconvex open set. We also prove a vanishing theorem for a fairly general class of analytic sheaves over pseudoconvex open sets of a large class of Banach spaces. Some applications are also given.

Patyi, Imre

2005-01-01

42

Examples of asymptotically \\ell_^1 Banach spaces  

CERN Document Server

Two examples of asymptotic $\\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of Tsirelson. We thus answer a question raised by W.T.Gowers.

Argyros, S A; Argyros, Spiros A.; Deliyanni, Irene

1994-01-01

43

Coorbit Space Theory for Quasi-Banach Spaces  

CERN Document Server

We generalize the classical coorbit space theory developed by Feichtinger and Gr"ochenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions are used to prove fast convergence rates of best $n$-term approximation schemes. We apply the abstract theory to time-frequency analysis of modulation spaces $M^{p,q}_m$, $0< p,q \\leq \\infty$.

Rauhut, H

2005-01-01

44

Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces  

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We introduce and study Clarkson, Dolnikov-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 Schffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hlder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the ...

Sergey Ajiev

2013-01-01

45

Isomorphic Schauder decompositions in certain Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We extend a theorem of Kato on similarity for sequences of projections in Hilbert spaces to the case of isomorphic Schauder decompositions in certain Banach spaces. To this end we use $\\ell_{\\Psi}$-Hilbertian and $\\infty$-Hilbertian Schauder decompositions instead of orthogonal Schauder decompositions, generalize the concept of an orthogonal Schauder decomposition in a Hilbert space and introduce the class of spaces with Schauder-Orlicz decompositions. Furthermore, we genera...

Marchenko, Vitalii

2013-01-01

46

On Uniform Exponential Trichotomy in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we consider three concepts of uniform exponential trichotomy on the half-line in the general framework of evolution operators in Banach spaces. We obtain a systematic classification of uniform exponential trichotomy concepts and the connections between them.

Kovacs Monteola Ilona

2014-06-01

47

Wiener Amalgam Spaces with respect to Quasi-Banach Spaces  

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We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is even new for the classical Banach space case. To illustrate our theory we discuss in detail an example on the $ax+b$ group.

Rauhut, Holger

2005-01-01

48

Banach spaces of vector-valued functions  

CERN Document Server

"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.

Cembranos, Pilar

1997-01-01

49

The structure of a subclass of amenable banach algebras  

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We give sufficient conditions that allow contractible (resp., reflexive amenable) Banach algebras to be finite-dimensional and semisimple algebras. Moreover, we show that any contractible (resp., reflexive amenable) Banach algebra in which every maximal left ideal has a Banach space complement is indeed a direct sum of finitely many full matrix algebras. Finally, we characterize Hermitian *-algebras that are contractible.

El Harti, R.

2004-01-01

50

Three-space problems in Banach space theory  

CERN Document Server

This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis and some familiarity with modern Banach space methods. It will be of interest to researchers for its methods and open problems, and to students for the exposition of techniques and examples.

Castillo, Jess M F

1997-01-01

51

Norm One Projections in Banach Spaces  

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This is the survey of results about norm one projections and 1-complemented subspaces in K\\"othe function spaces and Banach sequence spaces. The historical development of the theory is presented from the 1930's to the newest ideas. Proofs of the main results are outlined. Open problems are also discussed. Every effort has been made to include as complete a bibliography as possible.

Randrianantoanina, Beata

2001-01-01

52

An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces  

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Full Text Available We investigate an inexact proximal-type method, applied to the generalized variational inequality problem with maximal monotone operator in reflexive Banach spaces. Solodov and Svaiter (2000 first introduced a new proximal-type method for generating a strongly convergent sequence to the zero of maximal monotone operator in Hilbert spaces, and subsequently Kamimura and Takahashi (2003 extended Solodov and Svaiter algorithm and strong convergence result to the setting of uniformly convex and uniformly smooth Banach spaces. In this paper Kamimura and Takahashi's algorithm is extended to develop a generic inexact proximal point algorithm, and their convergence analysis is extended to develop a generic convergence analysis which unifies a wide class of proximal-type methods applied to finding the zeroes of maximal monotone operators in the setting of Hilbert spaces or Banach spaces.

Mastroeni G

2007-01-01

53

An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We investigate an inexact proximal-type method, applied to the generalized variational inequality problem with maximal monotone operator in reflexive Banach spaces. Solodov and Svaiter (2000 first introduced a new proximal-type method for generating a strongly convergent sequence to the zero of maximal monotone operator in Hilbert spaces, and subsequently Kamimura and Takahashi (2003 extended Solodov and Svaiter algorithm and strong convergence result to the setting of uniformly convex and uniformly smooth Banach spaces. In this paper Kamimura and Takahashi's algorithm is extended to develop a generic inexact proximal point algorithm, and their convergence analysis is extended to develop a generic convergence analysis which unifies a wide class of proximal-type methods applied to finding the zeroes of maximal monotone operators in the setting of Hilbert spaces or Banach spaces.

J. C. Yao

2008-01-01

54

Topological Vector-Space Valued Cone Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we introduce the notion of tvs-cone normed spaces, discuss related topological concepts and characterize the tvs-cone norm in various directions. We construct generalize locally convex tvs generated by a family of tvs-cone seminorms. The class of weak contractions properly includes large classes of highly applicable contractions like Banach, Kannan, Chatterjea and quasi etc. We prove fixed point results in tvs-cone Banach spaces for nonexpansive self mappings and self/non-self w...

Nayyar Mehmood; Akbar Azam; Suzana Aleksic

2014-01-01

55

Weakly Lindelof determined Banach spaces not containing $\\ell^1(N)$  

CERN Document Server

The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing $\\ell^{1}(\\NN )$. Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing $\\ell^{1}(\\NN )$ and not being itself a W.C.G. space.

Argyros, S A

1992-01-01

56

Banach frames for alpha-modulation spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper is concerned with the characterization of $\\alpha$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter $\\alpha \\in [0,1]$ governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The wel...

Fornasier, Massimo

2004-01-01

57

An Inexact Proximal-Type Method for the Generalized Variational Inequality in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We investigate an inexact proximal-type method, applied to the generalized variational inequality problem with maximal monotone operator in reflexive Banach spaces. Solodov and Svaiter (2000) first introduced a new proximal-type method for generating a strongly convergent sequence to the zero of maximal monotone operator in Hilbert spaces, and subsequently Kamimura and Takahashi (2003) extended Solodov and Svaiter algorithm and strong convergence result to the setting of uniformly con...

Mastroeni G; Jc, Yao; Lc, Ceng

2008-01-01

58

Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces  

CERN Document Server

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space valid for cone metric space automatically.

Asadi, Mehdi; Soleiman, Hossein

2011-01-01

59

Extension of multilinear operators on Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper considers the problem of extending multilinear forms on a Banach space X to a larger space Y containing it as a closed subspace. For instance, if X is a subspace of Y and X0 ! Y 0 extends linear forms, then the induced Nicodemi operators extend multilinear forms. It is shown that an extension operator X0 ! Y 0 exists if and only if X is locally complemented in Y . Also, these extension operators preserve the symmetry if and only if X is regular. Finally, multlinear characterization...

Villanueva, Ignacio; Cabello Sa?nchez, Fe?lix; Garcia, R.

2001-01-01

60

Smooth functions and partitions of unity on certain Banach spaces  

CERN Document Server

We construct infinitely differentiable norms and partitions of unity for a class of Banach spaces which includes all spaces $\\C(K)$ with $K$ a countable compact space, and all spaces $\\C_0[0,\\Omega )$ with $\\Omega $ an ordinal.

Haydon, R

1995-01-01

 
 
 
 
61

Unbounded operators on Banach spaces over the quaternion field  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups of quaternion quasi-linear operators are investigated and the polar decomposition theorem for them is proved.

Ludkovsky, S. V.

2004-01-01

62

Displaying Polish groups on separable Banach spaces  

CERN Document Server

A display of a topological group G on a Banach space X is a topological isomorphism of G with the isometry group Isom(X,||.||) for some equivalent norm ||.|| on X, where the latter group is equipped with the strong operator topology. Displays of Polish groups on separable real spaces are studied. It is proved that any closed subgroup of the infinite symmetric group S_\\infty containing a non-trivial central involution admits a display on any of the classical spaces c0, C([0,1]), lp and Lp for 1 <=p <\\infty. Also, for any Polsih group G, there exists a separable space X on which {-1,1} x G has a display.

Ferenczi, Valentin

2011-01-01

63

Cylindrical Levy processes in Banach spaces  

CERN Document Server

Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and hence weak (cylindrical) stochastic processes. In this paper we focus on cylindrical Levy processes. These have (weak) Levy-Ito decompositions and an associated Levy-Khintchine formula. If the process is weakly square integrable, its covariance operator can be used to construct a reproducing kernel Hilbert space in which the process has a decomposition as an infinite series built from a sequence of uncorrelated bona fide one-dimensional Levy processes. This series is used to define cylindrical stochastic integrals from which cylindrical Ornstein-Uhlenbeck processes may be constructed as unique solutions of the associated Cauchy problem. We demonstrate that such processes are cylindrical Markov processes and study their (cylindrical) invariant measures.

Applebaum, David

2009-01-01

64

Generalized quasi-Banach sequence spaces and measures of noncompactness  

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in portuguese Dado 0 [...] o compacidade de Hausdorff. Como uma aplicao, conjuntos compactos nos espa, cos de interpolao s ?, de um par quase-Banach so estudados. Abstract in english Given 0 [...] As an application, compact sets in s ? -interpolation spaces of a quasi-Banach couple are studied.

EDUARDO B., SILVA; DIOCESAR L., FERNANDEZ; LUDMILA, NIKOLOVA.

2013-06-01

65

Matrix transformations involving certain Banach space valued sequence spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper for Banach spaces $X$ and $Y$ we characterize matrix classes $ (\\Gamma (X,\\lambda$, $ l_\\infty(Y,\\mu$, $ (\\Gamma(X,\\lambda,C(Y,\\mu$, $ (\\Gamma(X,\\lambda$, $ c_0(Y,\\mu$, $ (\\Gamma(X,\\lambda$, $ \\Gamma^*(Y,\\mu$, $ (l_1(X,\\lambda$, $ \\Gamma(Y,\\mu$ and $ (c_0(X,\\lambda$, $ c_0(Y,\\mu$ of bounded linear operators involving $ X$- and $ Y$-valued sequence spaces. Further as an application of the matrix class $ (c_0(X,\\lambda$, $ c_0(Y,\\mu$ we investigate the Banach space $ B(c_0(X,\\lambda$, $ c_0(Y,\\mu$ of all bounded linear mappings of $ c_0(x,\\lambda$ to $ c_0(Y,\\mu$.

J. K. Srivastava

2000-06-01

66

Browder-Krasnoselskii-Type Fixed Point Theorems in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract We present some fixed point theorems for the sum of a weakly-strongly continuous map and a nonexpansive map on a Banach space . Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.

Taoudi Mohamed-Aziz

2010-01-01

67

On Uniform Exponential Trichotomy of Evolution Operators in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper presents necessary and sufficient conditions for uniform exponential trichotomy of nonlinear evolution operators in Banach spaces. Thus are obtained results which extend well-known results for uniform exponential stability in the linear case.

Megan, Mihail; Stoica, Codruta

2008-01-01

68

On second order impulsive functional differential equations in Banach spaces  

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Full Text Available In this paper, a fixed point theorem due to Schaefer is used to investigate the existence of solutions for second order impulsive functional differential equations in Banach spaces.

M. Benchohra

2002-01-01

69

A look at proximinal and Chebyshev sets in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The main aim of this survey is to present some classical as well asrecent characterizations involving the notion of proximinal and Chebyshev sets inBanach spaces. In particular, we discuss the convexity of Chebyshev sets.

Hadi Haghshenas; Amanollah Assadi; Narang, T. D.

2014-01-01

70

A look at proximinal and Chebyshev sets in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The main aim of this survey is to present some classical as well asrecent characterizations involving the notion of proximinal and Chebyshev sets inBanach spaces. In particular, we discuss the convexity of Chebyshev sets.

Hadi Haghshenas

2014-05-01

71

Stability of vector measures and twisted sums of Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A Banach space $X$ is said to have the $\\mathsf{SVM}$ (stability of vector measures) property if there exists a constant $v<\\infty$ such that for any algebra of sets $\\mathcal F$, and any function $\

Kochanek, Tomasz

2012-01-01

72

Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces  

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Full Text Available We introduce and study Clarkson, Dolnikov-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 Schffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hlder-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.

Sergey Ajiev

2013-05-01

73

Construction of generalized atomic decompositions in Banach spaces  

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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.

Raj Kumar

2014-06-01

74

Metric embeddings bilipschitz and coarse embeddings into Banach spaces  

CERN Document Server

Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc

Ostrovskii, Mikhail I

2013-01-01

75

Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces  

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Full Text Available Abstract Let be a reflexive Banach space with a uniformly Gteaux 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 solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.

Jung JongSoo

2008-01-01

76

Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces  

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Full Text Available Let be a reflexive Banach space with a uniformly Gteaux differentiable norm, let be a nonempty closed convex subset of , and let be a uniformly continuous pseudocontraction. If is any contraction map on and if every nonempty closed convex and bounded subset of has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers , , that the iteration process , , , strongly converges to the fixed point of , which is the unique solution of some variational inequality, provided that is bounded.

Udomene Aniefiok

2006-01-01

77

Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces  

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Full Text Available We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding's technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate solutions of the generalized nonlinear mixed variational-like inequality, and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend, and unify many known results in this area.

Yali Zhao

2006-05-01

78

Amenability of ultraproducts of Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of $\\mc A$ is Arens regular, and give some evidence that this is if and only if $\\mc A$ is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapower of a dual Banach algebra. We study how tensor products of ultrapowers...

Daws, Matthew

2007-01-01

79

Banach's space: Lviv and the Scottish cafe  

Directory of Open Access Journals (Sweden)

Full Text Available In a sense Stefan Banach is the patron saint of this workshop. He was one of the most prominent former residents of Lviv. His ``hangout'', the Scottish Cafe, is shown in the street scene that is the cover of the book of abstracts.

D.Henderson

2004-01-01

80

Reverses of the Triangle Inequality in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Recent reverses for the discrete generalised triangle inequality and its continuous version for vector-valued integrals in Banach spaces are surveyed. New results are also obtained. Particular instances of interest in Hilbert spaces and for complex numbers and functions are pointed out as well.

Dragomir, Sever Silvestru

2005-01-01

 
 
 
 
81

A *-Autonomous Category of Banach Spaces--Correction  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We describe a $\\C$-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category of topological $\\C$-linear spaces has been added to version 2.

Day, Brian

2009-01-01

82

Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers are primary  

CERN Document Server

In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary. Consequently, any infinite dimensional nonsuperreflexive Banach space can be isometrically embedded into its primary ultrapowers.

Wilzcek, Piotr

2011-01-01

83

Banach spaces and groups - order properties and universal models  

CERN Document Server

We deal with two natural examples of almost-elementary classes: the class of all Banach spaces (over R or C) and the class of all groups. We show both of these classes do not have the strict order property, and find the exact place of each one of them in Shelah's SOP_n (strong order property of order n) hierarchy. Remembering the connection between this hierarchy and the existence of universal models, we conclude, for example, that there are ``few'' universal Banach spaces (under isometry) of regular cardinalities.

Shelah, S; Shelah, Saharon; Usvyatsov, Alex

2003-01-01

84

Flows driven by Banach space-valued rough paths  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path, can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a si...

Bailleul, Ismael

2013-01-01

85

A Representation Theorem for Completely Contractive Dual Banach Algebras  

CERN Document Server

In this paper, we prove that every completely contractive dual Banach algebra is completely isometric to a $w^\\ast$-closed subalgebra the operator space of completely bounded linear operators on some reflexive operator space.

Uygul, F

2007-01-01

86

Fast regularizing sequential subspace optimization in Banach spaces  

International Nuclear Information System (INIS)

We are concerned with fast computations of regularized solutions of linear operator equations in Banach spaces in case only noisy data are available. To this end we modify recently developed sequential subspace optimization methods in such a way that the therein employed Bregman projections onto hyperplanes are replaced by Bregman projections onto stripes whose width is in the order of the noise level

87

The reconstruction property in Banach spaces and a perturbation theorem  

DEFF Research Database (Denmark)

Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop a more general perturbation theory that does not force equivalence of the sequences.

Casazza, P.G.; Christensen, Ole

2008-01-01

88

On Frchet differentiability of Lipschitz maps between Banach spaces  

CERN Document Server

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Frechet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality). Our aims are achieved by introducing a new class of null sets in Banach spaces (called $\\Gamma$-null sets), whose definition involves both the notions of category and measure, and showing that the required differentiability holds almost everywhere with respect to it. We even obtain existence of Fr\\'echet derivatives of Lipschitz functions between certain infinite-dimensional Banach spaces;no such results have been known previously. Our main result states that a Lipschitz map between separable Banach spaces is Fr\\'echet differentiable $\\Gamma$-almost everywhere provided that ...

Lindenstrauss, J; Lindenstrauss, Joram; Preiss, David

2003-01-01

89

On some impulsive fractional differential equations in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of PC-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

W. Wei

2010-01-01

90

Improved bounds in the metric cotype inequality for Banach spaces  

CERN Document Server

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)}.

Giladi, Ohad; Naor, Assaf

2010-01-01

91

Functional differential equations with infinite delay in Banach spaces  

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Full Text Available In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponential asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation, and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed only in the exponentially fading memory phase space.

Tijun Xiao

1991-09-01

92

Some remarks on controllability of evolution equations in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In almost all papers in the literature, the results on exact controllability hold only for finite dimensional Banach spaces, since compactness of the semigroup and the bounded invertibility of an operator implies finite dimensional. In this note we show that the existence theory on controllability in the literature, can trivially be adjusted to include the infinite dimensional space setting, if we replace the compactness of operators with the complete continuity of the nonlinearity.

Sotiris K. Ntouyas

2009-06-01

93

On best proximity points in metric and Banach spaces  

CERN Document Server

In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We do it from two different approaches, leading each one of them to different results which complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.

Espinola, Rafa

2009-01-01

94

Banach Spaces Of The Type Of Tsirelson  

CERN Document Server

To any pair ( M , theta ) where M is a family of finite subsets of N compact in the pointwise topology, and 0{1/n} then T_M^theta is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than omega then T_M^theta does not contain any l^p, while if the Cantor-Bendixson index of M is finite thenT_M^theta contains some l^p or c_o . In particular, if M ={ A subset N : |A| leq n } and {1/n}

Argyros, S A; Argyros, Spiros A.; Deliyanni, Irene

1992-01-01

95

Strong convergence of an iterative sequence for maximal monotone operators in a Banach space  

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Full Text Available We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

Wataru Takahashi

2004-04-01

96

Dual Banach algebras: representations and injectivity  

CERN Document Server

We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C$^*$- and W$^*$-algebras; we show that interpolation space techniques can be used in the place of GNS type arguments. We define a notion of injectivity for dual Banach algebras, and show that this is equivalent to Connes-amenability. We conclude by looking at the problem of defining a well-behaved tensor product for dual Banach algebras.

Daws, M

2006-01-01

97

Strictly stationary solutions of ARMA equations in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain assumptions. First, we obtain conditions for ARMA(1,$q$) equations by excluding zero and the unit circle from the spectrum of the operator of the AR part. We then extend this to ARMA($p$,$q$) equations. Finally, we discuss various examples.

Spangenberg, Felix

2012-01-01

98

Pointwise Trichotomy for Skew-Evolution Semiflows on Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The paper introduces the notion of skew-evolution semiflows and presents the concept of pointwise trichotomy in the case of skew-evolution semiflows on a Banach space. The connection with the classic notion of trichotomy presented by us in a previous paper in 2006 for evolution operators, is also emphasized, as well as some characterizations. The approach of the theory is from uniform point of view. The study can also be extended to systems with control whose state evolution...

Stoica, Codruta

2008-01-01

99

Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces  

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Full Text Available In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968 and Bose and Mukherjee (1981 as the special cases with a different and constructive method.

Bapurao C. Dhage

2014-10-01

100

Greedy Algorithms for Reduced Bases in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 reduc...

Devore, Ronald; Petrova, Guergana; Wojtaszczyk, Przemyslaw

2012-01-01

 
 
 
 
101

Weak convergence of an iterative sequence for accretive operators in Banach spaces  

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Full Text Available Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shte?n and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.

Iiduka Hideaki

2006-01-01

102

Some Representation Theorem for nonreflexive Banach space ultrapowers under the Continuum Hypothesis  

CERN Document Server

In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real-valued functions on the Parovicenko space. This Representation Theorem will be helpful in proving some facts from geometry and topology of nonreflexive Banach space ultrapowers.

Wilczek, Piotr

2011-01-01

103

Boundaries for algebras of holomorphic functions on Banach spaces  

CERN Document Server

We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space $X$ is the unit sphere $S_X$ if $X$ is locally c-convex. In particular, it is shown that the unit sphere of the Orlicz-Lorentz sequence space $\\lambda_{\\phi, w}$ is the Shilov boundary for algebras of holomorphic functions on $\\lambda_{\\phi, w}$ if $\\phi$ satisfies the $\\delta_2$-condition.

Choi, Yun Sung; Lee, Han Ju

2007-01-01

104

A proximal point method for nonsmooth convex optimization problems in Banach spaces  

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Full Text Available In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.

Y. I. Alber

1997-01-01

105

A proximal point method for nonsmooth convex optimization problems in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, we establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. We apply a new technique which includes Banach...

Iusem, A. N.; Burachik, R. S.; Alber, Y. I.

1997-01-01

106

Optimal quantizers for Radon random vectors in a Banach space  

CERN Document Server

For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\\_{n,r}(X,E) = inf{(E (\\min\\_{a \\in \\alpha} || X-a ||^r)^{1/r}}, where the infimum is taken over all subsets \\alpha of E with card(\\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.

Graf, S; Gilles, P; Graf, Siegried; Luschgy, Harald; Gilles, Pag\\`{e}s

2005-01-01

107

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+  

Directory of Open Access Journals (Sweden)

Full Text Available We study the spectrum of multipliers (bounded operators commuting with the shift operator on a Banach space of sequences on . Given a multiplier , we prove that where is the symbol of . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on . We generalize the results for multipliers on Banach spaces of sequences on .Estudiamos el espectro de los multiplicadores (operadores acotados que conmutan con el operador shift en un espacio de Banach de sucesiones en . Dado un multiplicador , probamos que donde es el smbolo de . Obtenemos un resultados similar para el espectro de un operador que conmuta con el shift en un espacio de Banach de sucesiones en . Generalizamos los resultados sobre multiplicadores en espacios de Banach de sucesiones en .

Violeta Petkova

2012-10-01

108

On moduli of convexity in Banach spaces  

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Full Text Available 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 .

Reif Ji?

2005-01-01

109

When symplectic topology meets Banach space geometry  

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In this paper we survey some recent works that take the first steps toward establishing bilateral connections between symplectic geometry and several other fields, namely, asymptotic geometric analysis, classical convex geometry, and the theory of normed spaces.

Ostrover, Yaron

2014-01-01

110

p-adic Banach space operators and adelic Banach space operators  

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Full Text Available In this paper, we study non-Archimedean Banach \\(*\\-algebras \\(\\frak{M}_{p}\\ over the \\(p\\-adic number fields \\(\\mathbb{Q}_{p}\\, and \\(\\frak{M}_{\\mathbb{Q}}\\ over the adele ring \\(\\mathbb{A}_{\\mathbb{Q}}\\. We call elements of \\(\\frak{M}_{p}\\, \\(p\\-adic operators, for all primes \\(p\\, respectively, call those of \\(\\frak{M}_{\\mathbb{Q}}\\, adelic operators. We characterize \\(\\frak{M}_{ \\mathbb{Q}}\\ in terms of \\(\\frak{M}_{p}\\'s. Based on such a structure theorem of \\(\\frak{M}_{\\mathbb{Q}}\\, we introduce some interesting \\(p\\-adic operators and adelic operators.

Ilwoo Cho

2014-01-01

111

Weakly convex and proximally smooth sets in Banach spaces  

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We establish interconnections between the conditions of weak convexity in the sense of Vial, weak convexity in the sense of Efimov-Stechkin, and proximal smoothness of sets in Banach spaces. We prove a theorem on the separation by a sphere of two disjoint sets, one of which is weakly convex in the sense of Vial and the other is strongly convex. We also prove that weakly convex and proximally smooth sets are locally connected, and study questions related to the preservation of the conditions of weak convexity and proximal smoothness under passage to the limit.

Balashov, M V; Ivanov, Grigorii E [Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Region, Russian Frderation (Russian Federation)

2009-06-30

112

Square variation of Brownian paths in Banach spaces  

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Full Text Available It is known that if {W(t,   0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n−W((i−1/2n|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.

Mou-Hsiung Chang

1982-09-01

113

Property (T) and rigidity for actions on Banach spaces  

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We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\\leq p<\\infty$. We show that the fixed point property for $L^p$ follows from property (T) when $1

Bader, U.; Furman, A.; Gelander, T.; Monod, N.

2005-01-01

114

Pointwise Trichotomy for Skew-Evolution Semiflows on Banach Spaces  

CERN Document Server

The paper introduces the notion of skew-evolution semiflows and presents the concept of pointwise trichotomy in the case of skew-evolution semiflows on a Banach space. The connection with the classic notion of trichotomy presented by us in a previous paper in 2006 for evolution operators, is also emphasized, as well as some characterizations. The approach of the theory is from uniform point of view. The study can also be extended to systems with control whose state evolution can be described by skew-evolution semiflows.

Stoica, Codruta

2008-01-01

115

Dynamical systems method (DSM) for nonlinear equations in Banach spaces  

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Let $F:X\\to X$ be a $C^2_\\loc$ map in a Banach space $X$, and $A$ be its Fr\\`echet derivative at the element $w:=w_\\ve$, which solves the problem $(\\ast) \\dotw=-A^{-1}_\\ve(F(w)+\\ve w)$, $w(0)=w_0$, where $A_\\ve:=A+\\ve I$. Assume that $\\|A^{-1}_\\ve\\|\\leq c \\ve^{-k}$, $0\\ve_0$. Then $(\\ast)$ has a unique global solution, $w(t)$, there exists $w(\\infty)$, and $(\\ast\\ast) F(w(\\infty))+\\ve w(\\infty)=0$. Thus the DSM (Dynamical Systems Method) is justified for eq...

Ramm, A. G.

2004-01-01

116

Square variation of Brownian paths in Banach spaces  

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It is known that if {W(t),   0≤t≤1} is a standard Brownian motion in ℝ then limn→∞∑i=12n|W(i/2n)−W((i−1)/2n)|2=1 almost surely. We generalize this celebrated theorem of Levy to Brownian motion in real separable Banach spaces.

Mou-Hsiung Chang

1982-01-01

117

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, ? 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

118

Generation theory for semigroups of holomorphic mappings in Banach spaces  

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Full Text Available We study nonlinear semigroups of holomorphic mappings in Banach spaces and their infinitesimal generators. Using resolvents, we characterize, in particular, bounded holomorphic generators on bounded convex domains and obtain an analog of the Hille exponential formula. We then apply our results to the null point theory of semi-plus complete vector fields. We study the structure of null point sets and the spectral characteristics of null points, as well as their existence and uniqueness. A global version of the implicit function theorem and a discussion of some open problems are also included.

Simeon Reich

1996-01-01

119

On Asymptotic Behaviors for Linear Skew-Product Semiflows in Banach Spaces  

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In this paper we give several characterizations of some asymptotic behaviours: stability, instability, dichotomy and trichotomy of linear skew product semiflows in Banach spaces. The obtained results are generalizations of some well-known results on asymptotic behaviours of linear differential equations. There are also presented several examples of semiflows and linear skew-product semiflows in Banach spaces.

Minda, Andrea A.; Tomescu, Mihaela A.

2006-01-01

120

On the Stability of Generalized Additive Functional Inequalities in Banach Spaces  

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Full Text Available Abstract We study the following generalized additive functional inequality , associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

Park Choonkil

2008-01-01

 
 
 
 
121

A note on nonfragmentability of Banach spaces  

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Full Text Available We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space X with the tree-completeness property contains a disjoint sequences of clopen sets, then (C(X, weak is not fragmented by any metric which is stronger than weak topology. In particular, C(X does not admit any equivalent locally uniformly convex renorming.

S. Alireza Kamel Mirmostafaee

2001-07-01

122

Stochastic integration in Banach spaces theory and applications  

CERN Document Server

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...

Mandrekar, Vidyadhar

2015-01-01

123

Porous sets for mutually nearest points in Banach spaces  

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Full Text Available Let $B(X$ denote the family of all nonempty closed bounded subsets of a real Banach space $X$, endowed with the Hausdorff metric. For $E, F \\in B(X$ we set $\\lambda _{EF} = inf \\{\\|z - x\\| : x \\in E, z \\in F \\}$. Let $D$ denote the closure (under the maximum distance of the set of all $(E, F \\in B(X \\times B(X$ such that $\\lambda {EF} > 0$. It is proved that the set of all $(E, F \\in D $ for which the minimization problem $min_{x \\in E, z\\in F}\\|x - z\\|$ fails to be well posed in a $\\sigma$-porous subset of $D$.

Chong Li

2008-01-01

124

Dynamical systems method (DSM) for nonlinear equations in Banach spaces  

CERN Document Server

Let $F:X\\to X$ be a $C^2_\\loc$ map in a Banach space $X$, and $A$ be its Fr\\`echet derivative at the element $w:=w_\\ve$, which solves the problem $(\\ast) \\dotw=-A^{-1}_\\ve(F(w)+\\ve w)$, $w(0)=w_0$, where $A_\\ve:=A+\\ve I$. Assume that $\\|A^{-1}_\\ve\\|\\leq c \\ve^{-k}$, $0\\ve_0$. Then $(\\ast)$ has a unique global solution, $w(t)$, there exists $w(\\infty)$, and $(\\ast\\ast) F(w(\\infty))+\\ve w(\\infty)=0$. Thus the DSM (Dynamical Systems Method) is justified for equation $(\\ast\\ast)$. The limit of $w_\\ve$ as $\\ve\\to 0$ is studied.

Ramm, A G

2004-01-01

125

Convergence Theorems for Asymptotically Nonexpansive Mappings in Banach Spaces  

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Full Text Available Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E. Let T: K E be an asymptotically nonexpansive mapping with {kn} [1, such that ( from n=1 to (kn - 1 and let F(T be nonempty, where F(T denotes the fixed points set of T. Let{an}, {bn},{gn}, {an}, {bn}, {gn}, {an}, {bn}and {gn}be real sequences in [0, 1] such that an +bn +gn =an +bn +gn =an +bn +gn = 1 and e an,an, an 1 - e for all n N and some e > 0, starting with arbitrary x1 K,define the sequence { xn} by setting zn = P(anT(PTn-1xn+ bnxn+ gnwn, yn =P(anT(PTn-1zn+ bnxn+ gnvn, xn+1 =P(anT(PTn-1yn+ bnxn+ gnun,with the restrictions ( from n=1 to (gn ,( from n=1 to (gn and ( from n=1 to (gn where { wn} , { vn} and { un} are bounded sequences in K. (i If E is realuniformly convex Banach space satisfying Opial's condition, then weak convergence of { xn} to some p F(T is obtained; (ii If T satisfies condition (A, then { xn} convergence strongly to some p F(T.

Meijuan Shang

2008-03-01

126

A note on local asymptotic behaviour for Brownian motion in Banach spaces  

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Full Text Available In this paper we obtain an integral characterization of a two-sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B=ℝn. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3]. The special case that when B is itself a real separable Hilbert space is also illustrated.

Mou-Hsiung Chang

1979-12-01

127

Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces  

International Nuclear Information System (INIS)

Let E be a real reflexive Banach space with uniform Gateaux differentiable norm, K be a nonempty bounded closed and convex subset of E , T : K ? K be a uniformly L-Lipschitzian mapping such that F (T) := {x element of K : Tx = x} ? 0, u element of K be fixed and let {?n}n?0 and {?n}n?0 subset of (0, 1) be such that limn?? ?n = 0 = limn? ? ?n and limn? ?(?n - 1)/ ?n = 0, where ?n ?j=0n ?j and ?j = 1 + ?j?jL. Let Sn := (1 - ?n?n)I + ?n?nTn. It is proved that there exists some integer N0 > 1, such that for each n ? N0, there exists unique xn element of K such that xn = ?nu+(1 -?n) 1/ (n + 1) ?j=0n Sjxn. If ? : E ? R is defined by ? (y) := LIMn vertical bar vertical bar xn -y vertical bar vertical bar2 for all y element of E here LIM denotes a Banach limit, vertical bar vertical bar xn - Txn vertical bar vertical bar ? 0 as n ? ? and Kmin intersection F (T) ? 0, where Kmin := {x element of E : ? (x) = min (u element of K) ? (u) }, then it is proved that {xn} converges strongly to a fixed point of T. As an application, it is proved that the iterative process, z0 element of K, zn+1 alpha#nu + (1 - ?n) 1/ (n + 1) ?j=0n Sjzn , n ? 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)

128

Mathematical simulation of almost periodic functions with values in Banach space by means of the multiplicator  

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Full Text Available Research of almost periodic functions with values in Banach space proceeds. The concept of the multiplicator by means of which the theorem of integral from almost periodic function is proved is entered.

Kretov M.

2013-01-01

129

Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces  

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Full Text Available A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.

Jin Liang

2010-01-01

130

Approximating zero points of accretive operators with compact domains in general Banach spaces  

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Full Text Available We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.

Wataru Takahashi

2005-04-01

131

Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces  

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We shall consider the behaviour of Ishikawa iteration with errors in a uniformly convex Banach space. Then we generalize the two theorems of Tan and Xu without the restrictions that C is bounded and limsupnsn<1.

Li Shenghong; Deng Lei

2000-01-01

132

Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces  

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Full Text Available In 1979, Ishikawa proved a strong convergence theorem for finite families of nonexpansive mappings in general Banach spaces. Motivated by Ishikawa's result, we prove strong convergence theorems for infinite families of nonexpansive mappings.

Suzuki Tomonari

2005-01-01

133

Ishikawa iterative sequence with errors for strongly pseudocontractive operators in arbitrary Banach spaces  

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The Ishikawa iterative sequences with errors are studied for Lipschitzian strongly pseudocontractive operators in arbitrary real Banach spaces; some well-known results of Chidume (1998) and Zeng (2001) are generalized.

Yongjin Li

2004-01-01

134

Nonsmooth and nonlocal differential equations in lattice-ordered Banach spaces  

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Full Text Available We derive existence results for initial and boundary value problems in lattice-ordered Banach spaces. The considered problems can be singular, functional, discontinuous, and nonlocal. Concrete examples are also solved.

S. Heikkil

2005-06-01

135

Nonsmooth and nonlocal differential equations in lattice-ordered Banach spaces  

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Full Text Available We derive existence results for initial and boundary value problems in lattice-ordered Banach spaces. The considered problems can be singular, functional, discontinuous, and nonlocal. Concrete examples are also solved.

Heikkil S

2005-01-01

136

Right-Existence and Left?Existence of Orthogonality in Quasi?Banach Spaces  

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Full Text Available A class of new generalized orthogonality of quasi?Banach spaces is given in this paper. It is a generalization of orthogonality. First, the relation of orthogonality and linear functional are introduced. At the same time, a necessary and sufficient condition of orthogonality in quasi?Banach spaces is given. Namely, let ?X? be a quasi?Banach spaces on * is equivalent to ?x?H?. The sufficient conditions of right?existence and left?existence of orthogonality are discussed. Finally, two examples which show that right?existence of orthogonality in quasi?Banach spaces does not exist for all elements are given.(* Indicates a formula, please see the full text

XUE Jian-ming

2012-09-01

137

On multivalued nonlinear variational inclusion problems with -accretive mappings in Banach spaces  

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Full Text Available Based on the notion of -accretive mappings and the resolvent operators associated with -accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problems with -accretive mappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving -accretive mappings. We also prove the existence of solutions and the convergence of the sequences generated by the algorithms in -uniformly smooth Banach spaces.

Lan Heng-You

2006-01-01

138

Iterative approximation of a solution of a general variational-like inclusion in Banach spaces  

CERN Document Server

In this paper, we introduce a class of $\\eta$-accretive mappings in a real Banach space, and show that the $\\eta$-proximal point mapping for $\\eta$-$m$-accretive mapping is Lipschitz continous. Further we develop an iterative for a class of general variational-like inclusions involving $\\eta$-accretive mappings in real Banach space, and discuss its convergence criteria. The class of $\\eta$-accretive mappings includes several important classes of operators that have been studied by various authors.

Chidume, C E; Zegeye, H

2002-01-01

139

Iterative approximation of a solution of a general variational-like inclusion in Banach spaces  

International Nuclear Information System (INIS)

In this paper, we introduce a class of ?-accretive mappings in a real Banach space, and show that the ?-proximal point mapping for ?-m-accretive mapping is Lipschitz continuous. Further we develop an iterative algorithm for a class of general variational-like inclusions involving ?-accretive mappings in real Banach space, and discuss its convergence criteria. The class of ?-accretive mappings includes several important classes of operators that have been studied by various authors. (author)

140

On the Stability of Generalized Additive Functional Inequalities in Banach Spaces  

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Full Text Available We study the following generalized additive functional inequality ‖af(x+bf(y+cf(z‖≤‖f(αx+βy+γz‖, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

Dong Yun Shin

2008-05-01

 
 
 
 
141

Growth estimates for pseudo-dissipative holomorphic maps in Banach spaces  

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In this paper we introduce a class of pseudo-dissipative holomorphic maps which contains, in particular, the class of infinitesimal generators of semigroups of holomorphic maps on the unit ball of a complex Banach space. We give a growth estimate for maps of this class. In particular, it follows that pseudo-dissipative maps on the unit ball of (infinite-dimensional) Banach spaces are bounded on each domain strictly contained inside the ball. We also present some applications.

Bracci, Filippo; Elin, Mark; Shoikhet, David

2013-01-01

142

Estimates of disjoint sequences in Banach lattices and R.I. function spaces  

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We introduce UDSp-property (resp. UDTq-property) in Banach lattices as the property that every normalized disjoint sequence has a subsequence with an upper p-estimate (resp. lower q-estimate). In the case of rearrangement invariant spaces, the relationships with Boyd indices of the space are studied. Some applications of these properties are given to the high order smoothness of Banach lattices, in the sense of the existence of differentiable bump functions.

Gonzalo, R.; Jaramillo Aguado, Jesu?s A?ngel

2005-01-01

143

Some classes of rational functions and related Banach spaces  

CERN Document Server

For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded above by M and below by 1/M. Each numerator is a monic monomial of the same degree as the corresponding denominator. Then we form the Banach space of countable linear combinations of such rational functions with absolutely summable coefficients, normed by the infimum of sums of absolute values of the coefficients. We show that for rational functions whose denominators are rth powers of a specific 1+Q, or differences of two such rational functions with the same numerator, the norm is achieved by and only by the obvious combination of one or two functions respectively. We also find bounds for coefficients in partial-fraction decompositions of some specific rational functions, which in some cases are quite sharp.

Dudley, R M; Wang, Zuoqin; Yang, Fangyun

2007-01-01

144

Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces  

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Full Text Available We prove two existence theorems for the integrodifferential equation of mixed type: x'(t=f(t,x(t,∫0tk1(t,sg(s,x(sds,∫0ak2(t,sh(s,x(sds, x(0=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP integral. Additionally, the functions f, g, h, x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.

Grzegorz Nowak

2007-09-01

145

Spectral results for operators commuting with translations on Banach spaces of sequences on Zk and Z+  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Estudiamos el espectro de los multiplicadores (operadores acotados que conmutan con el operador shift ) en un espacio de Banach [...] =24 id="_x0000_i1042" src="http://fbpe/img/cubo/v14n3/art02-03.jpg" alt="http://fbpe/img/cubo/v14n3/art02-03.jpg">de sucesiones en . Dado un multiplicador , probamos que donde es el smbolo de . Obtenemos un resultados similar para el espectro de un operador que conmuta con el shift en un espacio de Banach de sucesiones en . Generalizamos los resultados sobre multiplicadores en espacios de Banach de sucesiones en . Abstract in english We study the spectrum of multipliers (bounded operators commuting with the shift operator ) on a Banach space [...] 51" src="http://fbpe/img/cubo/v14n3/art02-03.jpg" alt="http://fbpe/img/cubo/v14n3/art02-03.jpg">of sequences on . Given a multiplier , we prove that where is the symbol of . We obtain a similar result for the spectrum of an operator commuting with the shift on a Banach space of sequences on . We generalize the results for multipliers on Banach spaces of sequences on .

Violeta, Petkova.

2012-10-01

146

A New System of Nonlinear Fuzzy Variational Inclusions Involving -Accretive Mappings in Uniformly Smooth Banach Spaces  

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Full Text Available Abstract A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion problems as special cases of this system. By using the resolvent operator technique associated with -accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures.

Cho YJ

2009-01-01

147

Lyapunov operator inequalities for exponential stability of linear skew-product semiflows in Banach spaces  

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Full Text Available In the present paper we prove a sufficient condition and a characterization for the stability of linear skew-product semiflows by using Lyapunov function, in Banach spaces. These are generalizations of the results obtained in Ahmed N. U., Semigroups Theory with Applications to Systems and Control, Pittman Research, Notes Math., 1991. and Preda C. and Preda P., Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators, Appl. Math. Letters 25(3 (2012, 401-403. for the case of C0-semigroups. Moreover, there are presented the discrete variants of the results mentioned above.

Pra?a C.

2013-09-01

148

The Failure of Rolle's Theorem in Infinite-Dimensional Banach Spaces  

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We prove the following new characterization of Cp Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a Cp smooth (Lipschitz) bump function if and only if it has another Cp smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in the interior of the support of f (that is, f does not satisfy Rolle's theorem). Moreover, the support of this bump can be assumed to be a smooth starlike body. The ``twisted tube'' method we use in ...

Azagra Rueda, Daniel; Jime?nez Sevilla, Mari?a Del Mar

2001-01-01

149

Iterative approximation of a solution of a general variational-like inclusion in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various...

Zegeye, H.; Kazmi, K. R.; Chidume, C. E.

2004-01-01

150

Iterative approximation of a solution of a general variational-like inclusion in Banach spaces  

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Full Text Available We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving η-accretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretive mappings includes several important classes of operators that have been studied by various authors.

H. Zegeye

2004-05-01

151

Lower estimates of random unconditional constants of Walsh-Paley martingales with values in banach spaces  

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For a Banach space X we define RUMD_n(X) to be the infimum of all c>0 such that (AVE_{\\epsilon_k =\\pm 1} || \\sum_1^n epsilon_k (M_k - M_{k-1} )||_{L_2^X}^2 )^{1/2} <= c || M_n ||_{L_2^X} holds for all Walsh-Paley martingales {M_k}_0^n subset L_2^X with M_0 =0. We relate the asymptotic behaviour of the sequence {RUMD(X)}_{n=1}^{infinity} to geometrical properties of the Banach space X such as K-convexity and superreflexivity.

Geiss, Stefan

1992-01-01

152

A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces  

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Full Text Available In this paper, a new two-step iterative scheme with errors is introduced for two asymptotically nonexpansive nonself-mappings. Several convergence theorems are established in real Banach spaces and real uniformly convex Banach spaces. Our theorems improve and extend the results due to Agarwal-O'Regan-Sahu [R.P. Agarwal, Donal O'Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J.Nonliear Convex. Anal.8(1(2007 61--79] and many other papers.

Esref Turkmen

2011-12-01

153

A New Two-Step Iterative Process with Errors for Common Fixed Points in Banach Spaces  

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In this paper, a new two-step iterative scheme with errors is introduced for two asymptotically nonexpansive nonself-mappings. Several convergence theorems are established in real Banach spaces and real uniformly convex Banach spaces. Our theorems improve and extend the results due to Agarwal-O'Regan-Sahu [R.P. Agarwal, Donal O'Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J.Nonliear Convex. Anal.8(1)(2007) 61--79] and many other ...

Esref Turkmen; Murat Ozdemir; Sezgin Akbulut

2011-01-01

154

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting  

International Nuclear Information System (INIS)

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions. (paper)

155

The approximate inverse in action: IV. Semi-discrete equations in a Banach space setting  

Science.gov (United States)

This article concerns the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search for a solution in an infinite-dimensional Banach space having only a finite number of data available. In this sense the situation is applicable to a large variety of applications where a measurement process delivers a discretization of an infinite-dimensional data space. The method of approximate inverse computes scalar products of the data with pre-computed reconstruction kernels which are associated with mollifiers and the dual of the model operator. The convergence, approximation power and regularization property of this method when applied to semi-discrete operator equations in Hilbert spaces has been investigated in three prequels to this paper. Here we extend these results to a Banach space setting. We prove convergence and stability for general Banach spaces and reproduce the results specifically for the integration operator acting on the space of continuous functions.

Schuster, T.; Rieder, A.; Schpfer, F.

2012-10-01

156

Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces  

CERN Document Server

{\\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $00$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces.

Sukochev, F

2010-01-01

157

N-th order impulsive integro-differential equations in Banach spaces  

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Full Text Available We investigate the maximal and minimal solutions of initial value problem for N-th order nonlinear impulsive integro-differential equation in Banach space by establishing a comparison result and using the upper and lower solutions methods.

Manfeng Hu

2004-03-01

158

The generalized hardy operator with kernel and variable integral limits in banach function spaces  

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Full Text Available 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

Lang J

1999-01-01

159

Strong Convergence Theorems for Common Fixed Points of Multistep Iterations with Errors in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We establish strong convergence theorem for multi-step iterative scheme with errors for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. Our results extend and improve the recent ones announced by Plubtieng and Wangkeeree (2006, and many others.

Feng Gu

2009-01-01

160

A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  

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Full Text Available The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003, Xu and Ori (2001, and Zhou and Chang (2002.

Jing Lu

2006-11-01

 
 
 
 
161

A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003), Xu and Ori (2001), and Zhou and Chang (2002).

Gu Feng; Lu Jing

2006-01-01

162

A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Chang and Cho (2003, Xu and Ori (2001, and Zhou and Chang (2002.

Gu Feng

2006-01-01

163

Convergence rates for an iteratively regularized NewtonLandweber iteration in Banach space  

International Nuclear Information System (INIS)

In this paper, we provide convergence and convergence rate results for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting. Numerical experiments illustrate the performance of the method. (paper)

164

Generalized Bohl-Perron principle for differential equations with delay in a Banach spaces  

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Full Text Available We consider a linear homogeneous functional differential equation with delay in a Banach space. It is proved that if the corresponding non-homogeneous equation, with an arbitrary free term bounded on the positive half-line and with the zero initial condition, has a bounded solution, then the considered homogeneous equation is exponentially stable.

Michael Gil'

2013-06-01

165

Generalized Bohl-Perron principle for differential equations with delay in a Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We consider a linear homogeneous functional differential equation with delay in a Banach space. It is proved that if the corresponding non-homogeneous equation, with an arbitrary free term bounded on the positive half-line and with the zero initial condition, has a bounded solution, then the considered homogeneous equation is exponentially stable.

Michael Gil'

2013-01-01

166

Bound and periodic solutions of the Riccati equation in Banach space  

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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.

A. Ya. Dorogovtsev

1995-01-01

167

Degenerate non-stationary differential equations with delay in Banach spaces  

Science.gov (United States)

A generalization of the operator method by Grisvard is used to ensure weak and strict solutions to some degenerate differential equations with delay in Banach spaces, whose operator coefficients are time depending. Some applications to ordinary and partial differential equations with delay are described.

Favini, Angelo; Vlasenko, Larisa

2003-07-01

168

Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections  

CERN Document Server

In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.

Dehghan, Hossein

2011-01-01

169

Equivalent Definitions for Uniform Exponential Trichotomy of Evolution Operators in Banach Spaces  

CERN Document Server

The aim of this paper is to give necessary and sufficient conditions for the uniform exponential trichotomy property of nonlinear evolution operators in Banach spaces. The obtained results are generalizations for infinite-dimensional case of some well-known results of Elaydi and Hajek on exponential trichotomy of differential systems.

Megan, Mihail

2008-01-01

170

On Fr\\'echet differentiability of Lipschitz maps between Banach spaces  

CERN Document Server

A well-known open question is whether every countable collection of Lipschitz functions on a Banach space X with separable dual has a common point of Frechet differentiability. We show that the answer is positive for some infinite-dimensional X. Previously, even for collections consisting of two functions this has been known for finite-dimensional X only (although for one function the answer is known to be affirmative in full generality). Our aims are achieved by introducing a new class of null sets in Banach spaces (called $\\Gamma$-null sets), whose definition involves both the notions of category and measure, and showing that the required differentiability holds almost everywhere with respect to it. We even obtain existence of Fr\\'echet derivatives of Lipschitz functions between certain infinite-dimensional Banach spaces;no such results have been known previously. Our main result states that a Lipschitz map between separable Banach spaces is Fr\\'echet differentiable $\\Gamma$-almost everywhere provided that ...

Lindenstrauss, J; Lindenstrauss, Joram; Preiss, David

2003-01-01

171

Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces  

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Full Text Available We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

Takahashi Wataru

2005-01-01

172

Approximating solution of nonlinear variational inclusions by Ishikawa iterative process with errors in Banach spaces  

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In this paper, we introduce and study the existence of solutions and convergence of Ishikawa iterative processes with errors for a class of nonlinear variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [49, 11, 1617,19].

Yuan George Xian-Zhi; Huang Nan-Jing

2001-01-01

173

Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces  

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Full Text Available We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.

Jen-Chih Yao

2003-02-01

174

Parametric general variational-like inequality problem in uniformly smooth Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Using the concept of - -proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important cl...

Kr, Kazmi; Fa, Khan

2006-01-01

175

Parametric general variational-like inequality problem in uniformly smooth Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available Using the concept of - -proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given by many authors in this direction.

Kazmi KR

2006-01-01

176

Existence and convergence theorems for a class of multi-valued variational inclusions in Banach spaces  

International Nuclear Information System (INIS)

An existence theorem for a new class of multi-valued variational inclusion problems is established in smooth Banach spaces. Further, it is shown that a sequence of a Mann-type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems. (author)

177

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces  

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Full Text Available In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

Isa Yildirim

2011-03-01

178

Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras  

CERN Document Server

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.

Muscat, Joseph

2014-01-01

179

Linearly ordered compacta and Banach spaces with a projectional resolution of the identity  

CERN Document Server

We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a Valdivia compact and every separable subspace of $C(K)$ is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos.

Kubis, W

2006-01-01

180

Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions  

International Nuclear Information System (INIS)

In this paper we deal with convergence rates for regularizing ill-posed problems with operator mapping from a Hilbert space into a Banach space. Since we cannot transfer the well-established convergence rates theory in Hilbert spaces, only few convergence rates results are known in the literature for this situation. Therefore we present an alternative approach for deriving convergence rates. Hereby we deal with so-called distance functions which quantify the violation of a reference source condition. With the aid of these functions we present error bounds and convergence rates for regularized solutions of linear and nonlinear problems when the reference source condition is not satisfied. We show that the approach of applying distance functions carries over the idea of considering generalized source conditions in Hilbert spaces to inverse problems in Banach spaces in a natural way. Introducing this topic for linear ill-posed problems we additionally show that this theory can be easily extended to nonlinear problems

 
 
 
 
181

Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces  

International Nuclear Information System (INIS)

This paper treats the embedding of finite-dimensional subsets of a Banach space B into finite-dimensional Euclidean spaces. When the Hausdorff dimension of X ? X is finite, dH(X ? X) k are injective on X. The proof motivates the definition of the 'dual thickness exponent', which is the key to proving that a prevalent set of such linear maps have Hlder continuous inverse when the box-counting dimension of X is finite and k > 2dB(X). A related argument shows that if the Assouad dimension of X ? X is finite and k > dA(X ? X), a prevalent set of such maps are bi-Lipschitz with logarithmic corrections. This provides a new result for compact homogeneous metric spaces via the Kuratowksi embedding of (X, d) into L?(X)

182

From Hahn-Banach to monotonicity  

CERN Document Server

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 techniquefor 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...

Simons, Stephen

2008-01-01

183

Amenability of ultraproducts of Banach algebras  

CERN Document Server

We study when certain properties of Banach algebras are stable under ultrapower constructions. In particular, we consider when every ultrapower of $\\mc A$ is Arens regular, and give some evidence that this is if and only if $\\mc A$ is isomorphic to a closed subalgebra of operators on a super-reflexive Banach space. We show that such ideas are closely related to whether one can sensibly define an ultrapower of a dual Banach algebra. We study how tensor products of ultrapowers behave, and apply this to study the question of when every ultrapower of $\\mc A$ is amenable. We provide an abstract characterisation in terms of something like an approximate diagonal, and consider when every ultrapower of a C$^*$-algebra, or a group $L^1$-convolution algebra, is amenable.

Daws, Matthew

2007-01-01

184

Convergence theorems of common elements for mixed equilibrium problems, variational inequality problems and fixed point problems in Banach spaces  

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Full Text Available In this paper, a hybrid iterative scheme is introduced for theapproximation method for finding a common element of the set of mixed equilibrium problems, variational inequality problems and fixed point problems of two quasi-$phi$-nonexpansive mappings ina real uniformly convex and uniformly smooth Banach space. Then, we obtain a strong convergence theorem for the sequence generated by those process in Banach spaces. Moreover, we obtain new resultfor finding a zero point of maximal monotone operators in a Banach space. Our results improve and extend the corresponding results announced by Takahashi and Zembayashi [Strong and weak convergencetheorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009 45--57.] Qin, Cho and Kang [Convergence theorems of common elements forequilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009, 20--30.] Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithmfor fixed point problems and equilibrium problems of tworelatively quasi-nonexpansive mappings, Nonlinear Anal: Hybrid Systems. 3 (2009 11--20.] Cholamjiak [A hybrid iterative scheme for equilibrium problems, variational inequality problems and fixed point problems in Banach spaces, Fixed Point Theory Appl., (2009, Article ID 719360, 18 pages] and many authors.

Kriengsak Wattanawitoon

2011-01-01

185

On the number of non permutatively equivalent sequences in a Banach space  

CERN Document Server

This paper contains results concerning the Borel reduction of the relation $E_0$ of eventual agreement between sequences of 0's and 1's, to the relation of permutative equivalence between basic sequences in a Banach space. For more clarity in this abstract, we state these results in terms of classification by real numbers. If $R$ is some (analytic) equivalence relation on a Polish space $X$, it is said that $R$ is classifiable (by real numbers) if there exists a Borel map $g$ from $X$ into the real line such that $x R x'$ if and only if $g(x)=g(x')$. If $R$ is not classifiable, there must be $2^{\\omega}$ $R$-classes. It is conjectured that any separable Banach space such that isomorphism between its subspaces is classifiable must be isomorphic to $l_2$. We prove the following results: - the relation $\\sim^{perm}$ of permutative equivalence between normalized basic sequences is analytic non Borel, - if $X$ is a Banach space with a Schauder basis $(e_n)$, such that $\\sim^{perm}$ between normalized block-sequenc...

Ferenczi, V

2005-01-01

186

Predual Spaces of Banach Completions of Orlicz-Hardy Spaces Associated with Operators  

CERN Document Server

Let $L$ be a linear operator in $L^2({{\\mathbb R}^n})$ and generate an analytic semigroup $\\{e^{-tL}\\}_{t\\ge 0}$ with kernels satisfying an upper bound of Poisson type, whose decay is measured by $\\theta(L)\\in (0,\\infty].$ Let $\\omega$ on $(0,\\infty)$ be of upper type 1 and of critical lower type $\\widetilde p_0(\\omega)\\in (n/(n+\\theta(L)), 1]$ and $\\rho(t)={t^{-1}}/\\omega^{-1}(t^{-1})$ for $t\\in (0,\\infty)$. In this paper, the authors first introduce the VMO-type space $\\mathrm{VMO}_{\\rho,L}({\\mathbb R}^n)$ and the tent space $T^{\\infty}_{\\omega,\\mathrm v}({\\mathbb R}^{n+1}_+)$ and characterize the space $\\mathrm{VMO}_{\\rho,L}({\\mathbb R}^n)$ via the space $T^{\\infty}_{\\omega,\\mathrm v}({{\\mathbb R}}^{n+1}_+)$. Let $\\widetilde{T}_{\\omega} ({{\\mathbb R}}^{n+1}_+)$ be the Banach completion of the tent space $T_{\\omega}({\\mathbb R}^{n+1}_+)$. The authors then prove that $\\widetilde{T}_{\\omega}({\\mathbb R}^{n+1}_+)$ is the dual space of $T^{\\infty}_{\\omega,\\mathrm v}({\\mathbb R}^{n+1}_+)$. As an application of t...

Jiang, Renjin

2009-01-01

187

Inexact NewtonLandweber iteration for solving nonlinear inverse problems in Banach spaces  

International Nuclear Information System (INIS)

By making use of duality mappings, we formulate an inexact NewtonLandweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

188

Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K?E be an asymptotically nonexpansive mapping with {kn}?[1,?) such that ?n=1?(kn?1)

Yongfu Su; Xiaolong Qin

2006-01-01

189

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory  

Directory of Open Access Journals (Sweden)

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.

Erzakova Nina A

2004-01-01

190

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory  

Directory of Open Access Journals (Sweden)

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.

Martin Vth

2004-12-01

191

Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces  

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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=?nxn-1+(1-?nyn, 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.

Huimin He

2010-01-01

192

Existence of weak and strong solutions of nonlinear differential equations with delay in Banach space  

International Nuclear Information System (INIS)

Existence of weak and strong solutions of nonlinear differential equations with delay in Banach space is discussed. In the present work we give a generalization to recent results. We prove that, with certain conditions, every nonlinear differential equation with delay has at least one weak solution, furthermore, under suitable assumptions, these equations have solutions. Next under a generalization of the compactness assumptions, we show the same equations have solutions too

193

Robustness of a nonuniform (mu,nu) trichotomy in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this article, we consider the robustness of a nonuniform $(mu,u)$ trichotomy in Banach spaces, in the sense that the existence of such a trichotomy for a given linear equation persists under sufficiently small linear perturbations. The continuous dependence with the perturbation of the constants in the notion of trichotomy is studied, and the related robustness of strong $(mu,u)$ trichotomy is also presented.

Yongxin Jiang

2012-01-01

194

A New Strong Convergence Theorem for Equilibrium Problems and Fixed Point Problems in Banach Spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We introduce a new iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach space. Then, we study the strong convergence of the sequences. With an appropriate setting, we obtain the corresponding results due to Takahashi-Takahashi and Takahashi-Zembayashi. Some of our results are established with weaker assumptions.

Nilsrakoo Weerayuth

2011-01-01

195

Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces  

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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 .

Suzuki Tomonari

2006-01-01

196

Iterations converging to distinct solutions of some nonlinear operator equations in Banach space  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…where Mk is a k-linear operator on a Banach space X and y∈X is fixed.

Argyros, Ioannis K.

1986-01-01

197

Impulsive moving mirror model and impulsive differential equations in Banach space  

International Nuclear Information System (INIS)

The dependence of vacuum state energy on the distance between the uniformly relatively moving mirrors is used to calculate impulsive differential equations in Banach space. We formulate the problem of moving mirrors, possibly with suddenly change of velocity v in t=tn, n=0, 1, 2, ..., upon which quantum fields satisfy Dirichlet boundary conditions, with the associated Casimir effect, in a functional Schroedinger picture. 10 refs

198

Parametric general variational-like inequality problem in uniformly smooth Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available Using the concept of p-η-proximal mapping, we study the existence and sensitivity analysis of solution of a parametric general variational-like inequality problem in uniformly smooth Banach space. The approach used may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given by many authors in this direction.

F. A. Khan

2006-07-01

199

Application of He's homotopy perturbation method for a nonlinear functional equation in Banach spaces  

Science.gov (United States)

In the present paper we extend the Homotopy Perturbation Method to find an approximate analytic solution for a nonlinear functional equation in a Banach space. While previously necessary and sufficient conditions were given for the existence of the solution only for the case of a non expansive operator, HPM allowed us to find solutions also for the case of an expansive operator T, as shown in the given example.

Bota, C.; C?runtu, B.; Bund?u, O.

2013-10-01

200

Abel averages and holomorphically pseudo-contractive maps in Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A class of maps in a complex Banach space is studied, which includes both unbounded linear operators and nonlinear holomorphic maps. The defining property, which we call {\\sl pseudo-contractivity}, is introduced by means of the Abel averages of such maps. We show that the studied maps are dissipative in the spirit of the classical Lumer-Phillips theorem. For pseudo-contractive holomorphic maps, we establish the power convergence of the Abel averages to holomorphic retractions.

Bracci, Filippo; Kozitsky, Yuri; Shoikhet, David

2013-01-01

 
 
 
 
201

Embedding theorems in Banach-valued -spaces and maximal -regular differential-operator equations  

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Full Text Available The embedding theorems in anisotropic Besov-Lions type spaces are studied; here and are two Banach spaces. The most regular spaces are found such that the mixed differential operators are bounded from to , where are interpolation spaces between and depending on and . By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal -regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.

Shakhmurov Veli B

2006-01-01

202

ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS DEFINED ON THE UNIT BALL OF A COMPLEX BANACH SPACE  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Sea X y Y espacios de Banach complejos, B X y B Y las bolas unitarias cerradas correspondientes. Las aplicaciones analticas : B Y [...] width=29 height=24 id="_x0000_i1044" src="http:/fbpe/img/cubo/v15n2/art04-02.jpg" alt="Descripcin: http:/fbpe/img/cubo/v15n2/art04-02.jpg">B X y: B X inducen el operador de composicin con pesos: C , : H (B Y) H (Bx), f (f o ), donde H (B Y) y H (Bx) denotan la coleccin de todas las funciones analticas f : Bx (resp. B Y) . Estudiamos cundo dichos operadores que actan entre los espacios con peso de funciones analticas son isomtricas. Abstract in english Let X and Y be complex Banach spaces and B X resp. B Y the closed unit ball. Analytic maps : B Y [...] " src="http:/fbpe/img/cubo/v15n2/art04-02.jpg" alt="Descripcin: http:/fbpe/img/cubo/v15n2/art04-02.jpg">B X and : B X induce the weighted composition operator: C , : H (B Y) H (Bx), f (f o ), where H (B Y) resp. H (Bx) denotes the collection of all analytic functions f : Bx (resp. B Y) . We study when such operators acting between weighted spaces of analytic functions are isometric.

Elke, Wolf.

203

Metatext Phenomenon: Mode of Irony in Reflexive-Interpretative Space  

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Full Text Available The article presents metatext and correlative interaction of irony in the reflexive-interpretative space of the literary text, clarifies the status of metatext space as linguo-cognitive activity of text producer. Irony serves as a system factor, forming metatext within the linguo-rhetoric script of text. Context plays special role in singling out of linguistic and discursive irony; multilevel character of irony is determined by context breadth, required for its decoding. The integrated nature of the information, represented in the text and metatext, actualizes implication of the literary text.

Anna V. Kuznetsova

2013-01-01

204

Maximally Modulated Singular Integral Operators and their Applications to Pseudodifferential Operators on Banach Function Spaces  

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We prove that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\\mathbb{R}^n)$ and on its associate space $X'(\\mathbb{R}^n)$ and a maximally modulated Calder\\'on-Zygmund singular integral operator $T^\\Phi$ is of weak type $(r,r)$ for all $r\\in(1,\\infty)$, then $T^\\Phi$ extends to a bounded operator on $X(\\mathbb{R}^n)$. This theorem implies the boundedness of the maximally modulated Hilbert transform on variable Lebesgue spaces $L^{p...

Karlovich, Alexei Yu

2014-01-01

205

On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi- -Asymptotically Nonexpansive Mappings in Banach Spaces  

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Full Text Available We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi- -asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Frchet differentiable norm under weaker conditions. The method of the proof is different from, S. Takahashi and W. Takahashi that by (2008 and that by Takahashi and Zembayashi (2008 and see references. It also shows that the type of projection used in the iterative method is independent of the properties of the mappings. The results presented in the paper improve and extend some recent results.

Liu Min

2010-01-01

206

On smooth extensions of vector-valued functions defined on closed subsets of Banach spaces  

CERN Document Server

Let $X$ and $Z$ be Banach spaces, $A$ a closed subset of $X$ and a mapping $f:A \\to Z$. We give necessary and sufficient conditions to obtain a $C^1$ smooth mapping $F:X \\to Z$ such that $F_{\\mid_A}=f$, when either (i) $X$ and $Z$ are Hilbert spaces and $X$ is separable, or (ii) $X^*$ is separable and $Z$ is an absolute Lipschitz retract, or (iii) $X=L_2$ and $Z=L_p$ with $1

Jimenez-Sevilla, M

2011-01-01

207

Convergence rates for the iteratively regularized GaussNewton method in Banach spaces  

International Nuclear Information System (INIS)

In this paper we consider the iteratively regularized GaussNewton method (IRGNM) in a Banach space setting and prove optimal convergence rates under approximate source conditions. These are related to the classical concept of source conditions that is available only in Hilbert space. We provide results in the framework of general index functions, which include, e.g. Hlder and logarithmic rates. Concerning the regularization parameters in each Newton step as well as the stopping index, we provide both a priori and a posteriori strategies, the latter being based on the discrepancy principle

208

Conical square functions associated with Bessel, Laguerre and Schr\\"odinger operators in UMD Banach spaces  

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In this paper we consider conical square functions in the Bessel, Laguerre and Schr\\"odinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hyt\\"onen, van Neerven and Portal, in order to define our conical square functions, we use $\\gamma$-radonifying operators. We obtain new equivalent norms in the Lebesgue-Bochner spaces $L^p((0,\\infty ),\\mathbb{B})$ and $L^p(\\mathbb{R}^n,\\mathbb{B})$, $1

Betancor, Jorge J.; Castro, Alejandro J.; Farin?a, Juan C.; Rodri?guez-mesa, Lourdes

2014-01-01

209

Backward Ornstein-Uhlenbeck Transition Operators and Mild Solutions of Non-Autonomous Hamilton-Jacobi Equations in Banach Spaces  

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Full Text Available In this paper we revisit the mild-solution approach to second-order semi-linear PDEs of Hamilton-Jacobi type in infinite-dimensional spaces. We show that a well-known result on existence of mild solutions in Hilbert spaces can be easily extended to non-autonomous Hamilton-Jacobi equations in Banach spaces. The main tool is the regularizing property of Ornstein-Uhlenbeck transition evolution operators for stochastic Cauchy problems in Banach spaces with time-dependent coefficients.

Rafael Serrano

2014-10-01

210

Modification of Otolith Reflex Asymmetries Following Space Flight  

Science.gov (United States)

We hypothesize that changes in otolith-mediated reflexes adapted for microgravity contribute to perceptual, gaze and postural disturbances upon return to Earth s gravity. Our goal was to determine pre- versus post-fight differences in unilateral otolith reflexes that reflect these adaptive changes. This study represents the first comprehensive examination of unilateral otolith function following space flight. Ten astronauts participated in unilateral otolith function tests three times pre-flight and up to four times after Shuttle flights from landing day through the subsequent 10 days. During unilateral centrifugation (UC, +/- 3.5cm at 400deg/s), utricular function was examined by the perceptual changes reflected by the subjective visual vertical (SVV) and by video-oculographic measurement of the otolith-mediated ocular counter-roll (OOR). Unilateral saccular reflexes were recorded by measurement of collic Vestibular Evoked Myogenic Potential (cVEMP). Although data from a few subjects were not obtained early post-flight, a general increase in asymmetry of otolith responses was observed on landing day relative to pre-flight baseline, with a subsequent reversal in asymmetry within 2-3 days. Recovery to baseline levels was achieved within 10 days. This fluctuation in the asymmetry measures appeared strongest for SVV, in a consistent direction for OOR, and in an opposite direction for cVEMP. These results are consistent with our hypothesis that space flight results in adaptive changes in central nervous system processing of otolith input. Adaptation to microgravity may reveal asymmetries in otolith function upon to return to Earth that were not detected prior to the flight due to compensatory mechanisms.

Clarke, Andrew H.; Schoenfeld, Uwe; Wood, Scott J.

2011-01-01

211

Infinitely delayed stochastic evolution equations in UMD Banach spaces  

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We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation $$dU(t) = &\\big(AU(t) + F(t,U_t)\\big) dt + B(t,U_t)dW_H(t), t\\in[0,T_0]$$ where $A$ is the generator of an analytic semigroup on a UMD space $E$, $F$ and $B$ satisfy Lipschitz conditions and $\\mathscr{B}$ is a weighted $L^p$ history space. This paper is based on recent work of van Neerven \\emph{et al.}~which developed the theory of abstract stochastic evolution equations in U...

Crewe, Paul

2010-01-01

212

Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi  

CERN Document Server

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 calculus of (A) on the Bochner spaces (L^p(\\R^n;X)) by checking appropriate conical square function estimates, and also a conical analogue of Bourgain's extension of the Littlewood-Paley theory to the UMD-valued context. Even when (X=\\C), our approach gives refined (p)-dependent versions of known results.

Hytonen, Tuomas; Portal, Pierre

2007-01-01

213

Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces  

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Full Text Available 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 strongly to some in , the set of common fixed points of , which is the unique solution of the variational inequality , for all .

Saeidi Shahram

2008-01-01

214

Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces  

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Full Text Available The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=?nxn+(1??n(Txn+en??n?nF(xn remains convergent in a Banach space setting where ?n,?n?[0,1], T a nonexpansive mapping, en, n=0,1,, errors and F a strongly accretive and strictly pseudocontractive mapping.

L. C. Ceng

2010-01-01

215

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

216

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

217

C0-semigroups of linear operators on some ultrametric Banach spaces  

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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.

Toka Diagana

2006-06-01

218

Study of an Approximation Process of Time Optimal Control for Fractional Evolution Systems in Banach Spaces  

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Full Text Available Abstract The paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems to successive approximation of the original time optimal control problem. Finally, a new approximation process is established to find the solution of time optimal control problem. Our method is different from the standard method.

Zhou Yong

2011-01-01

219

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces  

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Full Text Available Suppose is a nonempty closed convex subset of a real Banach space . Let be two asymptotically quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a converges strongly to some if and only if ; (b if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the sequence (with error member terms converges strongly to some .

Udomene Aniefiok

2006-01-01

220

Modulus of Convexity, the Coeffcient R(1,X), and Normal Structure in Banach Spaces  

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Let δX(ϵ) and R(1,X) be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space X has normal structure if 2δX(1+ϵ)>max{(R(1,x)-1)ϵ,1-(1-ϵ/R(1,X)-1)} for some ϵ∈[0,1] which generalizes the known result by Gao and Prus.

Fenghui Wang; Yunrui Guo; Hongwei Jiao

2008-01-01

 
 
 
 
221

A New System of Nonlinear Fuzzy Variational Inclusions Involving (A,?-Accretive Mappings in Uniformly Smooth Banach Spaces  

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Full Text Available A new system of nonlinear fuzzy variational inclusions involving (A,?-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion problems as special cases of this system. By using the resolvent operator technique associated with (A,?-accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variational inclusions is proved. We also construct some new iterative algorithms for the solutions of this system of nonlinear fuzzy variational inclusions in uniformly smooth Banach spaces and discuss the convergence of the sequences generated by the algorithms in uniformly smooth Banach spaces. Our results extend, improve, and unify many known results in the recent literatures.

M. Roohi

2009-01-01

222

Banach SSD spaces and classes of monotone sets  

CERN Document Server

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.

Simons, Stephen

2009-01-01

223

Banach SSD spaces and classes of monotone sets  

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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), type (NI) and strongly representable are equivalent concepts and, consequently, that the known properties of strongly representable sets follow from known properties of sets of type (ED).

Simons, Stephen

2009-01-01

224

A convergence rates result for an iteratively regularized GaussNewtonHalley method in Banach space  

Science.gov (United States)

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 GaussNewton 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.

Kaltenbacher, B.

2015-01-01

225

Improvised Admissible Kernel Function for Support Vector Machines in Banach Space for Multiclass Data  

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Full Text Available Classification based on supervised learning theory is one of the most significant tasks frequently accomplished by so-called Intelligent Systems. Contrary to the traditional classification techniques that are used to validate or contradict a predefined hypothesis, kernel based classifiers offer the possibility to frame new hypotheses using statistical learning theory (Sangeetha and Kalpana, 2010. Support Vector Machine (SVM is a standard kernel based learning algorithm where it improves the learning ability through experience. It is highly accurate, robust and optimal kernel based classification technique that is well-suited to many real time applications. In this paper, kernel functions related to Hilbert space and Banach Space are explained. Here, the experimental results are carried out using benchmark multiclass datasets which are taken from UCI Machine Learning Repository and their performance are compared using various metrics like support vector, support vector percentage, training time and accuracy.

Sangeetha Rajendran

2013-10-01

226

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

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The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001), Cho et al. (2005), Ofoedu (2006), Schu (1991) and Zeng (2003 and 2005), and many others.

Feng Gu

2010-01-01

227

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly L-Lipschitzian Mappings in Banach Spaces  

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Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991 and Zeng (2003 and 2005, and many others.

Feng Gu

2010-01-01

228

Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly -Lipschitzian Mappings in Banach Spaces  

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Full Text Available The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly -Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by Chang (2001, Cho et al. (2005, Ofoedu (2006, Schu (1991 and Zeng (2003 and 2005, and many others.

Gu Feng

2010-01-01

229

On the Krasnoselskii-type fixed point theorems for the sum of continuous and asymptotically nonexpansive mappings in Banach spaces  

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Full Text Available Abstract In this article, we prove some results concerning the Krasnoselskii theorem on fixed points for the sum A + B of a weakly-strongly continuous mapping and an asymptotically nonexpansive mapping in Banach spaces. Our results encompass a number of previously known generalizations of the theorem.

Arunchai Areerat

2011-01-01

230

Almost Stable Iteration Schemes for Local Strongly Pseudocontractive and Local Strongly Accretive Operators in Real Uniformly Smooth Banach Spaces  

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Full Text Available In this paper we establish the strong convergence and almost stability of the Ishikawa iteration methods with errors for the iterative approximations of either fixed points of local strongly pseudocontractive operators or solutions of nonlinear operator equations with local strongly accretive type in real uniformly smooth Banach spaces. Our convergence results extend some known results in the literature.

Shin Min Kang

2008-08-01

231

Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space  

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Full Text Available We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

Farrukh Mukhamedov

2010-01-01

232

Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces  

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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

Chen Rudong

2011-01-01

233

Picard iterations for nonlinear Lipschitz strong pseudo-contractions in uniformly smooth Banach spaces  

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

234

A Banach space-valued ergodic theorem for amenable groups and applications  

CERN Document Server

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.

Pogorzelski, Felix

2012-01-01

235

Application of Pettis integration to differential inclusions with three-point boundary conditions in Banach spaces  

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Full Text Available This paper provide some applications of Pettis integration to differential inclusions in Banach spaces with three point boundary conditions of the form $$ ddot{u}(t in F(t,u(t,dot u(t+H(t,u(t,dot u(t,quad hbox{a.e. } t in [0,1], $$ where $F$ is a convex valued multifunction upper semicontinuous on $Eimes E$ and $H$ is a lower semicontinuous multifunction. The existence of solutions is obtained under the non convexity condition for the multifunction $H$, and the assumption that $F(t,x,ysubset Gamma_{1}(t$, $H(t,x,ysubset Gamma_{2}(t$, where the multifunctions $Gamma_{1},Gamma_{2}:[0,1] ightrightarrows E$ are uniformly Pettis integrable.

Imen Boutana

2007-12-01

236

Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces  

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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, ...

Ramm, A. G.

2010-01-01

237

Improved bounds in the scaled Enflo type inequality for Banach spaces  

CERN Document Server

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].

Giladi, Ohad

2010-01-01

238

Evaluating the Performance of an Admissible Kernel Function in Banach Space for Binary Data  

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Full Text Available Classification is a learning function that maps a given data item into one of several predefined classes. It is a data analysis technique that extracts models describing important data classes and predicts future values. Basically, classification techniques have better capability to handle a wider variety of datasets than regression. It can also be described as a supervised learning algorithm in the machine learning process. Support Vector Machine (SVM is an emerging classifier based on supervised machine learning approach. It is originally used to symbolize popular and modern classifiers that have a well-defined theoretical foundation to provide some enviable performances [1]. In this paper, an admissible kernel function in Banach Space is proposed as an optimal kernel function for real time applications. The experimental results are carried out using benchmark binary datasets which are taken from UCI Machine Learning Repository and their performance are evaluated using various measures like support vector, support vector percentage, training time and accuracy.

Sangeeth.R

2013-09-01

239

On the Banach Problem on Surjections  

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Is shown that any separable superreflexive Banach space X may be isometrically embedded in a separable superreflexive Banach space Z=Z(X) (which, in addition, is of the same type and cotype as X) such that its conjugate admits a continuous surjection on each its subspace. This gives an affirmative answer on S. Banach problem: Whether there exists a Banach space X, non isomorphic to a Hilbert space, which admits a continuous linear surjection on each its subspace and is essen...

Tokarev, Eugene

2002-01-01

240

The equivalence between the convergences of Mann and Ishikawa iteration methods with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We investigate the equivalence between the convergences of the Mann iteration method and the Ishikawa iteration method with errors for demicontinuous φ-strongly accretive operators in uniformly smooth Banach spaces. A related result deals with the equivalence of the Mann iteration method and the Ishikawa iteration method for φ-pseudocontractive operators in nonempty closed convex subsets of uniformly smooth Banach spaces. The results presented in this paper extend and improve ...

Zeqing Liu; Li Wang; Jeong Sheok Ume; Shin Min Kang

2006-01-01

 
 
 
 
241

A Generalized Hybrid Steepest-Descent Method for Variational Inequalities in Banach Spaces  

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Full Text Available Abstract The hybrid steepest-descent method introduced by Yamada (2001 is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of convexly constrained nonlinear inverse problems in real Hilbert spaces. Lehdili and Moudafi (1996 introduced the new prox-Tikhonov regularization method for proximal point algorithm to generate a strongly convergent sequence and established a convergence property for it by using the technique of variational distance in Hilbert spaces. In this paper, motivated by Yamada's hybrid steepest-descent and Lehdili and Moudafi's algorithms, a generalized hybrid steepest-descent algorithm for computing the solutions of the variational inequality problem over the common fixed point set of sequence of nonexpansive-type mappings in the framework of Banach space is proposed. The strong convergence for the proposed algorithm to the solution is guaranteed under some assumptions. Our strong convergence theorems extend and improve certain corresponding results in the recent literature.

Wong NC

2011-01-01

242

A maximal inequality for stochastic convolutions in 2-smooth Banach spaces  

CERN Document Server

Let (e^{tA})_{t \\geq 0} be a C_0-contraction semigroup on a 2-smooth Banach space E, let (W_t)_{t \\geq 0} be a cylindrical Brownian motion in a Hilbert space H, and let (g_t)_{t \\geq 0} be a progressively measurable process with values in the space \\gamma(H,E) of all \\gamma-radonifying operators from H to E. We prove that for all 0

van Neerven, Jan

2011-01-01

243

Ishikawa Iterative Process for a Pair of Single-valued and Multivalued Nonexpansive Mappings in Banach Spaces  

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Full Text Available 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 that .

Kaewkhao A

2010-01-01

244

On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces  

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Full Text Available We establish the general solution of the functional equation f(nx+y+f(nx?y=n2f(x+y+n2f(x?y+2(f(nx?n2f(x?2(n2?1f(y for fixed integers n with n?0,1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

M. Eshaghi Gordji

2009-01-01

245

Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces  

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Full Text Available Let be an arbitrary real Banach space and a nonempty, closed, convex (not necessarily bounded subset of . If is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of .

Vara Prasad KNVV

2006-01-01

246

A New System of Nonlinear Fuzzy Variational Inclusions Involving (A,?)-Accretive Mappings in Uniformly Smooth Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A new system of nonlinear fuzzy variational inclusions involving (A,?)-accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with (A,?)-accretive operator due to Lan et al. and Nadler's fixed points theorem for set-valued mappings, an existence theorem of solutions for this system of fuzzy variat...

Roohi, M.; Alimohammady, M.; Balooee, J.; Cho, Y. J.

2009-01-01

247

Weak and strong convergence theorems for finite families of asymptotically nonexpansive mappings in Banach spaces  

International Nuclear Information System (INIS)

Let E be a real uniformly convex Banach space whose dual space E* satisfies the Kadec- Klee property, K be a closed convex nonempty subset of E . Let T1, T2, . . . , Tm : K ? K be asymptotically nonexpansive mappings of K into E with sequences (respectively) {kin}n=1? satisfying kin ? 1 as n ? ?, i = 1, 2 , ...,m and ?n=1?(kin - 1) in}n=1? be a sequence in [?, 1 - ? ], for each i element of { 1, 2 , . . . ,m} (respectively). Let {xn} be a sequence generated for m ? 2 by, x1 element of K, xn+1 = (1 - ?1n)xn + ?1nT1nyn+m-2, yn+m-2 = (1 - ?2n)xn + ?2nT2nyn+m-3, ..., yn = (1 - ?mn)xn + ?mnTmnxn , n ? 1. Let Intersectioni=1m F (Ti) ? 0 . Then, {xn} converges weakly to a common fixed point of the family {Ti}i=1m. Under some appropriate condition on the family {Ti}i=1m, a strong convergence theorem is also roved. (author)

248

Approximating fixed points of non-self asymptotically nonexpansive mappings in Banach spaces  

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Full Text Available Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T:K?E be an asymptotically nonexpansive mapping with {kn}?[1,? such that ?n=1?(kn?10. Starting from arbitrary x1?K, define the sequence {xn} by x1?K, zn=P(?n''T(PTn?1xn+(1??n''xn, yn=P(?n'T(PTn?1zn+(1??n'xn, xn+1=P(?nT(PTn?1yn+(1??nxn. (i If the dual E* of E has the Kadec-Klee property, then { xn} converges weakly to a fixed point p?F(T; (ii if T satisfies condition (A, then {xn} converges strongly to a fixed point p?F(T.

Yongfu Su

2006-01-01

249

Strong convergence and control condition of modified Halpern iterations in Banach spaces  

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Full Text Available Let C be a nonempty closed convex subset of a real Banach space X which has a uniformly Gâteaux differentiable norm. Let T∈ΓC and f∈ΠC. Assume that {xt} converges strongly to a fixed point z of T as t→0, where xt is the unique element of C which satisfies xt=tf(xt+(1−tTxt. Let {αn} and {βn} be two real sequences in (0,1 which satisfy the following conditions: (C1lim⁡n→∞αn=0;(C2∑n=0∞αn=∞;(C60

Yonghong Yao

2006-04-01

250

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in banach spaces  

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Full Text Available Suppose K is a nonempty closed convex subset of a real Banach space E . Let S,T:K?K be two asymptotically quasi-nonexpansive maps with sequences { u n },{ v n }?[ 0,? such that ? n=1 ? u n

2006-01-01

251

Microwave imaging of elliptically shaped dielectric cylinders by means of an Lp Banach-space inversion algorithm  

Science.gov (United States)

Microwave imaging apparatuses have become very important tools in the framework of imaging systems. However, particular care must be taken when developing the data-processing algorithm needed to solve the underlying nonlinear and ill-posed inverse problem. Usually, regularization techniques developed in the framework of Hilbert spaces are used. In this paper, a new approach based on a regularization in the framework of Lp Banach spaces is considered, and its performances are evaluated by considering a reference canonical target with elliptical cross section.

Estatico, C.; Fedeli, A.; Pastorino, M.; Randazzo, A.

2013-07-01

252

Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces  

CERN Document Server

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...

Ramm, A G

2010-01-01

253

Morse theory on banach manifolds  

International Nuclear Information System (INIS)

The Morse Theory of critical points was extended by Palais and Smale to a certain class of functions on Hilbert manifolds. However, there are many variational problems in a nonlinear setting which for technical reasons are posed not on Hilbert but on Banach manifolds of mappings. This paper introduces a concept of a multivalued gradient vector field for a function defined on a Banach manifold. Using this concept, the Morse theory is generalized to some kind of Banach manifolds. The first chapter gives a definition of nondegeneracy of critical points for a real valued function defined on a reflexive Banach manifold, and then a handle-body decomposition theorem and Morse inequalities for this manifold are obtained. The second chapter proves the existence of solutions for a differential inclusion for a so-called accretive multi-valued mapping on a Finsler manifold. The third chapter introduces a definition of nondegeneracy of critical points for a real valued function defined on a general Banach manifold and, furthermore, generalizes the Morse handle-body decomposition theorem and the Morse inequalities to the Banach manifold

254

Convergence in mean of weighted sums of {ank}-compactly uniformly integrable random elements in Banach spaces  

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The convergence in mean of a weighted sum ∑kank(Xk−EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {ank}-compactly uniform integrability of {Xn}. This condition, which is implied by the tightness of {Xn} and the {ank}-uniform integrability of {‖Xn‖}, is weaker than the compactly miform integrability of {Xn} and leads to a resul...

Ord Ez Cabrera, M.

1997-01-01

255

Convergence in mean of weighted sums of {ank}-compactly uniformly integrable random elements in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available The convergence in mean of a weighted sum ∑kank(Xk−EXk of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {ank}-compactly uniform integrability of {Xn}. This condition, which is implied by the tightness of {Xn} and the {ank}-uniform integrability of {‖Xn‖}, is weaker than the compactly miform integrability of {Xn} and leads to a result of convergence in mean which is strictly stronger than a recent result of Wang, Rao and Deli.

M. Ordez Cabrera

1997-09-01

256

Convex-transitivity of Banach algebras via ideals  

CERN Document Server

We investigate a method for producing concrete convex-transitive Banach spaces. The gist of the method is in getting rid of dissymmetries of a given space by taking a carefully chosen quotient. The spaces of interest here are typically Banach algebras and their ideals. We also investigate the convex-transitivity of ultraproducts and tensor products of Banach spaces.

Talponen, Jarno

2011-01-01

257

Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Suppose K is a nonempty closed convex subset of a real Banach space E. Let S,T:K→K be two asymptotically quasi-nonexpansive maps with sequences {un},{vn}⊂[0,∞ such that ∑n=1∞un<∞ and ∑n=1∞vn<∞, and F=F(S∩F(T:={x∈K:Sx=Tx=x}≠∅. Suppose {xn} is generated iteratively by x1∈K,xn+1=(1−αnxn+αnSn[(1−βnxn+βnTnxn],n≥1 where {αn} and {βn} are real sequences in [0,1]. It is proved that (a {xn} converges strongly to some x∗∈F if and only if liminfn→∞d(xn,F=0; (b if X is uniformly convex and if either T or S is compact, then {xn} converges strongly to some x∗∈F. Furthermore, if X is uniformly convex, either T or S is compact and {xn} is generated by x1∈K,xn+1=αnxn+βnSn[α′nxn+β′nTnxn+γ′nz′n]+γnzn,n≥1, where {zn}, {z′n} are bounded, {αn},{βn},{γn},{α′n},{β′n},{γ′n} are real sequences in [0,1] such that αn+βn+γn=1=α′n+β′n+γ′n and {γn}, {γ′n} are summable; it is established that the sequence {xn} (with error member terms converges strongly to some x∗∈F.

Aniefiok Udomene

2006-02-01

258

Uniformly convex metric spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers ...

Kell, Martin

2014-01-01

259

Iterative approximation of a solution of multi-valued variational-like inclusion in Banach spaces: A P-[eta]-proximal-point mapping approach  

Science.gov (United States)

In this paper, we introduce a class of P-[eta]-accretive mappings, an extension of [eta]-m-accretive mappings [C.E. Chidume, K.R. Kazmi, H. Zegeye, Iterative approximation of a solution of a general variational-like inclusion in Banach spaces, Int. J. Math. Math. Sci. 22 (2004) 1159-1168] and P-accretive mappings [Y.-P. Fang, N.-J. Huang, H-accretive operators and resolvent operator technique for solving variational inclusions in Banach spaces, Appl. Math. Lett. 17 (2004) 647-653], in real Banach spaces. We prove some properties of P-[eta]-accretive mappings and give the notion of proximal-point mapping, termed as P-[eta]-proximal-point mapping, associated with P-[eta]-accretive mapping. Further, using P-[eta]-proximal-point mapping technique, we prove the existence of solution and discuss the convergence analysis of iterative algorithm, for multi-valued variational-like inclusions in real Banach space. The theorems presented in this paper extend and improve many known results in the literature.

Kazmi, K. R.; Khan, F. A.

2007-01-01

260

A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states  

CERN Document Server

In this paper we consider bounded operators on infinite graphs, in particular Cayley graphs of amenable groups. The operators satisfy an equivariance condition which is formulated in terms of a colouring of the vertex set of the underlying graph. In this setting it is natural to expect that the integrated density of states (IDS), or spectral distribution function, exists. We show that it can be defined as the uniform limit of approximants associated to finite matrices. The proof is based on a Banach space valued ergodic theorem which even allows explicit convergence estimates. Our result applies to a variety of group structures and colouring types, in particular to periodic operators and percolation-type Hamiltonians.

Lenz, Daniel; Veseli?, Ivan

2010-01-01

 
 
 
 
261

Ring homomorphisms on real Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Let B be a strictly real commutative real Banach algebra with the carrier space ΦB. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ:A→B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A is contained in the radical of B.

Sin-Ei Takahasi

2003-08-01

262

Strong Convergence Theorems of the Ishikawa Process with Errors for Strictly Pseudocontractive Mapping of Browder-Petryshyn Type in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We prove several strong convergence theorems for the Ishikawa iterative sequence with errors to a fixed point of strictly pseudocontractive mapping of Browder-Petryshyn type in Banach spaces and give sufficient and necessary conditions for the convergence of the scheme to a fixed point of the mapping. The results presented in this work give an affirmative answer to the open question raised by Zeng et al. 2006, and generalize the corresponding result of Zeng et al. 2006, Osilike and Ud...

Tang Yu-Chao; Cai Yong; Liu Li-Wei

2011-01-01

263

Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces  

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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.

Raja P

2008-01-01

264

Connes amenability of the second dual of Arens regular Banach algebras  

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In this paper we study the Connes amenability of the second dual of Arens regular Banach algebras. Of course we provide a partial answer to the question posed by Volker Runde. Also we fined the necessary and sufficient conditions for the second dual of an Arens regular module extension Banach algebra to be Connes amenable when the module is reflexive.

Gordji, M. Eshaghi

2006-01-01

265

Frechet differential of a power series in Banach algebras  

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We present two new forms in which the Frechet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant $C(T) : A \\rightarrow [A,T]$. 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.

Benedetto Silvestri

2010-01-01

266

Functional analysis and applied optimization in Banach spaces applications to non-convex variational models  

CERN Document Server

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.

Botelho, Fabio

2014-01-01

267

Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space.I. Real-valued measures  

CERN Document Server

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\\bf R$. Theorems and criteria are formulated and proved about quasi-invariance and pseudo-differentiability of measures relative to linear and non-linear operators on $X$. Characteristic functionals of measures are studied. Moreover, the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonov theorems are investigated. Infinite products of measures also are considered. Convergence of quasi-invariant and pseudo-differentiable measures in the corresponding spaces of measures is investigated.

Ldkovsky, S V

2001-01-01

268

Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space. II. Measures with values in non-Archimedean fields  

CERN Document Server

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean fields, for example, the field $\\bf Q_p$ of $p$- adic numbers. Theorems and criteria are formulated and proved about quasi-invariance and pseudo-differentiability of measures relative to linear and non-linear operators on $X$. Characteristic functionals of measures are studied. Moreover, the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonov theorems are investigated. Infinite products of measures are considered and the analog of the Kakutani theorem is proved. Convergence of quasi-invariant and pseudo-differentiable measures in the corresponding spaces of measures is investigated.

Ldkovsky, S V

2001-01-01

269

A New System of Nonlinear Fuzzy Variational Inclusions Involving -Accretive Mappings in Uniformly Smooth Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Abstract A new system of nonlinear fuzzy variational inclusions involving -accretive mappings in uniformly smooth Banach spaces is introduced and studied many fuzzy variational and variational inequality (inclusion) problems as special cases of this system. By using the resolvent operator technique associated with -accretive ...

Yj, Cho; Alimohammady M; Balooee J; Roohi M

2009-01-01

270

Crossed products of Banach algebras. I  

CERN Document Server

We construct a crossed product Banach algebra from a Banach algebra dynamical system $(A,G,\\alpha)$ and a given uniformly bounded class $R$ of continuous covariant Banach space representations of that system. If $A$ has a bounded left approximate identity, and $R$ consists of non-degenerate continuous covariant representations only, then the non-degenerate bounded representations of the crossed product are in bijection with the non-degenerate $R$-continuous covariant representations of the system. This bijection, which is the main result of the paper, is also established for involutive Banach algebra dynamical systems and then yields the well-known representation theoretical correspondence for the crossed product $C^*$-algebra as commonly associated with a $C^*$-algebra dynamical system as a special case. Taking the algebra $A$ to be the base field, the crossed product construction provides, for a given non-empty class of Banach spaces, a Banach algebra with a relatively simple structure and with the property...

Dirksen, Sjoerd; Wortel, Marten

2011-01-01

271

n-Approximately Weak Amenability of Banach Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available We introduce new notions of approximate amenability for a Banach algebra A. A Banach algebra A is n-approximately weakly amenable, for n ? N, if every continuous derivation from A into the n-th dual space A(n is approximately inner. First we examine the relation between m-approximately weak amenability and n-approximately weak amenability for distinct m,n ? N. Then we investigate (2n+1-approximately weak amenability of module extension Banach algebras. Finally, we give an example of a Banach algebra that is 1-approximately weakly amenable but not 3-approximately weakly amenable.

H. Najafi

2009-01-01

272

Ultrapowers of Banach algebras and modules  

CERN Document Server

The Arens products are the standard way of extending the product from a Banach algebra $\\mc A$ to its bidual $\\mc A''$. Ultrapowers provide another method which is more symmetric, but one that in general will only give a bilinear map, which may not be associative. We show that if $\\mc A$ is Arens regular, then there is at least one way to use an ultrapower to recover the Arens product, a result previously known for C$^*$-algebras. Our main tool is a Principle of Local Reflexivity result for modules and algebras.

Daws, Matthew

2007-01-01

273

Modification of Otolith-Ocular Reflexes, Motion Perception and Manual Control During Variable Radius Centrifugation Following Space Flight  

Science.gov (United States)

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 with vibrotactile feedback of orientation.

Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.

2009-01-01

274

A noncommutative version of the Banach-Stone Theorem  

CERN Document Server

In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we prove that the structure of the liminal $C^{*}$-algebras $\\cal A$ determines the topology of its primitive ideal space.

Bouali, B

2001-01-01

275

Reduction of LieJordan Banach algebras and quantum states  

International Nuclear Information System (INIS)

In this paper, it is shown that the concept of dynamical correspondence for Jordan Banach algebras is equivalent to a Lie structure compatible with the Jordan one. Then a theory of reduction of LieJordan Banach algebras in the presence of quantum constraints is presented and compared to the standard reduction of C*-algebras of observables of a quantum system. The space of states of the reduced LieJordan Banach algebra is characterized in terms of Dirac states on the physical algebra of observables and its GNS representations described in terms of states on the unreduced algebra. (paper)

276

n-Approximately Weak Amenability of Banach Algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We introduce new notions of approximate amenability for a Banach algebra A. A Banach algebra A is n-approximately weakly amenable, for n ? N, if every continuous derivation from A into the n-th dual space A(n) is approximately inner. First we examine the relation between m-approximately weak amenability and n-approximately weak amenability for distinct m,n ? N. Then we investigate (2n+1)-approximately weak amenability of module extension Banach algebras. Finally, we give ...

Najafi, H.; Yazdanpanah, T.

2009-01-01

277

Ultrametric Banach algebras  

CERN Document Server

In this book, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebras, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. In uniform Banach algebras, the spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametri

Escassut, Alain

2003-01-01

278

The higher duals of certain class of Banach algebras  

CERN Document Server

Given a Banach space $A$ and fix a non-zero $\\varphi\\in A^*$ with $\\|\\varphi\\|\\leq 1$. Then the product $a\\cdot b=\\langle\\varphi, a\\rangle\\ b$ turning $A$ into a Banach algebra which will be denoted by $_\\varphi A.$ Some of the main properties of $_\\varphi A$ such as Arens regularity, $n$-weak amenability and semi-simplicity are investigated.

Khoddami, A R

2010-01-01

279

Module amenability for Banach modules  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in spanish Se estudia el mdulo de receptividad de los mdulos de Banach. Esta es una generalizacin natural de la receptividad de Johnson de las lgebras de Banach. Como ejemplo se muestra que para un grupo abeliano discreto G l p(G) es receptivo como un G l p(G)- mdulo, si y slo si G es receptivo, donde l [...] (G) es un lgebra de Banach con producto punto. Abstract in english We study the module amenability of Banach modules. This is a natural generalization of Johnsons amenability of Banach algebras. As an example we show that for a discrete abelian group G, l p(G) is amenable as an l(G)-module if and only if G is amenable, where l(G) is a Banach algebra with pointwi [...] se multiplication.

D, Ebrahimi Bagha; M, Amini.

2011-06-01

280

Module extensions of dual Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In this paper we define the module extension dual Banach algebras and we use this Banach algebras to finding the relationship between $weak^*-$continuous homomorphisms of dual Banach algebras and Connes-amenability. So we study the $weak^*-$continuous derivations on module extension dual Banach algebras.

Gordji, M. Eshaghi; Habibian, F.; Rejali, A.

2006-01-01

 
 
 
 
281

Reflexives in Veracruz Huastec.  

Science.gov (United States)

A study examines various Huastec clause types that are reflexive in some sense, including ordinary reflexives, which involve co-reference. Two mutually exclusive morphosyntactic devices are used in Huastec: reflexive pronouns and verbal morphology. In this way, Huastec is like various European languages. Clauses involving reflexive pronouns and

Constable, Peter G.

282

Reduction of Lie-Jordan Banach algebras and quantum states  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A theory of reduction of Lie-Jordan Banach algebras with respect to either a Jordan ideal or a Lie-Jordan subalgebra is presented. This theory is compared with the standard reduction of C*-algebras of observables of a quantum system in the presence of quantum constraints. It is shown that the later corresponds to the particular instance of the reduction of Lie-Jordan Banach algebras with respect to a Lie-Jordan subalgebra as described in this paper. The space of states of th...

Falceto, F.; Ferro, L.; Ibort, A.; Marmo, G.

2012-01-01

283

Derivation into duals of ideals of Banach algebras  

CERN Document Server

We introduce two notions of amenability for a Banach algebra $\\cal A$. Let $I$ be a closed two-sided ideal in $\\cal A$, we say $\\cal A$ is $I$-weakly amenable if the first cohomology group of $\\cal A$ with coefficients in the dual space $I^*$ is zero; i.e., $H^1({\\cal A},I^*)=\\{0\\}$, and, $\\cal A$ is ideally amenable if $\\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. 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 $I$-weak amenability of a Banach algebra $\\cal A$ for some special closed two-sided\\break ideal $I$.

Gorgi, M E

2005-01-01

284

ZAG-Otolith: Modification of Otolith-Ocular Reflexes, Motion Perception and Manual Control during Variable Radius Centrifugation Following Space Flight  

Science.gov (United States)

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 control performance can be improved with vibrotactile feedback of orientation.

Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.

2009-01-01

285

An absolute continuity for positive operators on Banach lattices  

Directory of Open Access Journals (Sweden)

Full Text Available For positive operators on a Banach lattice, absolute contnuity conditions are considered. An operator absolutely continuous with respect to T is compared to sums of compositions of T together with orthomorphisms or in special cases projections. Consequences For compact operators on functions spaces C(X are considered.

Calvin E. Piston

1991-03-01

286

A noncommutative version of the Banach-Stone theorem (II)  

CERN Document Server

In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we give a partial answere to the question 2.1 of [13], and we prove that the structure of the postliminal C*-algebras A determines the topology of its primitive ideals space.

Bouali, B

2001-01-01

287

Additive Functional Inequalities in Banach Modules  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Abstract We investigate the following functional inequality in Banach modules over a -algebra and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra in the spirit of the Th. M. Rassias stability approa...

An JongSu; Moradlou Fridoun; Park Choonkil

2008-01-01

288

A survey of weighted substitution operators and generalizations of Banach-stone theorem  

Directory of Open Access Journals (Sweden)

Full Text Available The classical Banach-Stone theorem characterizes linear surjective isometries between C(K-spaces. The main aim of this paper is to present a survey of Banach-Stone-theorem-type results between some function spaces. The weighted substitution operators play an important role in characterization of isometries, disjointness preserving operators, and lattice homomorphisms. Some open problems are given for further investigation.

R. K. Singh

2005-05-01

289

Endomorphic Elements in Banach Algebras  

CERN Document Server

The use of the properties of actions on an algebra to enrich the study of the algebra is well-trodden and still fashionable. Here, the notion and study of endomorphic elements of (Banach) algebras are introduced. This study is initiated, in the hope that it will open up, further, the structure of (Banach) algebras in general, enrich the study of endomorphisms and provide examples. In particular, here, we use it to classify algebras for the convenience of our study. We also present results on the structure of some classes of endomorphic elements and bring out the contrast with idempotents.

Babalola, V A

2004-01-01

290

Singular symmetric functionals and Banach limits with additional invariance properties  

International Nuclear Information System (INIS)

For symmetric spaces of measurable functions on the real half-line, we study the problem of existence of positive linear functionals monotone with respect to the Hardy-Littlewood semi-ordering, the so-called symmetric functionals. Two new wide classes of symmetric spaces are constructed which are distinct from Marcinkiewicz spaces and for which the set of symmetric functionals is non-empty. We consider a new construction of singular symmetric functionals based on the translation-invariance of Banach limits defined on the space of bounded sequences. We prove the existence of Banach limits invariant under the action of the Hardy operator and all dilation operators. This result is used to establish the stability of the new construction of singular symmetric functionals for an important class of generating sequences

291

Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We ...

Di Girolami, Cristina; Russo, Francesco

2011-01-01

292

The Banach-Tarski paradox  

CERN Document Server

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

Wagon, Stan

1985-01-01

293

On character amenability of Banach algebras  

Science.gov (United States)

We continue our work [E. Kaniuth, A.T. Lau, J. Pym, On [phi]-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc. 144 (2008) 85-96] in the study of amenability of a Banach algebra A defined with respect to a character [phi] of A. Various necessary and sufficient conditions of a global and a pointwise nature are found for a Banach algebra to possess a [phi]-mean of norm 1. We also completely determine the size of the set of [phi]-means for a separable weakly sequentially complete Banach algebra A with no [phi]-mean in A itself. A number of illustrative examples are discussed.

Kaniuth, E.; Lau, A. T.; Pym, J.

2008-08-01

294

Complex Interpolation and Regular Operators Between Banach  

CERN Document Server

We study certain interpolation and extension properties of the space of regular operators between two Banach lattices. Let $R_p$ be the space of all the regular (or equivalently order bounded) operators on $L_p$ equipped with the regular norm. We prove the isometric identity $R_p = (R_\\infty,R_1)^\\theta$ if $\\theta = 1/p$, which shows that the spaces $(R_p)$ form an interpolation scale relative to Calder\\'on's interpolation method. We also prove that if $S\\subset L_p$ is a subspace, every regular operator $u : S \\to L_p$ admits a regular extension $\\tilde u : L_p \\to L_p$ with the same regular norm. This extends a result due to Mireille L\\'evy in the case $p = 1$. Finally, we apply these ideas to the Hardy space $H^p$ viewed as a subspace of $L_p$ on the circle. We show that the space of regular operators from $H^p$ to $L_p$ possesses a similar interpolation property as the spaces $R_p$ defined above.

Pisier, G

1994-01-01

295

Modern methods in topological vector spaces  

CERN Document Server

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 Frecht spaces. Optional problems with hints and references introduce non-locally convex spaces, Kthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect

Wilansky, Albert

2013-01-01

296

Measures of non-compactness of operators on Banach lattices  

CERN Document Server

Andreu et al [2] and Sadovskii [11] used representation spaces to study measures of non-compactness and spectral radii of operators on Banach lattices. In this paper, we develop representation spaces based on the nonstandard hull construction (which is equivalent to the ultrapower construction). As a particular application, we present a simple proof and some extensions of the main result of de Pagter and Schep [6] on the monotonicity of the measure of non-compactness and the spectral radius of AM-compact operators. We also use the representation spaces to characterize d-convergence and discuss the relationship between d-convergence and the measures of non-compactness.

Troitsky, V G

2002-01-01

297

On some extensions of Banach's contraction principle and applications to the convergence and stability of some iterative processes  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we obtain existence and uniqueness results of fixed points of nonlinear operators satisfying the condition of the form (?1,?2 given as a perturbation of ?2 contraction by a convenable function ?1 in metric and Banach spaces, which enable us to extend the Banachs mapping principle and other results in the literature. Also, the ?-quasi nonexpansive character of our context is shown in order to obtain results of convergence and stability of iterative processes of Mann and Ishikawa.

Nadjeh Redjel

2014-09-01

298

Etnography and Reflexivity  

Directory of Open Access Journals (Sweden)

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.

Mario Cardano

2014-01-01

299

Natural examples of Valdivia compact spaces  

Science.gov (United States)

We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces.

Kalenda, Ondrej F. K.

2008-04-01

300

On Reflexive Data Models  

Energy Technology Data Exchange (ETDEWEB)

An information system is reflexive if it stores a description of its current structure in the body of stored information and is acting on the base of this information. A data model is reflexive, if its language is meta-closed and can be used to build such a system. The need for reflexive data models in new areas of information technology applications is argued. An attempt to express basic notions related to information systems is made in the case when the system supports and uses meta-closed representation of the data.

Petrov, S.

2000-08-20

 
 
 
 
301

Espaces de Banach analytiques p-adiques et espaces de Banach-Colmez  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Un espace de Banach spectral p-adique est un espace de~Banach p-adique muni d'une algbre de fonctions analytiques valeurs dans un corps complet et algbriquement clos C. Un espace de Banach-Colmez est un espace de Banach spectral qui s'obtient par extensions et quotients partir de C et Qp. Ces espaces forment une catgorie ablienne, qui est naturellement munie de fonctions additives dimension et hauteur; on retrouve ainsi une dmonstration du thorme faib...

Plu?t, Je?ro?me

2009-01-01

302

Volitional control of reflex cough  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Multiple studies suggest a role for the cerebral cortex in the generation of reflex cough in awake humans. Reflex cough is preceded by detection of an urge to cough; strokes specifically within the cerebral cortex can affect parameters of reflex cough, and reflex cough can be voluntarily suppressed. However, it is not known to what extent healthy, awake humans can volitionally modulate the cough reflex, aside from suppression. The aims of this study were to determine whether conscious humans ...

Hegland, Karen W.; Bolser, Donald C.; Davenport, Paul W.

2012-01-01

303

Tensor products of commutative Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1⊗∂A2 be their projective tensor product. We prove that, if A1⊗∂A2 is a group algebra (measure algebra of a locally compact abelian group, then so are A1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutative semi-simple Banach algebra, then the Banach algebra L1(G,A of A-valued Bochner integrable functions on G is a group algebra if and only if A is a group algebra. Furthermore, if A has the Radon-Nikodym property, then the Banach algebra M(G,A of A-valued regular Borel measures of bounded variation on G is a measure algebra only if A is a measure algebra.

Shobha Madan

1982-09-01

304

BanachMazur Distance Between Convex Quadrangles  

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Full Text Available It is proved that the Banach-Mazur distance between arbitrary two convex quadrangles is at most 2. The distance equals 2 if and only if the pair of these quadrangles is a parallelogram and a triangle.

Lassak Marek

2014-12-01

305

Dunford-Pettis sets in Banach lattices  

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Full Text Available We study the class of Dunford-Pettis sets in Banach lattices. In particular, we establish some sufficient conditions for which a Dunford-Pettis set is relatively weakly compact (resp. relatively compact

B. Aqzzouz

2012-09-01

306

The fourth duals of Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $\\cal A$ be a Banach algebra. Then $\\cal A^{**}$ the second dual of $\\cal A$ is a Banach algebra with first (second) Arens product. We study the Arens products of $\\cal A^{4}(=({\\cal A^{**}})^{**}).$ We found some conditions on $\\cal A^{**}$ to be a left ideal in $\\cal A^{4}.$ We found the biggest two sided ideal $I$ of ${\\cal A},$ in which $I$ is a left (right) ideal of ${\\cal A}^{**}$.

Gordji, M. Eshaghi; Hosseiniun, S. A. R.

2006-01-01

307

Continuous Frames, Function Spaces, and the Discretization Problem  

Digital Repository Infrastructure Vision for European Research (DRIVER)

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed...

Fornasier, Massimo; Rauhut, Holger

2004-01-01

308

Strong Banach Property (T) for Simple Algebraic Groups of Higher Rank  

Digital Repository Infrastructure Vision for European Research (DRIVER)

In [Laf08], [Laf09], Vincent Lafforgue proved strong Banach property (T) for $SL_3$ over a non archimedean local field $F.$ In this paper, we extend his results to $Sp_4$ and therefore to any connected almost $F$-simple algebraic group with $F$-split rank $\\geq 2.$ As applications, the family of expanders constructed from any lattice of such a group do not admit a uniform embedding into any Banach space of type $>1,$ and any isometric affine action of such a group, or its co...

Liao, Benben

2013-01-01

309

An elementary approach to a lattice-valued Banach-Stone Theorem  

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Full Text Available Let $ X $ and $ Y $ be compact Hausdorff spaces, and $ E $ be a nonzero real Banach lattice. In this note, we give an elementary proof of a lattice-valued Banach-Stone theorem by Cao, Reilly and Xiong [3] which asserts that if there exists a Riesz isomorphism $ \\Phi: C(X,E\\rightarrow C(Y,\\mathbb{R} $ such that $ \\Phi(f $ has no zeros if $ f $ has none, then $ X $ is homeomorphic to $ Y $ and $ E $ is Riesz isomorphic to $ \\mathbb{R} $.

Jinxi Chen

2007-09-01

310

A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal  

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Let $G$ be a locally compact group, and let $WAP(G)$ denote the space of weakly almost periodic functions on $G$. We show that, if $G$ is a $[SIN]$-group, but not compact, then the dual Banach algebra $WAP(G)^\\ast$ does not have a normal, virtual diagonal. Consequently, whenever $G$ is an amenable, non-compact $[SIN]$-group, $WAP(G)^\\ast$ is an example of a Connes-amenable, dual Banach algebra without a normal,virtual diagonal.

Runde, Volker

2003-01-01

311

Complemented subspaces of spaces obtained by interpolation  

CERN Document Server

If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to $X\\oplus V$, and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, having the Radon-Nikodym property, and having the analytic unconditional martingale difference sequence property, do not pass to intermediate spaces.

Garling, D J H; Montgomery-Smith, Stephen J.

1991-01-01

312

Spectrum of Weighted Composition Operators. Part II. Weighted composition operators on subspaces of Banach lattices  

CERN Document Server

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not limited to) weighted isometries of Hardy spaces on the polydisk and unit ball in $\\mathds{C}^n$.

Kitover, Arkady

2012-01-01

313

Existence and convergence theorems for a class of multi-valued variational inclusions in Banach spacess  

CERN Document Server

An existence theorem for a new class of multi-valued variational inclusion problems is established in smooth Banach spaces. Further, it is shown that a sequence of a Mann-type iteration algorithm is strongly convergent to the solutions in this class of variational inclusion problems.

Chidume, C E; Kazmi, K R

2002-01-01

314

On the Cauchy Functional Inequality in Banach Modules  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract We investigate the following functional inequality: in Banach modules over a -algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra.

Park Choonkil

2008-01-01

315

Isometries and Isomorphisms in quasi-Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we prove the Hyers-Ulam-Rassias stability of isometries and of homomorphisms for additive functional equations in quasi-Banach algebras. This is applied to investigate isomorphisms between quasi-Banach algebras.

Zhihua Wang

2011-09-01

316

Trichotomy for Dynamical Systems in Banach Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of ?-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sust...

Stoica, Codru X. A.

2013-01-01

317

Trichotomy for dynamical systems in Banach spaces.  

Science.gov (United States)

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of ?-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples. PMID:24223509

Stoica, Codru?a

2013-01-01

318

Regularity of difference equations on Banach spaces  

CERN Document Server

This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semigroup and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

Agarwal, Ravi P; Lizama, Carlos

2014-01-01

319

Trigeminocardiac reflex: current trends.  

Science.gov (United States)

Since the first introduction of the trigeminocardiac reflex (TCR) in 1999, substantial new knowledge about this brainstem reflex has been created. First, by different clinical case reports and case studies, and second, from basic research that gives inputs from bench to bedside. In the present work, the authors therefore introduce the molecular/anatomical knowledge of the TCR and show its different connections to clinical aspects. Special reference is given to prevention and treatment of the TCR; but always with a link to knowledge of the basis sciences. In such a context different topics of future interest are introduced. PMID:24308808

Chowdhury, Tumul; Sandu, Nora; Sadr-Eshkevari, Pooyan; Meuwly, Cyrill; Schaller, Bernhard

2014-01-01

320

On Reflection : Is Reflexivity Necessarily Beneficial in Intercultural Education?  

DEFF Research Database (Denmark)

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 notions of difference are constructed. First, I discuss how the dominant usages of reflexivity in intercultural education reflect and reproduce a Cartesian view of the self that shapes how ICC is conceptualized and taught. I discuss three assumptions that this view produces: that the self is accessible and transcendable, that reflexivity is universal across space and time, and that the self can act as its own remedial change agent or inner consultant. I argue that because reflexivity is understood in many different ways, attention to definition is crucial, both in designing learning objectives in intercultural education and in devising ways to attain them. Greater attention is also needed in intercultural education to the ways in which selfhood, and hence also reflexivity and constructions of difference, differ across space and time.

Blasco, Maribel

2012-01-01

 
 
 
 
321

Strong Banach property (T), after Vincent Lafforgue  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This text takes, with more details and simplifying a proof in section 3, the parts of [Laf08] and [Laf09] treating p-adic groups. We prove that $SL_{3}$ over a non archimedian local field $F$ has strong Banach property (T). The applications are as follows: any connected almost $F$-simple algebraic group $G$ over $F$ whose Lie algebra contains $sl_3(F)$ has strong Banach property (T), the family of expanders constructed from a lattice of $G(F)$ do not embed uniformly in any B...

Liao, Benben

2012-01-01

322

The inhibitory control reflex.  

Science.gov (United States)

Response inhibition is typically considered a hallmark of deliberate executive control. In this article, we review work showing that response inhibition can also become a 'prepared reflex', readily triggered by information in the environment, or after sufficient training, or a 'learned reflex' triggered by the retrieval of previously acquired associations between stimuli and stopping. We present new results indicating that people can learn various associations, which influence performance in different ways. To account for previous findings and our new results, we present a novel architecture that integrates theories of associative learning, Pavlovian conditioning, and executive response inhibition. Finally, we discuss why this work is also relevant for the study of 'intentional inhibition'. PMID:25149820

Verbruggen, Frederick; Best, Maisy; Bowditch, William A; Stevens, Tobias; McLaren, Ian P L

2014-12-01

323

Photosensitivity and Reflex Epilepsies  

Directory of Open Access Journals (Sweden)

Full Text Available Reflex epilepsies (RE objectively and consistently provoked by specific external or internal stimuli are important clues for investigating complex mechanisms of epileptogenesis. RE have many intriguing subtypes depending on the trigger. Visually-sensitive epilepsies or photosensitive epilepsies are genetically determined and constitute the major part of RE but their diversity is even huge both clinically and electrophysiologically. Reflex seizures can occur in both focal and generalized epilepsy syndromes and can also be associated with spontaneous seizures. Afferent external stimuli can be: elementary or elaborate, structured and complex. Moreover, triggering activity may also be elementary (motor movement or elaborate (reading, chess playing, or both (reading aloud. Complex forms of RE pose many different questions and there are reported cases with various symptomatic etiologies indicating some acquired factors besides genetics. This review will focus on the current understanding of RE and its pathogenetic implications.

Leyla Baysal

2014-06-01

324

A high-power reflex triode  

International Nuclear Information System (INIS)

The generation of gigahertz radiation via the reflex-mechanism in the diode of a pulsed-power generator has been investigated with particle simulations and laboratory experiments. The microwave triode was designed using the 2-1/2 D, fully electromagnetic and relativistic particle-in-cell code CCUBE. The simulations pertain to a stalk supporting a ''cup'' shaped 13-cm diameter cathode spaced 3-cm from a flat foil anode grid. Magnetic insulation produced by the 10-20 kiloampere current conducted by the stalk allows the field energy to be effectively transferred to the face of the cathode and to the subsequent electrons emitted off the surface. These field emitted electrons are accelerated through the foil and build up a space charge limited virtual cathode cloud beyond the anode, then reflex between the cathode and virtual cathode producing microwaves at a frequency of 1.6 Ghz

325

Character Inner Amenability of Certain Banach Algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Character inner amenability for certain class of Banach algebras consist of projective tensor product $A\\hat{\\otimes}B$, Lau product $A\\times_\\theta B$ and module extension $A\\oplus X$ are investigated. Some illuminating examples are also included.

Vishki, H. R. Ebrahimi; Khoddami, A. R.

2010-01-01

326

Derivations And Cohomological Groups Of Banach Algebras  

CERN Document Server

Let $B$ be a Banach $A-bimodule$ and let $n\\geq 0$. We investigate the relationships between some cohomological groups of $A$, that is, if the topological center of the left module action $\\pi_\\ell:A\\times B\\rightarrow B$ of $A^{(2n)}$ on $B^{(2n)}$ is $B^{(2n)}$ and $H^1(A^{(2n+2)},B^{(2n+2)})=0$, then we have $H^1(A,B^{(2n)})=0$, and we find the relationships between cohomological groups such as $H^1(A,B^{(n+2)})$ and $H^1(A,B^{(n)})$, spacial $H^1(A,B^*)$ and $H^1(A,B^{(2n+1)})$. We obtain some results in Connes-amenability of Banach algebras, and so for every compact group $G$, we conclude that $H^1_{w^*}(L^\\infty(G)^*,L^\\infty(G)^{**})=0$. Let $G$ be an amenable locally compact group. Then there is a Banach $L^1(G)-bimodule$ such as $(L^\\infty(G),.)$ such that $Z^1(L^1(G),L^\\infty(G))=\\{L_{f}:~f\\in L^\\infty(G)\\}.$ We also obtain some conclusions in the Arens regularity of module actions and weak amenability of Banach algebras. We introduce some new concepts as $left-weak^*-to-weak$ convergence property [...

Azar, Kazem Haghnejad

2010-01-01

327

Banach ultrapowers and multivalued nonexpansive mappings  

Science.gov (United States)

The Banach ultrapower construction is applied in fixed point theory for multivalued mappings. We introduce the notion of ultra-asymptotic centers and use it to remove the separability assumption from the results of Dominguez Benavides, Lorenzo Ramirez (2004) and Dhompongsa, Kaewcharoen, Kaewkhao (2006).

Wisnicki, Andrzej; Wosko, Jacek

2007-02-01

328

A note on mutiplication operators on Kthe-Bochner spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let (?, A, ?) is a finite measure space, E an order continuous Banach function space over ?, X a Banach space and E(X) the Kthe-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

Khurana, S. S.

2012-01-01

329

A note on Banach algebras that are not isomorphic to a group algebra / Una nota sobre lgebras de Banach no isomorfas a una lgebra de grupos  

Scientific Electronic Library Online (English)

Full Text Available SciELO Colombia | Language: English Abstract in spanish En este artculo se prueba que algunas lgebras de Banach clsicas no son isomorfas a un lgebra de grupo. Estas lgebras incluyen a las lgebras C(K) donde K es un espacio de Hausdorff Compacto. En el caso de las amalgamas, damos condiciones para que una amalgama sea un lgebra de grupo. [...] Abstract in english It is proved in this paper that several classical Banach algebras are not isomorphic to a group algebra. These algebras includes C(K) algebras where K is a compact Hausdorff space. In the case of amalgams, we give conditions for an amalgam to be a group algebra. [...

DIOMEDES, BARCENAS; WALTER, ESPINOZA; EDIXON, ROJAS.

2008-06-15

330

Module-Amenability on Module Extension Banach Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available Let $A$ be a Banach algebra and $E$ be a Banach? ?$A$-bimodule then $S=A\\oplus E$?, ?the $l^1$-direct sum of $A$ and $E$? ?becomes a module extension Banach algebra when equipped with the? ?algebras product $ (a? , ?x?. ?(a'?, ?x' = (aa'? , ?a.x'? + ?x.a'$?. ?In this? ?paper?, ?we investigate $\\triangle$-amenability for these Banach? ?algebras and we show that for discrete inverse semigroup $S$ with? ?the set of idempotents $E_{S}$?, ?the module extension Banach algebra $S=l^{1} (E_{S} \\op l^{1} (S$ is $ \\tr$-amenable? ?as a $l^{1}(E_{S} $-module if and only if $l^{1}(E_{S}$ is amenable as Banach algebra?.

Davood Ebrahimi Bagha

2014-05-01

331

A G.N.S.-type theorem for a non-involutive Banach algebra  

International Nuclear Information System (INIS)

Given an involutive Banach algebra A with a bounded approximate identity, the elegant construction by Gelfand, Naimark and Segal, associates to each positive linear functional f on A, a triple (Hf, ?f, ?f), where Hf is a Hilbert space with scalar product denoted by: , ?f is a representation of A into L(Hf), the space of bounded linear operators on Hf, ?f is a cyclic vector in Hf, such that: f(x)=f(x)?f, ?f >, for all x is an element of A. In this result, the existence of a (multiplicative) involution on A, is central. The aim of this paper is to show that such a construction may be performed for a non-involutive Banach algebra, to obtain a similar triple (H, ?, ?) as above. Moreover, this procedure indeed enables us to associate to the topological dual of any Banach space, a liminary C*-subalgebra of L(H). A notion of compact Hilbert algebras will be introduced, together with a method of construction of a large collection of such spaces. (author). 14 refs

332

Hereditary properties of Amenability modulo an ideal of Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show thatif $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity modulo $I$ of a Banach algebra $A$ and $X$ is a neo-unital modulo $I$, then $(e_{\\alpha}_{\\alpha}$ is a bounded approximate identity for $X$. Moreover we show that amenability modulo an ideal of a Banach algebra $A$ can be only considered by the neo-unital modulo $I$ Banach algebra over $A$

Hamidreza Rahimi

2014-10-01

333

The Banach-Lie algebra of multiplication operators on a JBW*-triple  

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The Banach-Lie algebra L (A) of multiplication operators on the JB*-triple A is introduced and it is shown that the hermitian part L (A)h of L (A) is a unital GM-space the base of the dual cone in the dual GL-space (L (A)h)* of which is affine isomorphic and weak*-homeomorphic to the state space of L (A). In the case in which A is a JBW*-triple, it is shown that tripotents u and v in A are orthogonal if and only if the corresponding multiplication operators in the unital GM-space L (A)h satis...

Altwaijry, Na; Edwards, Cm

2008-01-01

334

Approximate weak amenability of Banach algebras  

CERN Document Server

In this paper we deal with three generalized notions of amenability, approximate, approximate weak and approximate n-weak amenability. The first two were introduced and studied by Ghahramani and Loy in [5]. We introduce the third one. Then we investigate some properties of Banach algebras in each of these classes. Also we consider approximate weak amenability and approximate n-weak amenability of second duals.

Esslamzadeh, G H

2009-01-01

335

UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces  

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We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued Hardy and BMO spaces equivalent norms involving $\\gamma$-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by using Hardy and BMO-boundedness properties of g-functions associated to Bessel-P...

Betancor, J. J.; Castro, A. J.; Rodri?guez-mesa, L.

2013-01-01

336

Left introverted subspaces of duals of Banach algebras and $WEAK^*-$continuous derivations on dual Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $X$ be a left introverted subspace of dual of a Banach algebra. We study $Z_t(X^*),$ the topological center of Banach algebra $X^*$. We fined the topological center of $(X\\cA)^*$, when $\\cA$ has a bounded right approximate identity and $\\cA\\subseteq X^*.$ So we introduce a new notation of amenability for a dual Banach algebra $\\cal A$. A dual Banach algebra $\\cal A$ is weakly Connes-amenable if the first $weak^*-$continuous cohomology group of $\\cal A$ with coefficients ...

Gordji, M. Eshaghi

2006-01-01

337

Supersets for the spectrum of elements in extended Banach algebras  

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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¯.

Morteza Seddighin

1989-09-01

338

On Automatic Continuity of 3-Homomorphisms on Banach Algebras  

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A linear map $\\phi:{\\mathcal A}\\to {\\mathcal B} $ between (Banach) algebras is called 3-homomorphism if $\\phi(abc)=\\phi(a)\\phi(b)\\phi(c)$ for each $a, b, c \\in {\\mathcal A}$. We investigate 3-homomorphisms on Banach algebras with bounded approximate identities and establish in two ways that every involution preserving homomorphism between $C^*$-algebras is norm decreasing.

Bracic, Janko; Moslehian, Mohammad Sal

2006-01-01

339

Supersets for the spectrum of elements in extended Banach algebras  

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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¯.

Morteza Seddighin

1989-01-01

340

A Note on Banach Principle for JW-algebras  

CERN Document Server

In the sequel we establish the Banach Principle for semifinite JW-algebras without direct summand of type I sub 2, which extends the recent results of Chilin and Litvinov on the Banach Principle for semifinite von Neumann algebras to the case of JW-algebras.

Grabarnik, Genady Ya

2008-01-01

 
 
 
 
341

Normas tensoriales construidas mediante espacios de sucesiones de Banach  

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Full Text Available En este art culo se de ne una norma tensorial gc a partir de un espacio de sucesiones de Banach . Para cada par de espacios de Banach E y F, se caracterizan los elementos de la complecci n del espacio E g F, Eb g F, y se caracteriza su espacio dual (E g F0

Patricia G\\u00F3mez Palacio

2003-01-01

342

Reflexivity in precompact groups and extensions  

CERN Document Server

We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that: (1) A precompact Abelian group G of bounded order is reflexive iff the dual group $\\hat{G}$ has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G. (2) Any extension of a reflexive P-group by another reflexive P-group is again reflexive. We show on the other hand that an extension of a compact group by a reflexive $\\omega$-bounded group (even dual to a reflexive P-group) can fail to be reflexive. We also show that the P-modification of a reflexive $\\sigma$-compact group can be nonreflexive (even if the P-modification of a locally compact Abelian group is always reflexive).

Bruguera, Monteserrat; Hernndez, Constancio; Tkachenko, Mikhail

2012-01-01

343

Soleus stretch reflex during cycling  

DEFF Research Database (Denmark)

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 active cycling as has been shown with the H-reflex. This lack of depression may reflect a decreased susceptibility of the stretch reflex to inhibition, possibly originating from presynaptic mechanisms.

Grey, Michael James; Pierce, C. W.

2001-01-01

344

Left introverted subspaces of duals of Banach algebras and $WEAK^*-$continuous derivations on dual Banach algebras  

CERN Document Server

Let $X$ be a left introverted subspace of dual of a Banach algebra. We study $Z_t(X^*),$ the topological center of Banach algebra $X^*$. We fined the topological center of $(X\\cA)^*$, when $\\cA$ has a bounded right approximate identity and $\\cA\\subseteq X^*.$ So we introduce a new notation of amenability for a dual Banach algebra $\\cal A$. A dual Banach algebra $\\cal A$ is weakly Connes-amenable if the first $weak^*-$continuous cohomology group of $\\cal A$ with coefficients in $\\cal A$ is zero; i.e., $H^1_{w^*}(\\cal A, \\cal A)=\\{o\\}$. We study the weak Connes-amenability of some dual Banach algebras.

Gordji, M E

2006-01-01

345

Ideal amenability of Banach algebras on locally compact groups  

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In this paper we study the ideal amenability of Banach algebras. Let $\\cal A$ be a Banach algebra and let $I$ be a closed two-sided ideal in $\\cal A$, $\\cal A$ is $I$-weakly amenable if $H^{1}({\\cal A},I^*)=\\{0\\}$. Further, $\\cal A$ is ideally amenable if $\\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorph...

Gordji, M. Eshaghi; Hosseiniun, S. A. R.

2005-01-01

346

Spatial numerical ranges of elements of Banach algebras  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, the notion of spatial numerical range of elements of Banach algebras without identity is studied. Specifically, the relationship between spatial numerical ranges, numerical ranges and spectra is investigated. Among other results, it is shown that the closure of the spatial numerical range of an element of a Banach algebra without Identity but wlth regular norm is exactly its numerical range as an element of the unitized algebra. Futhermore, the closure of the spatial numerical range of a hermitian element coincides with the convex hull of its spectrum. In particular, spatial numerical ranges of the elements of the Banach algebra C0(X are described.

T. Husain

1989-09-01

347

Reflexive algebras and sigma algebras  

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Full Text Available The concept of a reflexive algebra (σ-algebra β of subsets of a set X is defined in this paper. Various characterizations are given for an algebra (σ-algebra β to be reflexive. If V is a real vector lattice of functions on a set X which is closed for pointwise limits of functions and if β={A|A⫅X   and   CA(x∈V} is the σ-algebra induced by V then necessary and sufficient conditions are given for β to be reflexive (where CA(x is the indicator function.

V. K. Srinivasan

1986-12-01

348

A note on &-Jordan homomorphism on Banach algebras  

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Full Text Available In this paper we show that, under special hypotheses, each &-Jordan homomorphism ' between Banach algebras A and B is continuous and almost multiplicative. Keywords: &-Jordan homomorphism, almost multiplicative, Semisimple.

Abbas Zivari-Kazempour

2014-03-01

349

Ideal amenability of Banach algebras on locally compact groups  

CERN Document Server

In this paper we study the ideal amenability of Banach algebras. Let $\\cal A$ be a Banach algebra and let $I$ be a closed two-sided ideal in $\\cal A$, $\\cal A$ is $I$-weakly amenable if $H^{1}({\\cal A},I^*)=\\{0\\}$. Further, $\\cal A$ is ideally amenable if $\\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. 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.

Gordji, M E

2005-01-01

350

Constructions preserving $n$-weak amenability of Banach algebras  

CERN Document Server

A surjective bounded homomorphism fails to preserve $n$-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.

Jabbari, A; Vishki, H R E

2009-01-01

351

Exponential type vectors in Wiener algebras on a Banach ball  

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Full Text Available We consider Wiener type algebras on an open Banach ball. In particular, we prove that such algebras consist of functions analytic in this ball. We also consider a property of one-parameter groups generated by an isometric group acting on a Banach ball. We establish that the subspace of exponential type vectors of its generators form a dense subalgebra in a Wiener algebra and a generator is a derivation on this subspace.

Adam Bednarz

2008-01-01

352

On the Cauchy Functional Inequality in Banach Modules  

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Full Text Available We investigate the following functional inequality: ‖f(x+f(y+f(z‖≤‖f(x+y+z‖ in Banach modules over a C∗-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a C∗-algebra.

Choonkil Park

2008-05-01

353

Educating the Reflexive Practitioner  

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Full Text Available I cannot teach anybody anything, I can only make them think.SocratesIntroductionStudio as a model of education is distinct from many other professionaldisciplines and although it can be quite rewarding on many levels it mayalso be an extremely unconstructive endeavor.1 The amount of time spent in studio typically far outweighs that spent for other courses and often atthe expense of such other courses. The dedication that students bring tothe studio is remarkable, yet much of the time spent in studio is not alwaysproductive. Students often complain of not knowing what is expected ofthem and as a result much of the time is spent thinking about what they think the professor wants to see as opposed to working through theirprojects. In an alternate scenario, students are crushed by the workload, tasks, demands or expectations of their instructors. In either case, the work is almost invariably driven by the students own creativity and imagination; unlike law, medicine, business, or engineering for example, where the interpretation and inquiry into case studies and cadaversis much less based on the personal introspection than established traditions. This extremely personal nature of the architectural studio canmake reviews either a devastating or extremely empowering process. As seen from the perspective of the larger university community, the studio is simply not an efficient way of education. The faculty to student ratio, for example, is not in accordance with other undergraduate disciplines. But this ratio, as we all know can also be a real strength. The often hermeticnature of the studio offers latitude for students to develop theirwork in relatively safe surroundings. This environment, however, may also foster the cult of personality that develops around certain professorsthat harkens back to the very roots of education but can also lead to anentourage of disciples who have no incentive to inform the Emperor that he or she is no longer 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. Ive 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 Schn. Though I see much merit in the Boyer Report, and Schnsproposals, 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.

Marc J. Neveu

2012-09-01

354

Mazur spaces  

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A Mazur space is a locally convex topological vector space X such that every fϵXs is continuous where Xs is the set of sequentially continuous linear functionals on X; Xs is studied when X is of the form C(H), H a topological space, and when X is the weak * dual of a locally convex space. This leads to a new classification of compact T2 spaces H, those for which the weak * dual of C(H) is a Mazur space. An open question about Banach spaces with weak * sequentially compact dual ball is ...

Albert Wilansky

1981-01-01

355

Derivations into n-th duals of ideals of Banach algebras  

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We introduce two notions of amenability for a Banach algebra $\\cal A$. Let $n\\in \\Bbb N$ and let $I$ be a closed two-sided ideal in $\\cal A$, $\\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\\cal A},I^{(n)})=\\{0\\}$. Further, $\\cal A$ is n-ideally amenable if $\\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. We find some relationships of $n-I-$ ...

Gordji, M. Eshaghi; Memarbashi, R.

2006-01-01

356

Orlicz modulation spaces  

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In this thesis we extend the definition of modulation spaces associated to mixed-norm Lebesgue spaces to Orlicz spaces and mixed-norm Orlicz spaces and analyse their properties. In particular we characterize embedding relations between these spaces and prove entropy inequalities of the short-time Fourier transform. The basic idea of modulation spaces is to impose a norm on the short-time Fourier transform of tempered distributions that leads to Banach spaces of distributions with a given time...

Schnackers, Catherine

2014-01-01

357

Modulation of somatocardiac sympathetic reflexes mediated by opioid receptors at the spinal and brainstem level.  

Science.gov (United States)

Modulation of somatosympathetic reflexes at the spinal cord and the brainstem was studied by administering opioid receptor agonists into the intrathecal space of the lumbar spinal cord and into the subarachnoid space of the cisterna magna in rats anesthetized with alpha-chloralose and urethane. Somatocardiac sympathetic A- and C-reflexes were elicited by electrical stimulation of myelinated (A) and unmyelinated (C) afferent fibers of the tibial nerve, respectively. Intrathecal administration of the mu-opioid receptor agonist DAMGO selectively depressed the C-reflex in a dose-dependent manner (minimum effective dose 10 ng), whereas the intrathecal injection of the delta-opioid receptor agonist DPDPE and the kappa-opioid receptor agonist U-50,488H only at doses of 10 micrograms and 100 micrograms, respectively, led to a significant depression of the C-reflex. Injection of DAMGO into the cisterna magna enhanced both A- and C-reflexes in a dose-dependent manner (minimum effective dose 1 ng). The administration of neither DPDPE nor U-50,488H into the cisterna magna affected A- or C-reflexes. It is concluded that the activation of mu-opioid receptors is mainly or exclusively responsible for suppressing somatosympathetic C-reflexes at the spinal cord and for enhancing them at the brainstem. PMID:7589306

Sato, A; Sato, Y; Schmidt, R F

1995-01-01

358

Cauchy-Jensen additive mappings in quasi-Banach algebras and its applications  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, we prove the Hyers-Ulam stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following Cauchy-Jensen additive mappings

Choonkil Park

2013-02-01

359

Integrating Reflexivity in Livelihoods Research  

DEFF Research Database (Denmark)

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 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.

Prowse, Martin

2010-01-01

360

Reflex responses of masseter muscles to sound  

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Acoustic stimuli can evoke reflex EMG responses (acoustic jaw reflex) in the masseter muscle. Although these were previously ascribed to activation of cochlear receptors, high intensity sound can also activate vestibular receptors. Since anatomical and physiological studies, both in animals and humans, have shown that masseter muscles are a target for vestibular inputs we have recently reassessed the vestibular contribution to masseter reflexes. We found that high intensity sound evokes two b...

Deriu, Franca; Giaconi, Elena; Rothwell, John C.; Tolu, Eusebio

2010-01-01

 
 
 
 
361

Perspective on the human cough reflex  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Abstract This review dissects the complex human cough reflex and suggests hypotheses about the evolutionary basis for the reflex. A mechanosensory-induced cough reflex conveys through branches of myelinated A? nerve fibers is not chemically reactive (i.e., capsaicin, bradykinin); possibly, its evolution is to prevent the harmful effects of aspiration of gastric or particulate contents into the lungs. This became necessary as the larynx moves closer to the opening of the esophagus a...

Brooks Stuart M

2011-01-01

362

Generalized versus partial reflex seizures: a review.  

Science.gov (United States)

In this review we assess our currently available knowledge about reflex seizures with special emphasis on the difference between "generalized" reflex seizures induced by visual stimuli, thinking, praxis and language tasks, and "focal" seizures induced by startle, eating, music, hot water, somatosensory stimuli and orgasm. We discuss in particular evidence from animal, clinical, neurophysiological and neuroimaging studies supporting the concept that "generalized" reflex seizures, usually occurring in the setting of IGE, should be considered as focal seizures with quick secondary generalization. We also review recent advances in genetic and therapeutic approach of reflex seizures. PMID:24766826

Italiano, Domenico; Ferlazzo, Edoardo; Gasparini, Sara; Spina, Edoardo; Mondello, Stefania; Labate, Angelo; Gambardella, Antonio; Aguglia, Umberto

2014-08-01

363

N^p Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We introduce a new norm, called $N^{p}$-norm $(1\\leq{p}<\\infty)$ on a space $N^{p}(V,W)$ where $V$ and $W$ are abstract operator spaces. By proving some fundamental properties of the space $N^{p}(V,W)$, we also obtain that if $W$ is complete, then the space $N^{p}(V,W)$ is also a Banach space with respect to this norm for $1\\leq{p}<\\infty$.

Kim, Yun-su

2007-01-01

364

Generalized covariation and extended Fukushima decompositions for Banach valued processes. Application to windows of Dirichlet processes  

CERN Document Server

This paper concerns a class of Banach valued processes which have finite quadratic variation. The notion introduced here generalizes the classical one, of M\\'etivier and Pellaumail which is quite restrictive. We make use of the notion of $\\chi$-covariation which is a generalized notion of covariation for processes with values in two Banach spaces $B_{1}$ and $B_{2}$. $\\chi$ refers to a suitable subspace of the dual of the projective tensor product of $B_{1}$ and $B_{2}$. We investigate some $C^{1}$ type transformations for various classes of stochastic processes admitting a $\\chi$-quadratic variation and related properties. If $\\X^1$ and $\\X^2$ admit a $\\chi$-covariation, $F^i: B_i \\rightarrow \\R$, $i = 1, 2$ are of class $C^1$ with some supplementary assumptions then the covariation of the real processes $F^1(\\X^1)$ and $F^2(\\X^2)$ exist. A detailed analysis will be devoted to the so-called window processes. Let $X$ be a real continuous process; the $C([-\\tau,0])$-valued process $X(\\cdot)$ defined by $X_t(y)...

Di Girolami, Cristina

2011-01-01

365

Geometry of Mntz spaces and related questions  

CERN Document Server

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.

Gurariy, Vladimir

2005-01-01

366

Very smooth points of spaces of operators  

CERN Document Server

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 $M$-ideal in the space of bounded operators, a very smooth operator $T$ attains its norm at a unique vector $x$ (up to a constant multiple) and $T(x)$ 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--Nikod\\'{y}m property. We give an example of a smooth Banach space without any very smooth points.

Rao, T S S R K

2003-01-01

367

Derivations into duals of closed ideals of Banach algebras  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let $\\cal A$ be a Banach algebra. We study those closed ideals $I$ of $\\cal A$ for which the first cohomology group of $\\cal A$ with coefficients in $I^*$ is trivial; i.e. $H^1(\\cal A,I^*)=\\{0\\}$. We investigate such closed ideals when $\\cal A$ is weakly amenable or biflat. Also we give some hereditary properties of ideal amenability.

Gordji, M. Eshaghi; Hayati, B.; Hosseiniun, S. A. R.

2006-01-01

368

Stochastic processes on non-Archimedean Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. They are used for the development of stochastic antiderivations. The non-Archimedean analog of the Itô formula is proved.

Ludkovsky, S. V.

2003-01-01

369

Stability of stationary and periodic solutions equations in Banach space  

Directory of Open Access Journals (Sweden)

Full Text Available Linear difference and differential equations with operator coefficients and random stationary (periodic input are considered. Conditions are presented for the mean stability of stationary (periodic solutions under small perturbation of the coefficients.

A. Ya. Dorogovtsev

1997-01-01

370

SOME LYAPUNOV TYPE POSITIVE OPERATORS ON ORDERED BANACH SPACES  

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In this paper we investigate several properties of Lyapunov type operators occurring in connection with the characterization of exponential stability in mean square of systems of linear It^o differential equations perturbed by a Markov process with an innite countable number of states. A criterion for exponential stability of linear differential equations defined by a Lyapunov operator is derived under the assumption of property of detetability adequately defined for this type of operator val...

Vasile Dragan; Toader Morozan; Viorica Ungureanu

2013-01-01

371

SOME LYAPUNOV TYPE POSITIVE OPERATORS ON ORDERED BANACH SPACES  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper we investigate several properties of Lyapunov type operators occurring in connection with the characterization of exponential stability in mean square of systems of linear It^o differential equations perturbed by a Markov process with an innite countable number of states. A criterion for exponential stability of linear differential equations defined by a Lyapunov operator is derived under the assumption of property of detetability adequately defined for this type of operator valued functions.

Vasile Dragan

2013-07-01

372

On some fixed point theorems in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available In this paper, some fixed point theorems are proved for multi-mappings as well as a pair of mappings. These extend certain known results due to Kirk, Browder, Kanna, Ćirić and Rhoades.

P. Veeramani

1982-03-01

373

Fixed points of holomorphic mappings for domains in Banach spaces  

Directory of Open Access Journals (Sweden)

Full Text Available We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

Lawrence A. Harris

2003-03-01

374

On multi-ideals and polynomial ideals of Banach spaces  

CERN Document Server

The notion of coherent sequences of polynomial ideals and the notion of compatibility of a polynomial ideal with a given operator ideal were recently introduced by D. Carando, V. Dimant and S. Muro. These concepts play an important role in the theory of polynomial ideals, since they offer some properties that polynomial ideals must satisfy in order to keep the spirit of a given operator ideal and also maintain some coherence between the different levels of $n$-homogeneity. However, it seems to exist no reason to omit the multi-ideals from these cycle of ideas. In the present paper we revisit these notions; more precisely, we propose that these concepts are considered for a pair $(\\mathcal{P}_{k},\\mathcal{M}_{k})_{k=1}^{\\infty}$, where $(\\mathcal{P}%_{k})_{k=1}^{\\infty}$ is a polynomial ideal and $(\\mathcal{M}_{k}%)_{k=1}^{\\infty}$ is a multi-ideal. The construction of our approach is inspired by the important special case of absolutely summing operators.

Pellegrino, Daniel

2011-01-01

375

Fixed points for weakly inward mappings in Banach spaces  

Science.gov (United States)

S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,[Omega],P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=[mu]x, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works.

Xu, Shaoyuan; Jia, Baoguo; Li, Guo-Zhen

2006-07-01

376

Stochastic processes on non-Archimedean spaces. III. Stochastic processes on totally disconnected topological groups  

CERN Document Server

Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudo-differentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including irreducible of these groups. In addition stochastic processes on general Banach-Lie groups, loop monoids, loop spaces and path spaces of manifolds on Banach spaces over non-Archimedean local fields also are investigated.

Ldkovsky, S V

2001-01-01

377

Achilles tendon reflex measuring system  

Science.gov (United States)

The examination of Achilles tendon reflex is widely used as a simple, noninvasive clinical test in diagnosis and pharmacological therapy monitoring in such diseases as: hypothyroidism, hyperthyroidism, diabetic neuropathy, the lower limbs obstructive angiopathies and intermittent claudication. Presented Achilles tendon reflect measuring system is based on the piezoresistive sensor connected with the cylinder-piston system. To determinate the moment of Achilles tendon stimulation a detecting circuit was used. The outputs of the measuring system are connected to the PC-based data acquisition board. Experimental results showed that the measurement accuracy and repeatability is good enough for diagnostics and therapy monitoring purposes. A user friendly, easy-to-operate measurement system fulfills all the requirements related to recording, presentation and storing of the patients' reflexograms.

Szebeszczyk, Janina; Straszecka, Joanna

1995-06-01

378

Astronomical Data Reduction Workflows with Reflex  

Science.gov (United States)

Reflex (http://www.eso.org/reflex) is an environment that provides an easy and flexible way to reduce VLT/VLTI science data using the ESO. Its top-level functionalities are: (1) Reflex allows to graphically specify the sequence in which the data reduction steps are executed, including conditional stops, loops and conditional branches, (2) Reflex makes it easy to inspect the intermediate and final data products and to repeat selected processing steps to optimize the data reduction, (3) the data organization necessary to reduce the data is built into the system and is fully automatic, (4) advanced users can plug-in their own Python or IDL modules and steps into the data reduction sequence, and (5) Reflex supports the development of data reduction workflows based on the ESO Common Pipeline Library. Reflex is based on the concept of a scientific workflow, whereby the data reduction cascade is rendered graphically and data seamlessly flow from one processing step to the next. It is distributed with a number of complete test datasets so that users can immediately start experimenting and familiarize themselves with the system (http://www.eso.org/pipelines). In this demo, we present the latest version of Reflex and its applications for astronomical data reduction processes.

Ballester, P.; Bramich, D.; Forchi, V.; Freudling, W.; Garcia-Dab, C. E.; klein Gebbinck, M.; Modigliani, A.; Moehler, S.; Romaniello, M.

2014-05-01

379

Absolutely continuous functions with values in metric spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

We present a general theory of absolutely continuous paths with values in metric spaces using the notion of metric derivatives. Among other results, we prove analogues of the Banach-Zarecki and Vallee Poussin theorems.

Duda, Jakub

2005-01-01

380

Changes in the Achilles tendon reflexes following Skylab missions  

Science.gov (United States)

Postflight measurements of Achilles tendon reflex duration on Skylab crewmen indicate a state of disequilibrium between the flexor and extensor muscle groups with an initial decrease in reflex duration. As the muscles regain strength and mass there occurs an overcompensation reflected by increased reflex duration. Finally, when a normal neuromuscular state is reached the reflex duration returns to baseline value.

Baker, J. T.; Nicogossian, A. E.; Hoffler, G. W.; Johnson, R. L.; Hordinsky, J. R.

1977-01-01

 
 
 
 
381

Loading and reflexes : the influence of body weight and active movements on reflex responses in humans  

Digital Repository Infrastructure Vision for European Research (DRIVER)

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 were measured. After a general introduction (chapter 1), the studies are described. In chapter 2 a description is given about the influence of body (un)loading on cutaneous reflex responses during ...

Bastiaanse, Catharina Maria

2003-01-01

382

Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices  

Scientific Electronic Library Online (English)

Full Text Available SciELO Brazil | Language: English Abstract in english An n n real matrix P is said to be a generalized reflection matrix if P T = P and P = I (where P T is the transpose of P). A matrix A ? Rnn is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = P A P (A = - P A P). The reflexive and anti-ref [...] lexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations { A1 XB1 + C1X T D1 = M1. A2 XB2 + C2X T D2 = M2. over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms. Mathematical subject classification: 15A06, 15A24, 65F15, 65F20.

Mehdi, Dehghan; Masoud, Hajarian.

383

On the Banach $*$-algebra crossed product associated with a topological dynamical system  

CERN Document Server

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.

Svensson, Christian

2009-01-01

384

Derivations into n-th duals of ideals of Banach algebras  

CERN Document Server

We introduce two notions of amenability for a Banach algebra $\\cal A$. Let $n\\in \\Bbb N$ and let $I$ be a closed two-sided ideal in $\\cal A$, $\\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\\cal A},I^{(n)})=\\{0\\}$. Further, $\\cal A$ is n-ideally amenable if $\\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\\cal A$. We find some relationships of $n-I-$ weak amenability and $m-J-$ weak amenability for some different m and n or for different closed ideals $I$ and $J$ of $\\cal A$.

Gordji, M E

2006-01-01

385

Lectures given at the Banach Center and C.I.M.E. Joint Summer School  

CERN Document Server

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.

Lachowicz, Miros?aw

2008-01-01

386

[Anatomophysiological consideration on the sacral reflex].  

Science.gov (United States)

Sacral reflex testing is a very specific one. Coming from sensory receptors afferent neuronal pudendal passway enters the spinal cord S2 to S4 via spinal dorsal roots and transmits the bioelectrical activity to a complex interneuronal circuitry. Information is processed at this level and dispached into spinal motoneurones for innervating the pelviperineal muscles according to their specific radicular origins. Selective staged sacral reflexes contribute to locate the site of compression. Sacral reflex configuration was based on clinical and electrophysiological findings which is actually confirmed and valided by anatomical studies. This testing is the most efficacious and useful procedure of assessing the pudendal neuralgia, the S2 to S4 reflexes and the pelvic floor dysfunctions. PMID:18402408

de Bisschop, G; Spinosa, J P; de Bisschop, E; Nundlall, R

2008-02-27

387

Reflections on Reflexivity: Sociological Issues and Perspectives  

Directory of Open Access Journals (Sweden)

Full Text Available This paper attempts to comprehensively concentrate and critically reflect upon the theoretical and methodological conception of sociological reflexivity. It thus concisely presents some relevant debates on reflexivitys most influential sociological and epistemological definitions, as well as on its varied and complex relationship with the contentious notions of the self and spokespersonship. The conceptual elaboration on both notions emphatically highlights the crucial importance of the relational dimension over against the ubiquitous risks and dangers of subjectivism/objectivism, reification (blackboxing and essentialism. In addition, it is described and demonstrated the particular significance of the apophatic dimension of reflexivity over against its eurocentric (or western-centric and over-activistic (or cataphatic dimension, which inevitably leads to an excessive analytic emphasis upon a highly ordering, instrumental, and chronically monitoring approach to the inherently dynamic and fluid processes of self-awareness, self-experience, self-definition and self-identity.

Charalambos Tskekeris

2010-12-01

388

Threat of suffocation and defensive reflex activation  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The current study examined emotional reflex reactions of participants threatened with respiratory distress caused by imposing a resistive load at inspiration. Cues signaling threat (breathing MAY be difficult) and safe periods were intermixed while startle reflexes, heart rate, skin conductance and facial EMG activity were measured. Compared to safe cues, threat cues elicited significant startle potentiation, enhanced skin conductance, heightened corrugator EMG changes and pronounced "fear br...

Lang, Peter J.; Wangelin, Bethany C.; Bradley, Margaret M.; Versace, Francesco; Davenport, Paul W.; Costa, Vincent D.

2011-01-01

389

A Generalization of the Weak Amenability of some Banach Algebra  

CERN Document Server

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$ dual of $A$, $A^{(n+2)}$, is $T-S-$weakly amenable, then $A^{(n)}$ is $T-S-$weakly amenable where $T$ and $S$ are continuous linear mappings from $A^{(n)}$ into $A^{(n)}$.

Haghnejad, Kazem

2010-01-01

390

A generalization of the weak amenability of some Banach algebra  

CERN Document Server

Let $A$ be a Banach algebra and $A^{**}$ be the second dual of it. We show that by some new conditions, $A$ is weakly amenable whenever $A^{**}$ is weakly amenable. We will study this problem under generalization, that is, if $(n+2)-th$ dual of $A$, $A^{(n+2)}$, is $T-S-$weakly amenable, then $A^{(n)}$ is $T-S-$weakly amenable where $T$ and $S$ are continuous linear mappings from $A^{(n)}$ into $A^{(n)}$.

Azar, Kazem Haghnejad

2010-01-01

391

Adductor T and H reflexes in humans.  

Science.gov (United States)

In the belief that changes in the adductor reflex (AR) may be helpful in evaluating lumbar root and plexus lesions, expression of the AR was studied in 43 healthy human subjects. ARs elicited with an electronic reflex hammer were recorded from the inner side of the proximal thigh using needle and surface electrodes, and patellar reflexes (PRs) were recorded simultaneously. These reflexes were obtained by tapping the ipsilateral medial aspect of the knee, the contralateral patellar tendon, the ipsilateral and contralateral anterior superior iliac spines, and the Achilles tendon. The H reflex of the obturator nerve was also evaluated in 17 cases. ARs were evoked consistently by tapping the ipsilateral medial aspect of the knee and by contralateral patellar tap, and by tapping ipsilateral and contralateral anterior superior iliac spines when a needle recording electrode was used. Sometimes an Achilles tendon tap also elicited the AR ipsilaterally. By contrast, the PR could only be elicited by a tap to the ipsilateral patellar tendon. ARs have somewhat different features than other well-known tendon reflexes such as the PR and are recorded consistently when a needle electrode is used, being elicited from both distal and proximal areas of the legs by tapping the Achilles tendon or anterior superior iliac spines unilaterally or bilaterally. Their role in evaluating lumbar root disease and monitoring adductor spasticity merits investigation. PMID:16941659

Ertekin, Cumhur; Bademkiran, Fikret; Tataroglu, Cengiz; Aydogdu, Ibrahim; Karapinars, Nevin

2006-11-01

392

The passive of reflexive verbs in Icelandic  

Directory of Open Access Journals (Sweden)

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 (tmarit.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.

Hlf rnadttir

2011-10-01

393

Brauer-Thrall for totally reflexive modules  

CERN Document Server

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...

Christensen, Lars Winther; Rahmati, Hamidreza; Striuli, Janet; Wiegand, Roger

2010-01-01

394

Variability in Hoffmann and tendon reflexes in healthy male subjects  

Science.gov (United States)

There is a time dependent decrease in amplitude of H- and T-reflexes during Zero-G exposure and subsequently an increase in the amplitude of the H-reflex 2-4 hours after return to a 1-G environment. These alterations have been attributed to the adaptation of the human neurosensory system to gravity. The Hoffman reflex (H-reflex) is an acknowledged method to determine the integrity of the monosynaptic reflex arc. However deep tendon reflexes (DTR's or T-reflexes), elicited by striking the tendon also utilize the entire reflex arc. The objective of this study was to compare the variability in latency and amplitude of the two reflexes in healthy subjects. Methods: Nine healthy male subjects, 27-43 years in age, 161-175 cm in height plus 60-86 Kg in weight, underwent weekly testing for four weeks with a Dan-Tec EMG counterpoint EMG system. Subjects were studied prone and surface EMG electrodes were placed on the right and left soleus muscles. The H-reflex was obtained by stimulating the tibial nerve in the politeal fossa with a 0.2 msec square wave pulse delivered at 2 Hz until the maximum H-reflex was obtained. The T-reflex was invoked by tapping the achilles tendon with a self triggering reflex hammer connected to the EMG system. The latencies and amplitudes for the H- and T-reflexes were measured. Results: These data indicate that the amplitudes of these reflexes varied considerably. However, latencies to invoked responses were consistent. The latency of the T-reflex was approximately 3-5 msec longer than the H-reflex. Conclusion: The T-reflex is easily obtained, requires less time, and is more comfortable to perform. Qualitative data can be obtained by deploying self triggering, force plated reflex hammers both in the 1-G and Zero-G environment.

Good, E.; Do, S.; Jaweed, M.

1992-01-01

395

Om Banachs fikspunktteorem og The Scottish Caf :-Anvendelser av Banachs fikspunktteorem. -Kulturhistorisk bakgrunn for forstelsen av The Scottish Caf.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Sammendrag I kapittel 1 gjres klart hvilke forkunnskaper som er ndvendige for kunne forst og ha utbytte av lese denne oppgaven. Det henvises ogs til litteratur som kan brukes som oppslagsverk hvis noen begreper under lesningen skulle vre ukjente. I kapittel 2 klargjres sentrale begreper som fikspunkt, kontraksjon og kompletthet. Dernest presenteres Banachs fikspunktteorem med bevis. Kapitlet peker ogs mot ulike anvendelser av teoremet. Kapittel 3 handler i sin helhet...

Nilsen, Torger Johannes

2006-01-01

396

Intrasession and intersession reliability of the soleus H-reflex in supine and standing positions.  

Science.gov (United States)

The Hoffmann reflex (H-reflex) is a measure of motoneuron pool excitability, which is valuable in determining muscle inhibition caused by joint damage (arthrogenic muscle inhibition). In order to detect changes in H-reflex due to injury, the reliability of such a measurement must be established. The purpose of this study was to establish the intrasession and intersession reliability of soleus H-reflex in a supine and standing position. Thirteen healthy volunteers (age 10 +/- 2.63 yr, height 171.35 +/- 10.19 cm, mass 69.62 +/- 13.03 Kg) with no lower extremity orthopedic or neurological disorders within the past year participated in this study. To determine the intrasession and intersession reliability of this measure in a supine resting position and a one-leg standing position, EMG data were collected from the soleus while the tibial nerve was stimulated in the popliteal space. A high voltage (120-200 V), short duration (1.0 msec) stimulus was automatically triggered, eliciting a reflex twitch detected by surface EMG. Several of these measurements were performed with 20 second rest intervals to find the maximum H-reflex. The maximum H-reflex was located by adjusting the intensity of the stimulus. Once a maximum H-reflex was found, 12 measurements were taken in that position with 20 second rest intervals. These steps were repeated for each position (supine and standing) at the same time for 5 consecutive days. Intrasession reliability was computed using 12 measurement trials (12), 12 measurement trials dropping the high and low score (12x), the first 7 measurement trials dropping the high and low score (7x), and the first 5 measurement trials (5). Intrasession and intersession reliability over five consecutive days was estimated using intraclass correlation coefficients (ICC (3, 1)). The supine intrasession reliability measurements were as follows: 0.932 (12), 0.932 (12x), 0.935 (7x), and 0.932 (5). The standing intrasession reliability was 0.853 (12), 0.852 (12x), 0.865 (7x), and 0.862 (5). The intersession reliability was 0.938 in the supine position and 0.803 in the standing position. These results indicate that the H-reflex measured using our protocol in a supine and standing position is a reliable assessment within sessions and between sessions. Five measurements are sufficient to observe reliable measurements within a single session. Most importantly, this data shows that the H-reflex is a reliable assessment that may be used to measure small changes in motoneuron pool excitability over time. PMID:10746184

Hopkins, J T; Ingersoll, C D; Cordova, M L; Edwards, J E

2000-03-01

397

Evidence for sustained cortical involvement in peripheral stretch reflex during the full long latency reflex period.  

Science.gov (United States)

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 magnetic stimulation (TMS) and upper extremity muscle stretch reflexes at high temporal precision. In twelve participants (age 4913 years, eight male), afferent signals were evoked by 40ms ramp and subsequent hold stretches of the m. flexor carpi radialis (FCR). Motor conduction delays (TMS time of arrival at the muscle) and TMS-motor threshold were individually assessed. Subsequently TMS pulses at 96% of active motor threshold were applied with a resolution of 5-10ms between 10ms before and 120ms after onset of series of FCR stretches. Controlled for the individually assessed motor conduction delay, subthreshold TMS was found to significantly augment EMG responses between 60 and 90ms after stretch onset. This sensitive temporal window suggests a cortical integration consistent with a long latency reflex period rather than a spinal integration consistent with a short latency reflex period. The potential cortical role in reflex adaptation extends over the full long latency reflex period, suggesting adaptive mechanisms beyond reflex onset. PMID:25449867

Perenboom, M J L; Van de Ruit, M; De Groot, J H; Schouten, A C; Meskers, C G M

2015-01-01

398

Depending on the mode of application morphine enhances or depresses somatocardiac sympathetic A- and C-reflexes in anesthetized rats.  

Science.gov (United States)

The effects of morphine on the reflex discharges in sympathetic efferents recorded from branches of the inferior cardiac nerve (ICN) were studied in rats anesthetized with alpha-chloralose and urethane. Somatocardiac sympathetic A- and C-reflexes were elicited by single shock electrical stimulation of myelinated (A) and unmyelinated (C) afferent fibers of the tibial nerve, respectively. Application of morphine either into the femoral vein or into the subarachnoid space of the cisterna magna enhanced both the A- and C-reflexes in a dose-dependent manner, while application of morphine into the intrathecal space of the lumbar spinal cord selectively inhibited C-reflexes. All effects of morphine were antagonized by naloxone. Application of morphine via the internal carotid artery to central nervous structures above the brainstem had no effect on the somatocardiac sympathetic reflexes. It is concluded that in the anesthetized rat morphine in a dose-dependent and naloxone-reversible manner (1) depresses spinal transmission of C-afferent activity, whereas (2) at the brainstem it enhances the transmission of somatocardiac sympathetic A- and C-reflexes. PMID:1337580

Adachi, T; Sato, A; Sato, Y; Schmidt, R F

1992-12-01

399

Multiplication operators in Kothe-Bochner spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let X be a Banach space and E an order continuous Banach function space over a finite measure mu. We prove that an operator T in the Kothe-Bochner space E(X) is a multiplication operator (by a function in L(infinity)(mu)) if and only if the equality T(g x) = g x holds for every g is an element of L(infinity)(mu), f is an element of E(X), x is an element of X and x* is an element of X*. (C) 2010 Elsevier Inc.

Calabuig Rodriguez, Jose Manuel; Sa?nchez Pe?rez, Enrique Alfonso; Rodriguez, J.

2011-01-01

400

Reflexive composites: self-healing composite structures  

Science.gov (United States)

Cornerstone Research Group Inc. has developed reflexive composites achieving increased vehicle survivability through integrated structural awareness and responsiveness to damage. Reflexive composites can sense damage through integrated piezoelectric sensing networks and respond to damage by heating discrete locations to activate the healable polymer matrix in areas of damage. The polymer matrix is a modified thermoset shape memory polymer that heals based on phenomena known as reptation. In theory, the reptation healing phenomena should occur in microseconds; however, during experimentation, it has been observed that to maximize healing and restore up to 85 % of mechanical properties a healing cycle of at least three minutes is required. This paper will focus on work conducted to determine the healing mechanisms at work in CRG's reflexive composites, the optimal healing cycles, and an explanation of the difference between the reptation model and actual healing times.

Margraf, Thomas W., Jr.; Barnell, Thomas J.; Havens, Ernie; Hemmelgarn, Christopher D.

2008-03-01

 
 
 
 
401

Apnea of prematurity: II. Respiratory reflexes.  

Science.gov (United States)

Airway obstruction is a cause of apnea in preterm infants. The activity of protective respiratory reflexes was determined in 18 preterm infants with apnea (mean of 32 episodes of more than 20 seconds duration per day) and in 18 neonates without apnea used as control subjects. This was done in order to elucidate the role of respiratory reflexes in apnea of prematurity. The infants were matched for birth weight (1,068 g v 1,065 g), gestational age (30.2 weeks v 30.2 weeks), and postnatal age (8.6 days v 8.3 days). The airway occlusion technique was used to determine the inspiratory prolongation of the occluded breath and the effective elastance of the respiratory system. Inspiratory prolongation is a measure for the reflex influence on inspiratory duration, and effective elastance reflects load compensating ability. Inspiratory prolongation was 7.3% +/- 33.5% in infants with apnea and 30.6% +/- 22.7% in the control group (P less than .025). Effective elastance was 1.1 +/- 0.5 cm H2O/mL in the apneic group and 1.5 +/- 0.5 cm H2O/mL in the infants without apnea (P less than .025). The results indicate that during exposure to respiratory loads, the infants with apnea maintained inspiratory effort poorly and had a decreased ability for load compensation. Their respiratory reflexes were significantly more immature than the reflex activity of the infants without apnea. This functional immaturity of respiratory reflexes may be a contributing factor in the etiology of apnea of prematurity. PMID:6739219

Gerhardt, T; Bancalari, E

1984-07-01

402

Reflex control for safe autonomous robot operation  

International Nuclear Information System (INIS)

This paper describes the design of an autonomous, sonar-based world mapping system for collision prevention in robotic systems. Obstacle detection and mapping is performed as a task that competes with higher-level tasks for the robot's attention. All tasks are integrated within a hierarchy, organized and co-ordinated by schemes analogous to biological reflexes and fixed action patterns. It is illustrated how the existence of low-level reflex behaviours can enhance the survivability and autonomy of complex systems and simplify the design of complex higher-level controls like our autonomous sonar-based world mapping system

403

Threat of suffocation and defensive reflex activation.  

Science.gov (United States)

The current study examined emotional reflex reactions of participants threatened with respiratory distress caused by imposing a resistive load at inspiration. Cues signaling threat (breathing MAY be difficult) and safe periods were intermixed while startle reflexes, heart rate, skin conductance, and facial EMG activity were measured. Compared to safe cues, threat cues elicited significant startle potentiation, enhanced skin conductance, heightened corrugator EMG changes, and pronounced "fear bradycardia" consistent with defensive activation in the context of threatened respiratory dysfunction. These data indicate that anticipating respiratory resistance activates defensive responding, which may mediate symptomatology in patients with panic and other anxiety disorders. PMID:20667037

Lang, Peter J; Wangelin, Bethany C; Bradley, Margaret M; Versace, Francesco; Davenport, Paul W; Costa, Vincent D

2011-03-01

404

On the dual space C0*(S, X)  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let S be a locally compact Hausdorff space and let us consider the space C0(S, X) of continuous functions vanishing at infinity, from S into the Banach space X. A theorem of I. Singer, settled for S compact, states that the topological dual C0*(S, X) is isometrically isomorphic to the Banach space r?bv(S, X*) of all regular vector measures of bounded variation on ...

Meziani, L.

2009-01-01

405

Continuous Frames, Function Spaces, and the Discretization Problem  

CERN Document Server

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed by Feichtinger and Groechenig. As an important tool the concept of localization of frames is extended to continuous frames. As a byproduct we give a partial answer to the question raised by Ali, Antoine and Gazeau whether any continuous frame admits a corresponding discrete realization generated by sampling.

Fornasier, M; Fornasier, Massimo; Rauhut, Holger

2004-01-01

406

The reflexive self and culture: a critique.  

Science.gov (United States)

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

Adams, Matthew

2003-06-01

407

Orthodoxy and reflexivity in international comparative analysis  

DEFF Research Database (Denmark)

This contribution aims at four points.First we want to argue why we think a reflexive social science is more adequate than the orthodox consensus. In current practice much of the criticism on the orthodox consensus is shared on a theoretical level, without considering the implications and acting upon the consequences on the level of empirical research. We want to avoid that, so our second and third subject will be the practical implications of reflexivity for empirical research as well as for social policy. Our discussion on these subjects is based on the practical experiences in the INPART project, in which we have tried to deal with these consequences. Fourth, and hopefully as a result of the first three aims, we want to argue that a reflexive approach of international, comparative research is not only desirable, but attainable as well. In order to do so, we begin with a short discussion of the main methodological principles of the orthodox consensus and the empirical-analytical research model that is basedupon them. In that paragraph we will also argue why this approach apparently gives their adherents little problems in doing international research. Next, we will explore and elaborate on the main issues in the so-called ?reflexive approach? and consider the main consequences of this approach for both social science and social policy. Against this background we will discuss the implications for comparative research and the experiences of the INPART project end up with a few central issues for further debate.

Lind, Jens; Valkenburg, Ben

2002-01-01

408

Perspective on the human cough reflex  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract This review dissects the complex human cough reflex and suggests hypotheses about the evolutionary basis for the reflex. A mechanosensory-induced cough reflex conveys through branches of myelinated A? nerve fibers is not chemically reactive (i.e., capsaicin, bradykinin; possibly, its evolution is to prevent the harmful effects of aspiration of gastric or particulate contents into the lungs. This became necessary as the larynx moves closer to the opening of the esophagus as human ancestors adapt phonation over olfaction beginning less than 10 million years ago. The second type of cough reflex, a chemosensory type, is carried by unmyelinated C fibers. Supposedly, its origin dates back when prehistoric humans began living in close proximity to each other and were at risk for infectious respiratory diseases or irritant-induced lung injury. The mechanism for the latter type of cough is analogous to induced pain after tissue injury; and, it is controlled by the identical transient receptor potential vanilloid cation channel (TRPV1. The airways do not normally manifest nociceptive pain from a stimulus but the only consistent response that capsaicin and lung inflammation provoke in healthy human airways is cough. TRPA1, another excitatory ion channel, has been referred to as the "irritant receptor" and its activation also induces cough. For both types of cough, the motor responses are identical and via coordinated, precisely-timed and sequential respiratory events orchestrated by complex neuromuscular networking of the diaphragm, chest and abdominal respiratory muscles, the glottis and parts of the brain.

Brooks Stuart M

2011-11-01

409

Spaces of continuous functions over Dugundji compacta  

CERN Document Server

We show that for every Dugundji compact $K$ the Banach space $C(K)$ is 1-Plichko and the space $P(K)$ of probability measures on $K$ is Valdivia compact. Combining this result with the existence of a non-Valdivia compact group, we answer a question of Kalenda.

Banakh, T; Banakh, Taras; Kubis, Wieslaw

2006-01-01

410

Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I  

Directory of Open Access Journals (Sweden)

Full Text Available We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let be a Banach algebra and a Banach -module, and . The mappings , and are defined and it is proved that if (resp., is dominated by then is a generalized (resp., linear module- left derivation and is a (resp., linear module- left derivation. It is also shown that if (resp., is dominated by then is a generalized (resp., linear module- derivation and is a (resp., linear module- derivation.

Rassias JM

2009-01-01

411

Stable Ranks, K-Groups and Witt Groups of some Banach and C-star Algebras  

CERN Document Server

We show that certain dense and spectral invariant subalgebras of a $C^*$-algebra have the same bilateral Bass stable rank. This is a partial answer for (a version of) an open problem raised by R.G. Swan. Then, for certain Banach algebras, we indicate when the homotopy groups result due to G. Corach and A. Larotonda. Using some results due to M. Karoubi, we show the isomorphism of the Witt group of a symmetric Banach algebra with the $K_0$-group of its enveloping $C^*$-algebra. The question if this is true for all involutive Banach algebras was raised by A. Connes.

Badea, C

1999-01-01

412

Ciliospinal reflex response in cluster headache.  

Science.gov (United States)

The ciliospinal reflex response is mainly mediated by second- and third-order sympathetic nerves to the dilatator muscle of the iris. As the pupillary response to various pharmacological agents indicates a sympathetic dysfunction in patients with cluster headache, the ciliospinal reflex was studied in 25 patients. Five of these patients with cluster headache exhibited a Horner-like syndrome (miosis, ptosis) on the symptomatic side. The pupillary responses to phenylephrine and tyramine showed that the Horner-like syndrome was due to postganglionic sympathetic nerve dysfunction. Their ciliospinal reflex response on the symptomatic side was significantly less than in controls and in other patients with cluster headache, lacking a Horner-like syndrome. This also applied to the nonsymptomatic side compared to the majority of cluster headache patients without any clinical evidence of sympathetic nerve dysfunction. These findings seem to delineate those patients with a Horner-like syndrome as a subgroup, distinctly separated from the majority of cluster headache patients. Furthermore, the findings indicate that the Horner-like syndrome is not a consequence of repeated attacks of headache over many years, but is a manifestation of bilateral cephalic sympathetic dysfunction being more marked on the symptomatic side. In 18 (72%) of our 25 patients, an asymmetric and lower ciliospinal reflex response on the symptomatic side was seen. In 3 (12%) patients, there was no difference in the response. In 4 patients (16%), the incorrect side was indicated by an asymmetric reflex response. Two of these patients (8%) had suffered from cluster headache on alternating sides. In summary, the findings support the concept that dysfunction of the sympathetic nervous system, whether peripheral or central is involved in the pathophysiology of cluster headache. PMID:8916567

Havelius, U; Heuck, M; Milos, P; Hindfelt, B

1996-10-01

413

Investigation to predict patellar tendon reflex using motion analysis technique.  

Science.gov (United States)

The investigation of patellar tendon reflex involves development of a reflex hammer holder, kinematic data collection and analysis of patellar reflex responses using motion analysis techniques. The main aim of this research is to explore alternative means of assessing reflexes as a part of routine clinical diagnosis. The motion analysis system was applied to provide quantitative data which is a more objective measure of the patellar tendon reflex. Kinematic data was collected from 28 males and 22 females whilst subjected to a knee jerk test. Further analysis of kinematic data was performed to predict relationships which might affect the patellar tendon reflex. All subjects were seated on a high stool with their legs hanging freely within the capture volume of the motion analysis system. Knee jerk tests were applied to all subjects, on both sides of the leg, by eliciting hypo, hyper, and normal reflexes. An additional reinforcement technique called the Jendrassik manoeuvre was also performed under the same conditions to elicit a normal patellar tendon reflex. The comparison of reflex response between genders showed that female subjects generally had a greater response compared to males. However, the difference in reflex response between the left leg and the right leg was not significant. Tapping strength to elicit a hyper-reflex produced greater knee-jerk compared to the normal clinical tapping strength. All results were in agreement with clinical findings and results found by some early researchers. PMID:21146440

Tham, L K; Osman, N A Abu; Lim, K S; Pingguan-Murphy, B; Abas, W A B Wan; Zain, N Mohd

2011-05-01

414

Feminist Politics as Reflexive Citizenship  

Directory of Open Access Journals (Sweden)

Full Text Available This article examines the potential feminist contribution to a radically renovated citizenship, according to which we all ought to undertake our responsibilities towards family, society and world. This contribution mainly consists in the critical transgression of the traditional dualism between private and public space, which arises from the politicization of everyday experience and results to the emergence of an essentially participial civil society.

Nikos Katrivesis

2008-11-01

415

A note on mutiplication operators on Kthe-Bochner spaces  

Directory of Open Access Journals (Sweden)

Full Text Available Let (?, A, ? is a finite measure space, E an order continuous Banach function space over ?, X a Banach space and E(X the Kthe-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 f, x* > x =g T(f, x* > x for everyg L, f E(X, x X, x* X*.

S. S. Khurana

2012-02-01

416

On the dual space C0*(S, X  

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Full Text Available Let S be a locally compact Hausdorff space and let us consider the space C0(S, X of continuous functions vanishing at infinity, from S into the Banach space X. A theorem of I. Singer, settled for S compact, states that the topological dual C0*(S, X is isometrically isomorphic to the Banach space r?bv(S, X* of all regular vector measures of bounded variation on S, with values in the strong dual X*. Using the Riesz-Kakutani theorem and some routine topological arguments, we propose a constructive detailed proof which is, as far as we know, different from that supplied elsewhere.

L. Meziani

2009-02-01

417

Fixed Points of Non-expansive Operators on Weakly Cauchy Normed Spaces  

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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.

Sahar M. Ali

2007-01-01

418

Stick balancing with reflex delay in case of parametric forcing  

Science.gov (United States)

The effect of parametric forcing on a PD control of an inverted pendulum is analyzed in the presence of feedback delay. The stability of the time-periodic and time-delayed system is determined numerically using the first-order semi-discretization method in the 5-dimensional parameter space of the pendulum's length, the forcing frequency, the forcing amplitude, the proportional and the differential gains. It is shown that the critical length of the pendulum (that can just be balanced against the time-delay) can significantly be decreased by parametric forcing even if the maximum forcing acceleration is limited. The numerical analysis showed that the critical stick length about 30 cm corresponding to the unforced system with reflex delay 0.1 s can be decreased to 18 cm with keeping maximum acceleration below the gravitational acceleration.

Insperger, Tamas

2011-04-01

419

Intraoperative recording of the bulbocavernosus reflex.  

Science.gov (United States)

: The bulbocavernosus reflex (BCR) is mediated by the sacral somatic afferent/efferent periphery as well as the sacral cord. Unfortunately, the reflex has suffered from a partly deserved reputation as difficult to implement. However, recent stratagems have improved the test's reliability. Multipulse stimulation (enhanced by double trains as required) and exacting recording technique can yield positive and remarkably reproducible results in patients of all ages and either sex. In this review, we document a 94% baseline BCR acquisition rate among 100 consecutive cases in one institution. Acceptance and routine use of the BCR is needed to help assure optimal post-operative low sacral function in intradural and extradural surgeries at the level of conus medullaris, cauda equina, sacral plexus, and the pudendal nerve. Case studies within this review illustrate the power of the BCR to predict patient outcome or, much more importantly, reverse incipient patient injury in real time. PMID:25083842

Skinner, Stanley A; Voduek, David B

2014-08-01

420

Creativity in ethnographic interviews : reflexive participatory observation  

DEFF Research Database (Denmark)

The article discusses interviews as participatory reflexive observation. It is based on experiences of interviewing policymakers and researchers about knowledge and evidence in health promotion. This particular group of informants challenged an approach to interviews as getting informants to describe their everyday work life. By employing a methodological framework focusing on reflexive processes, interviews became consensual interactions, and the content of the interviews turned out to be analyses, interpretations and meaning making, that is, knowledge production. Interpretation and meaning making drew on ideologies, norms and values central to the field and thereby the strategies employed by the informants as well as by the researcher could be seen as wayfaring strategies; creating the paths in the field as they go along. Such an approach to interviews opens up the creative character of knowledge production and points out the role of the researcher as an active participant in the creative process.

Kauffmann, Lene Teglhus

2014-01-01

 
 
 
 
421

How to Classify Reflexive Gorenstein Cones  

CERN Document Server

Two of my collaborations with Max Kreuzer involved classification problems related to string vacua. In 1992 we found all 10,839 classes of polynomials that lead to Landau-Ginzburg models with c=9 (Klemm and Schimmrigk also did this); 7,555 of them are related to Calabi-Yau hypersurfaces. Later we found all 473,800,776 reflexive polytopes in four dimensions; these give rise to Calabi-Yau hypersurfaces in toric varieties. The missing piece - toric constructions that need not be hypersurfaces - are the reflexive Gorenstein cones introduced by Batyrev and Borisov. I explain what they are, how they define the data for Witten's gauged linear sigma model, and how one can modify our classification ideas to apply to them. I also present results on the first and possibly most interesting step, the classification of certain basic weights systems, and discuss limitations to a complete classification.

Skarke, Harald

2012-01-01

422

Reflexivity in performative science shop projects  

Directory of Open Access Journals (Sweden)

Full Text Available Science shop research projects offer possibilities for universities to engage with communities. Many science shop projects directly or indirectly intend to empower certain marginalised groups or interests within a decision-making process. In this article we argue that it is important to reflect on the role and position the researchers have in these projects. We present three science shop projects to illustrate some of the dilemmas that may arise in relation to citizen empowerment, democracy, and ethics in the field of action research and community engagement. We present reflexivity as a strategy for creating greater awareness of the power?knowledge relationship, the nature of the democratic process and the consequences of empowerment for other vulnerable groups. Keywords: Action research, community engagement, reflexivity, science shop

Raoul Beunen

2012-08-01

423

Influence of Age on Patellar Tendon Reflex Response  

Science.gov (United States)

Background A clinical parameter commonly used to assess the neurological status of an individual is the tendon reflex response. However, the clinical method of evaluation often leads to subjective conclusions that may differ between examiners. Moreover, attempts to quantify the reflex response, especially in older age groups, have produced inconsistent results. This study aims to examine the influence of age on the magnitude of the patellar tendon reflex response. Methodology/Principal Findings This study was conducted using the motion analysis technique with the reflex responses measured in terms of knee angles. Forty healthy subjects were selected and categorized into three different age groups. Patellar reflexes were elicited from both the left and right patellar tendons of each subject at three different tapping angles and using the Jendrassik maneuver. The findings suggested that age has a significant effect on the magnitude of the reflex response. An angle of 45 may be the ideal tapping angle at which the reflex can be elicited to detect age-related differences in reflex response. The reflex responses were also not influenced by gender and were observed to be fairly symmetrical. Conclusions/Significance Neurologically normal individuals will experience an age-dependent decline in patellar reflex response. PMID:24260483

Chandrasekhar, Annapoorna; Abu Osman, Noor Azuan; Tham, Lai Kuan; Lim, Kheng Seang; Wan Abas, Wan Abu Bakar

2013-01-01

424

The higher-dimensional amenability of tensor products of Banach algebras  

CERN Document Server

We investigate the higher-dimensional amenability of tensor products $\\A \\ptp \\B$ of Banach algebras $\\A$ and $\\B$. We prove that the weak bidimension $db_w$ of the tensor product $\\A \\ptp \\B$ of Banach algebras $\\A$ and $\\B$ with bounded approximate identities satisfies \\[ db_w \\A \\ptp \\B = db_w \\A + db_w \\B. \\] We show that it cannot be extended to arbitrary Banach algebras. For example, for a biflat Banach algebra $\\A$ which has a left or right, but not two-sided, bounded approximate identity, we have $db_w \\A \\ptp \\A \\le 1$ and $db_w \\A + db_w \\A =2.$ We describe explicitly the continuous Hochschild cohomology $\\H^n(\\A \\ptp \\B, (X \\ptp Y)^*)$ and the cyclic cohomology $\\H\\C^n(\\A \\ptp \\B)$ of certain tensor products $\\A \\ptp \\B$ of Banach algebras $\\A$ and $\\B$ with bounded approximate identities; here $(X \\ptp Y)^*$ is the dual bimodule of the tensor product of essential Banach bimodules $X$ and $Y$ over $\\A$ and $\\B$ respectively.

Lykova, Zinaida A

2009-01-01

425

An experimental model of oculorespiratory reflex.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

An experimental study of the oculorespiratory reflex (ORR) was conducted on 20 albino rabbits using a square wave (SW) type of stimulus. The ORR could be elicited in 100% of animals. The medial rectus was observed to be most reflexogenic for ORR. The frequency and pattern of ORR was not affected by bilateral vagotomy, intravenous atropine or glycopyrrolate, but could be completely abolished by retrobular block.

Khurana, A. K.; Khurana, I.; Yadav, R. N.; Singh, P. I.; Gombar, K. K.; Ahluwalia, B. K.

1992-01-01

426

Central pathway of photic reflex myoclonus.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Direct, new evidence for the cortical origin of photic reflex myoclonus in a patient with "posterior cortical atrophy" is provided. Photic stimulation elicited myoclonic jerks in the right upper limb muscles. An H2(15)O-PET activation study with photic stimulation showed increased regional cerebral blood flow not only in both striate cortices but in the left premotor and primary motor areas as well. Transcranial magnetic stimulation over the area of the left occipital cortex elicited motor ev...

Kanouchi, T.; Yokota, T.; Kamata, T.; Ishii, K.; Senda, M.

1997-01-01

427

Carbamazepine, clonazepam and focal reflex proprioceptive seizures  

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We studied a 34-year-old man with focal tonic-clonic seizures sometimes elicited by some active postures of the right hand and evolving at times to secondary generalization. Treatment with carbamazepine (CBZ) in combination with parenteral diazepam induced both a dramatic increase of focal reflex proprioceptive seizures and choreoathetoid dyskinesias in the affected hand. CBZ was withdrawn and clonazepam (CZP) given 2 mg daily, with complete relief of seizures and choreoathetoid dyskinesias. ...

Sechi, Gianpietro; Corda, Davide; Deiana, Giovanni Andrea; Contu, Sabrina; Rosati, Giulio

2003-01-01

428

Basic Gravitational Reflexes in the Larval Frog  

Science.gov (United States)

This investigation was designed to determine how a primitive vertebrate, the bullfrog tadpole, is able to sense and process gravitational stimuli. Because of the phylogenetic similarities of the vestibular systems in all vertebrates, the understanding of the gravitational reflexes in this relatively simple vertebrate should elucidate a skeletal framework on a elementary level, upon which the more elaborate reflexes of higher vertebrates may be constructed. The purpose of this study was to understand how the nervous system of the larval amphibian processes gravitational information. This study involved predominantly electrophysiological investigations of the isolated, alert (forebrain removed) bullfrog tadpole head. The focus of these experiments is threefold: (1) to understand from whole extraocular nerve recordings the signals sent to the eye following static gravitational tilt of the head; (2) to localize neuronal centers responsible for generating these signals through reversible pharmacological ablation of these centers; and (3) to record intracellularly from neurons within these centers in order to determine the single neuron's role in the overall processing of the center. This study has provided information on the mechanisms by which a primitive vertebrate processes gravitational reflexes.

Cochran, Stephen L.

1996-01-01

429

The swallowing reflex and its significance as an airway defensive reflex  

Directory of Open Access Journals (Sweden)

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.

TakashiNishino

2013-01-01

430

Short reflex expirations (expiration reflexes induced by mechanical stimulation of the trachea in anesthetized cats  

Directory of Open Access Journals (Sweden)

Full Text Available Abstract Fifty spontaneously breathing pentobarbital-anesthetized cats were used to determine the incidence rate and parameters of short reflex expirations induced by mechanical stimulation of the tracheal mucosa (ERt. The mechanical stimuli evoked coughs; in addition, 67.6% of the stimulation trials began with ERt. The expiration reflex mechanically induced from the glottis (ERg was also analyzed (99.5% incidence, p In an additional 8 cats, the effect of codeine administered via the vertebral artery was tested. Codeine, in a dose (0.03 mg/kg that markedly suppressed cough did not significantly alter either the incidence rate or magnitudes of ERt. In the anesthetized cat the ERt induced by mechanical stimulation of the trachea was similar to the ERg from the glottis. These two reflex responses differ substantially only in the frequency of occurrence in response to mechanical stimulus and in the intensity of motor output.

Stransky Albert

2008-04-01

431

Representation of contractively complemented Hilbertian operator spaces and the Fock space  

CERN Document Server

The operator spaces $H_n^k$ $1\\le k\\le n$, generalizing the row and column Hilbert spaces, and arising in the authors' previous study of contractively complemented subspaces of $C^*$-algebras, are shown to be homogeneous and completely isometric to a space of creation operators on a subspace of the anti-symmetric Fock space. The completely bounded Banach-Mazur distance from $H_n^k$ to row or column space is explicitly calculated.

Neal, M; Neal, Matthew; Russo, Bernard

2004-01-01

432

Characterization of atomic decompositions, Banach frames, Xd-frames, duals and synthesis-pseudo-duals, with application to Hilbert frame theory  

CERN Document Server

In this paper we give a characterization of atomic decompositions, Banach frames, $X_d$-Riesz bases, $X_d$-frames, $X_d$-Bessel sequences, sequences satisfying the lower $X_d$-frame condition, duals of $X_d$-frames and synthesis pseudo-duals, based on an operator acting on the canonical basis of a sequence space. We discuss expansions in $X$ and $X^*$. Further, we consider necessary and sufficient conditions on operators to preserve the sequence type of the listed concepts. As a consequence, we solve some problems in Hilbert frame theory.

Stoeva, Diana T

2011-01-01

433

Tsirelson's space  

CERN Document Server

This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases, while topics of a more advanced nature are presented for the specialist. Bounded linear operators are studied through the use of finite-dimensional decompositions, and complemented subspaces are studied at length. A myriad of variant constructions are presented and explored, while open questions are broached in almost every chapter. Two appendices are attached: one dealing with a computer program which computes norms of finitely-supported vectors, while the other surveys recent work on weak Hilbert spaces (where a Tsirelson-type space provides an example).

Casazza, Peter G

1989-01-01

434

The exercise pressor reflex and peripheral artery disease.  

Science.gov (United States)

The exercise pressor reflex contributes to increases in cardiovascular and ventilatory function during exercise. These reflexive increases are caused by both mechanical stimulation and metabolic stimulation of group III and IV afferents with endings in contracting skeletal muscle. Patients with peripheral artery disease (PAD) have an augmented exercise pressor reflex. Recently, an animal model of PAD was established which allows further investigation of possible mechanisms involved in this augmented reflex. Earlier studies have identified ASIC3 channels, bradykinin receptors, P2X receptors, endoperoxide receptors, and thromboxane receptors as playing a role in evoking the exercise pressor reflex in healthy rats. This review focuses on recent studies using a rat model of PAD in order to determine possible mechanisms contributing to the exaggerated exercise pressor reflex seen in patients with this disease. PMID:25458431

Stone, Audrey J; Kaufman, Marc P

2014-10-22

435

Assessment of Hyperactive Reflexes in Patients with Spinal Cord Injury  

Science.gov (United States)

Hyperactive reflexes are commonly observed in patients with spinal cord injury (SCI) but there is a lack of convenient and quantitative characterizations. Patellar tendon reflexes were examined in nine SCI patients and ten healthy control subjects by tapping the tendon using a hand-held instrumented hammer at various knee flexion angles, and the tapping force, quadriceps EMG, and knee extension torque were measured to characterize patellar tendon reflexes quantitatively in terms of the tendon reflex gain (Gtr), contraction rate (Rc), and reflex loop time delay (td). It was found that there are significant increases in Gtr and Rc and decrease in td in patients with spinal cord injury as compared to the controls (P < 0.05). This study presented a convenient and quantitative method to evaluate reflex excitability and muscle contraction dynamics. With proper simplifications, it can potentially be used for quantitative diagnosis and outcome evaluations of hyperreflexia in clinical settings. PMID:25654084

Yang, Chung-Yong

2015-01-01

436

Admissibility for $\\alpha$-Modulation Spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This paper is concerned with frame decompositions of $\\alpha$-modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory yields canonical constructions for Banach frames or atomic decompositions in $\\alpha$-modulation spaces. A necessary ingredient in this abstract machinery is the existence of generating functions that are admissible for the representation....

Balazs, Peter; Bayer, Dominik; Speckbacher, Michael

2014-01-01

437

Formation of H- beams in reflex systems  

International Nuclear Information System (INIS)

The formation of H- beams in reflex systems has been studied. The use of charge-exchange method and suppression of the background from protons accelerated from the anode made it possible to determine the concentration of H- ions in the plasma near the cathode at the level of 0.5--2%. The H- current density lies in the range 0.25 +- 0.15 A/cm2. A significant improvement in measurement accuracy can be achieved by using a deuterated coating on the cathode and by switching to a high accelerator current density

438

Completeness of regular inductive limits  

Directory of Open Access Journals (Sweden)

Full Text Available Regular LB-space is fast complete but may not be quasi-complete. Regular inductive limit of a sequence of fast complete, resp. weakly quasi-complete, resp. reflexive Banach, spaces is fast complete, resp. weakly quasi-complete, resp. reflexive complete, space.

Kelly McKennon

1989-09-01

439

Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: , , which were introduced and investigated by Baak (2006. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978.

Park Choonkil

2007-01-01

440

Inductive limits of vector-valued sequence spaces.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind En be a separated inductive limit of locally convex spaces. Then ind L(En) is a topological subspace of L(E).

Bonet, Jose?

1989-01-01

 
 
 
 
441

Approaches to Reflexivity: Navigating Educational and Career Pathways  

Science.gov (United States)

This paper provides a critical appraisal of approaches to reflexivity in sociology. It uses data from social network research to argue that Archer's approach to reflexivity provides a valuable lens with which to understand how people navigate their education and career pathways. The paper is also critical of Archer's methodology and typology of

Dyke, Martin; Johnston, Brenda; Fuller, Alison

2012-01-01

442

Reflexivity and adjustment strategies at the interfaces  

Directory of Open Access Journals (Sweden)

Full Text Available I argue in this work that Reinhart & Reulands (1993 conditions A and B hold for Spanish. I provide evidence supporting the hypothesis that this language makes use of both SE and SELF-anaphors. Inherent reflexive verbs undergo an internal argument reduction operation in the lexicon. However, the syntax always requires two arguments. Therefore certain clitics, which are SE-anaphors, are inserted in these derivations. This is a last-resort mechanism that makes an adjustment between the valence of the lexical entry of the verb and the requirements of the syntax in order for the derivation to converge at the C-I interface. These clitics are syntactic arguments. Nevertheless, they are not interpreted as semantic arguments since they violate the double chain condition, which forces nominal elements to share both a tense and thematic features with the verb and the tense heads. Non- inherent reflexive verbs require the presence of a SELF-anaphor, which is formed out of a SE-anaphor along with a protector SELF element. Therefore, both syntactic elements are interpreted as two distinguishable semantic elements at C-I despite the fact that there is binding between them both. The interpretation of both syntactic elements as just one semantic element is a pragmatic epiphenomenon.

Ismael Teomiro

2011-10-01

443

Reflex switch experiments with capacitor bank drivers  

International Nuclear Information System (INIS)

Pulsed power systems based on power amplifications of magnetic energy stored in vacuum offer significant advantages in power scaling, compactness and cost over conventional technology. The key component of such a system is the vacuum switch, which is to stay closed for a long enough time to energize an inductor with current and then to open in a short enough time to produce a power-amplified output pulse near the final vacuum load. The reflex switch is a simple system that meets these requirements. It consists of a primary cathode, a thin anode, and an electrically floating secondary electrode that acts first as a cathode and then as the anode. The closed mode of the switch is characterized by the presence of a population of reflexing electrons (passing many times through the thin anode, depositing a fraction of their initial energy on each pass) and counterstreaming ions. The current can be orders of magnitude greater than the Langmuir bipolar current for the same geometry and voltage. Previous experiments employed high voltage, short pulse drivers. The authors report their bank drivers. They measured scaling laws and an empirical figure-of-merit that allows them to design experiments for desired results

444

Stochastic processes on non-Archimedean spaces. I. Stochastic processes on Banach spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. Thery are used for the development of stochastic antiderivations. The non-Archimedean analog of the It$\\hat o$ formula is proved.

Ludkovsky, S. V.

2001-01-01

445

Hypercyclic operators on countably dimensional spaces  

Digital Repository Infrastructure Vision for European Research (DRIVER)

According to Grivaux, the group $GL(X)$ of invertible linear operators on a separable infinite dimensional Banach space $X$ acts transitively on the set $\\Sigma(X)$ of countable dense linearly independent subsets of $X$. As a consequence, each $A\\in \\Sigma(X)$ is an orbit of a hypercyclic operator on $X$. Furthermore, every countably dimensional normed space supports a hypercyclic operator. We show that for a separable infinite dimensional Fr\\'echet space $X$, $GL(X)$ a...

Schenke, Andre; Shkarin, Stanislav

2012-01-01

446

Arens Regularity of Tensor Products and Weak Amenability of Banach Algebras  

CERN Document Server

In this note, we study the Arens regularity of projective tensor product $A\\hat{\\otimes}B$ whenever $A$ and $B$ are Arens regular. We establish some new conditions for showing that the Banach algebras $A$ and $B$ are Arens regular if and only if $A\\hat{\\otimes}B$ is Arens regular. We also introduce some new concepts as left-weak$^*$-weak convergence property [$Lw^*wc-$property] and right-weak$^*$-weak convergence property [$Rw^*wc-$property] and for Banach algebra $A$, suppose that $A^*$ and $A^{**}$, respectively, have $Rw^*wc-$property and $Lw^*wc-$property. Then if $A^{**}$ is weakly amenable, it follows that $A$ is weakly amenable. We also offer some results concerning the relation between these properties with some special derivation $D:A\\rightarrow A^*$. We obtain some conclusions in the Arens regularity of Banach algebras.

Azar, Kazem Haghnejad

2010-01-01

447

Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Let V be an arbitrary system of weights on an open connected subset G of ℂN(N≥1) and let B(E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb(G,E) and HV0(G,E) be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical spaces of analytic functions H(G) to the weighted spaces of analytic functions...

Manhas, J. S.

2007-01-01

448

Composition Operators and Multiplication Operators on Weighted Spaces of Analytic Functions  

Directory of Open Access Journals (Sweden)

Full Text Available Let V be an arbitrary system of weights on an open connected subset G of ℂN(N≥1 and let B(E be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb(G,E and HV0(G,E be the weighted locally convex spaces of vector-valued analytic functions. In this survey, we present a development of the theory of multiplication operators and composition operators from classical spaces of analytic functions H(G to the weighted spaces of analytic functions HVb(G,E and HV0(G,E.

J. S. Manhas

2007-01-01

449

Approximately Lie ternary $(\\sigma,\\tau,\\xi)-$derivations on Banach ternary algebras  

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Let $A$ be a Banach ternary algebra over a scalar field $\\Bbb R$ or $\\Bbb C$ and $X$ be a ternary Banach $A-$module. Let $\\sigma,\\tau$ and $\\xi$ be linear mappings on $A$, a linear mapping $D:(A,[]_A)\\to (X,[]_X)$ is called a Lie ternary $(\\sigma,\\tau,\\xi)-$derivation, if $$D([abc]_A)=[[D(a)bc]_X]_{(\\sigma,\\tau,\\xi)}+[[D(b)ac]_X]_{(\\sigma,\\tau,\\xi)}+[[D(c)ba]_X]_{(\\sigma,\\tau,\\xi)},$$ for all $a,b,c\\in A$, where $[abc]_{(\\sigma,\\tau,\\xi)}=a\\tau(b)\\xi(c)-\\sigma(c)\\tau(b)a.$ I...

Gordji, M. Eshaghi; Farrokhzad, R.; Hosseinioun, S. A. R.

2009-01-01

450

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras  

Science.gov (United States)

It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

Byrnes, C. I.

1980-01-01

451

Effects of Bed Rest on Conduction Velocity of the Triceps Surae Stretch Reflex and Postural Control  

Science.gov (United States)

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 rest period, with a return to baseline 3 to 5 days after bed rest, depending on the duration of bed rest. In addition, a relationship between CV and loss of muscle strength in the lower leg was observed post bed rest for most subjects. Immediately post-bed rest, most subjects showed decreased performance on SOTs, with the greater decrements on sway-referenced support and head movement conditions. Post-bed rest decrements were less than typically observed following spaceflight. Decrements in postural control and the stretch reflex can be primarily attributed to the unloading mechanisms this ground-based analog provides. The stretch reflex is a concise test measurement that can be obtained during the head-down phase of bed rest, as it does not interfere with the bed rest paradigm. This makes it an ideal tool that can detect, early on, whether a countermeasure is successful in preserving muscle function.

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

452

The swallowing reflex and its significance as an airway defensive reflex  

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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 ...

TakashiNishino

2013-01-01

453

Conditioning the middle ear reflex at sensation levels below reflex threshold: air jet and electrical stimulation.  

Science.gov (United States)

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. PMID:7429033

McDaniel-Bacon, L; Fulton, R T; Laskowski, R P

1980-01-01

454

Study of the Reflex-Klystron  

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)

455

Is Palmomental Reflex Actually A Part of Feeding Behavior?  

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Full Text Available Purpose and hypothesis: Palmomental reflex is considered to be a primitive reflex and related to pathologic processes. The reflex can be obtained from every individual by electrophysiologic measures. There have been no reports concerning submental, orbicularis oris and masseter muscle reflex responses provoked by median nerve stimulation in healthy elderly individuals and patients with dementia up to now.Method: In the present study the median nerve was stimulated below the pain threshold and activities obtained from mental, submental, orbicularis oris and masseter muscles were recorded simultaneously in patients with dementia (n = 18 and in healthy elderly individuals (n = 18.Result: Latencies obtained from mental, submental, orbicularis oris and masseter muscles were approximately recorded within 80 100 milliseconds and the differences between the latencies were not statistically significant.Conclusion: The palmomental reflex seems to be an activity co-occurring with functions like mouth opening and swallowing, and reflecting hand mouth reaction, rather than being only a primitive reflex involving mental muscle. We believe close temporal relationship among the activities of mental, submental, orbicularis oris and masetter muscles after hand stimulation requires these reflexes to be investigated in the physiology of hand and mouth coordination in further studies.

Burcu UGUREL

2009-06-01

456

The oculocardiac reflex in aponeurotic blepharoptosis surgery.  

Science.gov (United States)

The purpose of this study was to investigate the correlation between the oculocardiac reflex (OCR) and blepharoptosis surgery for safe eyelid surgery. Fifty-four consecutive patients with bilateral aponeurotic blepharoptosis were enrolled in this study. Changes in electrocardiography (ECG) monitoring were recorded during surgery. Preoperative pressing on the globe and intraoperative stretching of the levator aponeurosis were also carried out and the occurrence rate of the OCR was recorded. A positive OCR was observed in 12 patients (22.2%) in the preoperative globe-pressing test, whereas a positive OCR was observed in 22 patients (40.7%) in the levator-stretching test. The levator-stretching test did not indicate a significant difference in the rate of heart rate decrease with respect to laterality. No correlation was observed between age and the occurrence of OCR. On the other hand, there was a significant difference in the percentage of heart rate decrease between patients with positive OCR and negative OCR as determined in the globe-pressing test (mean = 13.1% vs. 5.4%). During the practical operative manoeuvre, no bradycardia was observed in any case. This study confirmed that a rapid and strong traction of levator aponeurosis induces the OCR regardless of laterality and age. Atraumatic and gentle handling are essential to prevent OCR. The preoperative globe-pressing test may be an index of the OCR in reflex-prone patients. Intraoperative ECG monitoring will be useful for early onset detection, although positive OCR was not observed in any patient during the practical surgical manoeuvre. PMID:24828860

Uda, Hirokazu; Sugawara, Yasusih; Sarukawa, Syunji; Sunaga, Ataru

2014-06-01

457

Interindividual differences in H reflex modulation during normal walking  

DEFF Research Database (Denmark)

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 (group S) showed a suppressed H reflex during the swing phase, and 9 subjects (group LS) showed increasing reflex excitability during the swing phase. The plantar flexor dominated moment about the ankle joint was greater for group LS. In contrast, the extensor dominated moment about the knee joint was greater for the S group. The hip joint moment was similar for the groups. The EMG activity in the vastus lateralis and anterior tibial muscles was greater prior to heel strike for the S group. These data indicate that human walking exhibits at least two different motor patterns as evaluated by gating of afferent input to the spinal cord, by EMG activity and by walking mechanics. Increasing H reflex excitability during the swing phase appears to protect the subject against unexpected perturbations around heel strike by a facilitated stretch reflex in the triceps surae muscle. Alternatively, in subjects with a suppressed H reflex in the swing phase the knee joint extensors seem to form the primary protection around heel strike.

Simonsen, Erik B; Dyhre-Poulsen, Poul

2002-01-01

458

The functional and pragmatic features of assonance phraseological reflexes  

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Full Text Available This paper analyzes a specific group of phraseological reflexes based on an assonance rhyme with an initial interrogative utterance. Assonance phraseological reflexes cannot perform a descriptive or nominative function acting in the process of verbal interaction only as markers of pragmatic intentions. Therefore, the attempts to describe them in terms of traditional semantics prove unsuccessful. A proper study of assonance phraseological reflexes is possible only in the framework of speech act theory. From the cognitive perspective, these units of speech are an example of a language game typical of speech subcultures.

Shkapenko T.

2014-09-01

459

GENERALIZED ULAM-HYERS STABILITIES OF QUARTIC DERIVATIONS ON BANACH ALGEBRAS  

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Let A , B be two rings. A mapping ? : A ? B is called quartic derivation, if ? is a quartic function satisfies ?(ab) = a4?(b) + ?(a)b4 for all a, b ? A. The main purpose of this paper to prove the generalized Hyers-Ulam-Rassias stability of the quartic derivations on Banach algebras.

Eshaghi Gordji, M.; Ghobadipour, N.

2010-01-01

460

GENERALIZED ULAM-HYERS STABILITIES OF QUARTIC DERIVATIONS ON BANACH ALGEBRAS  

Directory of Open Access Journals (Sweden)

Full Text Available Let A , B be two rings. A mapping ? : A ? B is called quartic derivation, if ? is a quartic function satisfies ?(ab = a4?(b + ?(ab4 for all a, b ? A. The main purpose of this paper to prove the generalized Hyers-Ulam-Rassias stability of the quartic derivations on Banach algebras.

M Eshaghi Gordji

2010-12-01

 
 
 
 
461

On solvability of some quadratic functional-integral equation in Banach algebra  

International Nuclear Information System (INIS)

Using the technique of a suitable measure of non-compactness in Banach algebra, we prove an existence theorem for some functional-integral equations which contain, as particular cases, a lot of integral and functional-integral equations that arise in many branches of nonlinear analysis and its applications. Also, the famous Chandrasekhar's integral equation is considered as a special case. (author)

462

Uniform Asymptotic Stability and Robust Stability for Positive Linear Volterra Difference Equations in Banach Lattices  

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Full Text Available For positive linear Volterra difference equations in Banach lattices, the uniform asymptotic stability of the zero solution is studied in connection with the summability of the fundamental solution and the invertibility of the characteristic operator associated with the equations. Moreover, the robust stability is discussed and some stability radii are given explicitly.

Nagabuchi Yutaka

2008-01-01

463

Structure d'algbre de Banach sur l'espace poids L_?^p(G)  

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Let G be a locally compact group and ? be a weight on G. For p ? ]1, +? [, we give a necessary and sufficient condition, on ?, for L_?^p (G) to be a Banach algebra. The case where ? is biinvariant under a subgroup K of G is also considered.

Abdellah El Kinani; Roukbi, A.; Benazzouz, A.

2009-01-01

464

Structure d'algbre de Banach sur l'espace poids L_?^p(G  

Directory of Open Access Journals (Sweden)

Full Text Available Let G be a locally compact group and ? be a weight on G. For p ? ]1, +? [, we give a necessary and sufficient condition, on ?, for L_?^p (G to be a Banach algebra. The case where ? is biinvariant under a subgroup K of G is also considered.

Abdellah El Kinani

2009-05-01

465

Bessel and Grss Type Inequalities in Inner Product Modules over Banach -Algebras  

Directory of Open Access Journals (Sweden)

Full Text Available We give an analogue of the Bessel inequality and we state a simple formulation of the Grss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.

Dragomir SS

2011-01-01

466

On the gastrocecal inhibitory reflex in the rat.  

Directory of Open Access Journals (Sweden)

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.

Lee,Zai-Liu

1981-11-01

467

Sustainable Development: Representing a Reflexive Modernity Inside the United Nations  

Directory of Open Access Journals (Sweden)

Full Text Available This paper suggests that the discourse of sustainable development (SD within the United Nations (UN represents a paradigm shift from first/industrial modernity to a reflexive modernity. Reflexive modernity is defined by the changing nature of political structures in the face of globalised environmental risk, as well as a questioning of the hegemony of the scientific process as a basis for the development of humanity and the planet. SD is a concept that innately reflects these concerns, questioning normative assumptions. This paper will argue that the rise of SD in governance discourse is not only a catalyst for a reflexive modernity, but also is representative of a modernity that is already in a state of reflexivity. This proposition is examined by exploring the various ways that SD is utilised in the governance structure of the United Nations (UN.

Dr. Gregory Borne

2010-01-01

468

Speech Performance, Dysphagia and Oral Reflexes in Cerebral Palsy.  

Science.gov (United States)

The adequacy of biting, sucking, swallowing, and chewing as well as the presence or absence of nine infantile oral reflexes were assessed in 60 cerebral palsied individuals (ages 3 to 23). (Author/PHR)

Love, Russell J.; And Others

1980-01-01

469

REFLEX MODIFICATION AND THE ASSESSMENT OF SENSORY DYSFUNCTION  

Science.gov (United States)

In summary, reflex modification of the startle response is a technique that can provide rapid, objective, and quantitative assessments of sensorimotor function. dvantages of this technique involve the ability to test animals rapidly, test without prior training, test without util...

470

Soleus H-reflex excitability during pedaling post-stroke  

DEFF Research Database (Denmark)

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 which abnormal muscle phasing is evident. Our hypothesis predicted that H-reflexes would be elevated during the flexion phase of pedaling where inappropriate SO activity occurs. H-reflexes were elicited in paretic (n = 13) and neurologically intact (NI, n = 26) individuals at 11 different positions 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 the pedaling cycle. H-reflexes were large during extension and small during flexion. Reduced H-reflex modulation post-stroke was associated with the level of neuromuscular impairment as indicated by Fugl-Meyer score. However, regardless of impairment level, stroke subjects displayed H-reflex suppression during the flexion phase of pedaling. After correcting for the level of background muscle activity, H-reflexes were found to be larger in paretic as compared to NI individuals, regardless of the phase of the pedaling cycle. We conclude that Group Ia afferent transmission is enhanced in the paretic SO of people post-stroke as compared to NI individuals. However, contrary to our hypothesis, enhanced transmission in the Group Ia monosynaptic spinal pathway is not specifically associated with extraneous extensor muscle activity during the flexion phase of pedaling and is unlikely to account for abnormal locomotor muscle phasing post-stroke. This result is important because it suggests that, despite the presence of hyperactive monosynaptic reflexes post-stroke, this impairment may not make an important contribution to abnormal locomotor muscle activity.

Schindler-Ivens, Sheila; Brown, David A.

2008-01-01

471

Neuroanatomical basis of Sandifer's syndrome: a new vagal reflex?  

Science.gov (United States)

Sandifer's syndrome is a gastrointestinal disorder with neurological features. It is characterized by reflex torticollis following deglutition in patients with gastroesophageal reflux and/or hiatal hernia. The authors believe that neurological manifestations of the syndrome are the consequence of vagal reflex with the reflex center in nucleus tractus solitarii (NTS). Three models for the neuroanatomical basis of the hypothetic reflex arc are presented. In the first one the hypothetic reflex arc is based on the classic hypothesis of two components nervus accessorius (n.XI) - radix cranialis (RC) and radix spinalis (RS) The nervous impulses are transmitted by nervus vagus (n.X) general visceral afferent (GVA) fibers to NTS situated in medulla oblongata, then by interneuronal connections on nucleus ambiguus (NA) and nucleus dorsalis nervi vagi (NDX). Special visceral efferent fibers (SVE) impulses from NA are in part transferred to n.XI ramus externus (RE) (carrying the majority of general somatic efferent (GSE) fibers) via hypothetic anastomoses in the region of foramen jugulare. This leads to contraction of trapezius and sternocleidomastoideus muscles, and the occurrence of intermittent torticollis. In the second suggested neuroanatomical model the hypothetic reflex arc is organized in the absence of n.XI RC, the efferent part of the reflex arc continues as NA, which is motor nucleus of nervus glossopharyngeus (n.IX) and n.X in this case while distal roots of n.XI that appear at the level of the olivary nucleus lower edge represent n.X roots. In the third presented model the hypothetic reflex arc includes no jugular transfer and could be realized via interneuronal connections directly from NTS to the spinal motoneurons within nucleus radicis spinalis nervi accessorii (NRS n.XI) or from NA to NRS n.XI. The afferent segment of the postulated reflex arc in all three models is mediated via n.X. We conclude that Sandifer's syndrome is a clinical manifestation of another vagal reflex that could be termed a "vagocervical" or "esophagocervical" reflex, based on the neuroanatomical hypotheses elaborated in this paper. PMID:18031943

Cerimagic, Denis; Ivkic, Goran; Bilic, Ervina

2008-01-01

472

Using Standing Postures as a Practical Alternative to Gait Analysis for Assessing Normal Neuromotor Activity Variation of the Ankle Muscle Antagonists: A Soleus H-Reflex and EMG Activity Study Uso de Posturas Erguidas como Alternativa al Anlisis de Marcha para Evaluar la Variacin en la Actividad Neuromotora de los Msculos Antagonistas del Tobillo: Un Estudio Utilizando el Reflejo H del Msculo Sleo y EMG  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Soleus and tibialis anterior muscle EMG and soleus H-reflex are widely used to study ankle motor control during gait. Normally, the soleus H-reflex amplitude and EMG activity varies greatly through the course of walking. The examining of these events during walking requires space and resources that are generally found only in research oriented facilities, making difficult a more practical use. Earlier reports have suggested that normal variation of the soleus H-reflex and EMG could be determi...

Pineda, E. E.; Sabbahi, M. A.; Etnyre, B. R.

2010-01-01

473

Variable Patterned Pudendal Nerve Stimuli Improves Reflex Bladder Activation  

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We evaluated variable patterns of pudendal nerve (PN) stimuli for reflex bladder excitation. Reflex activation of the bladder has been demonstrated previously with 2033 Hz continuous stimulation of PN afferents. Neuronal circuits accessed by afferent mediated pathways may respond better to physiological patterned stimuli than continuous stimulation. Unilateral PN nerve cuffs were placed in neurologically intact male cats. PN stimulation (0.5100 Hz) was performed under isovolumetric cond...

Bruns, Tim M.; Bhadra, Narendra; Gustafson, Kenneth J.

2008-01-01

474

Functional principal component analysis of H-reflex recruitment curves  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The primary purpose of this study was to use Functional Principal Component Analysis (FPCA) to analyze Hoffman-reflex (H-Reflex) recruitment curves. Smoothed and interpolated recruitment curves from 38 participants were used for analysis. Standard methods were used to calculate three discrete variables (i.e, Hmax/Mmax ratio, Hth, Hslp). FPCA was then used to extract principal component functions (PCFs) from the processed recruitment curves. PCF scores were calculated to determine how much ...

Kipp, Kristof; Johnson, Samuel T.; Hoffman, Mark A.

2011-01-01

475

Pain-related somatosensory evoked potentials in cortical reflex myoclonus.  

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To elucidate the sensitivity to pain stimuli in patients with cortical reflex myoclonus, pain-related somatosensory evoked potentials (pain SEPs) following CO2 laser stimulation and conventional electrically-stimulated SEPs (electric SEPs) were compared in four patients with cortical reflex myoclonus. The P25 peak of electric SEPs was considerably enhanced but the P320 potential of pain SEPs was of normal amplitude in all patients. After medication, myoclonus was reduced and the amplitude of ...

Kakigi, R.; Shibasaki, H.; Neshige, R.; Ikeda, A.; Mamiya, K.; Kuroda, Y.

1990-01-01

476

The Codex and the Computer as Self-Reflexive Machines  

Digital Repository Infrastructure Vision for European Research (DRIVER)

This lecture looks at self-reflexive mechanisms in codices and computers. It contains a brief introduction to the use of books and computers as expressive media in literature. I want to explore the hypothesis that self-reflexivity in artists books and in digital poems is useful for understanding the literary dynamics of writing and reading. Self-referential enactments of reading will be shown in works by Johanna Drucker and Jason Nelson. In the selected works, bookness and digi...

Portela, Manuel Jose? Freitas

2010-01-01

477

Open subgroups, compact subgroups amd Binz-Butzmannn reflexivity  

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A number of attempts to extend Pontryagin duality theory to categories of groups larger than that of locally compact abelian groups have been made using different approaches. The extension to the category of topological abelian groups created the concept of reflexive group. In this paper we deal with the extension of Pontryagin duality to the category of convergence abelian groups. Reflexivity in this category was defined and studied by E. Binz and H. Butzmann. A convergence group is reflexiv...

Marti?n Peinador, Elena; Bruguera Padro?, M. Montserrat

1996-01-01

478

Language trends: Reflexivity in commercial language policies and practices  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Financier, philanthropist and economist George Soros is not the first to have used or derived the notion of reflexivity (for example, Anthony Giddens, Ulrich Beck and others have found it useful in their work).What is different about the approach of Soros is that he has used the concept of reflexivity to explain the workings of global markets, and for this reason his work seems to me to have particular potential for explaining language trends in the linguistic policies and p...

Kelly-holmes, Helen

2010-01-01

479

Impaired control of the oculomotor reflexes in Parkinson's disease  

Digital Repository Infrastructure Vision for European Research (DRIVER)

To investigate the role of the basal ganglia in integrating voluntary and reflexive behaviour, the current study examined the ability of patients with Parkinson's disease to voluntarily control oculomotor reflexes. We measured the size of the fixation offset effect (the reduction in saccadic reaction time when a fixation point is removed) during a block of pro- and a block of anti-saccades. Healthy controls showed the expected reduction of the FOE during the anti-saccades, which results from ...

Koningsbruggen, Martijn G.; Pender, Tom; Machado, Liana; Rafal, Robert D.

2009-01-01

480

The photomyoclonic reflex: an artefact in the clinical electroretinogram.  

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An artefact may appear in the clinical electroretinogram (ERG) that can interfere with the recording and interpretation of the ERG b wave. This artefact, the photomyoclonic reflex (PMR), was studied by covering the eye containing the recording electrode and stimulating the fellow eye. Records obtained by this technique before and after administration of a modified Van Lint lid block demonstrated that most of the PMR is due to a reflex contraction of the orbicularis muscle. The remaining part ...

Johnson, M. A.; Massof, R. W.

1982-01-01

 
 
 
 
481

Creating safety by strengthening clinicians' capacity for reflexivity  

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This commentary explores the nature of creating safety in the here-and-now. Creating safety encompasses two dimensions: revisiting specific behaviours by focusing on substandard performance (reflection), and a more broad-ranging attention to everyday behaviours that are taken as given (reflexivity). The piece pays particular attention to this second dimension of creating safety. Two techniques that promote reflexivity are discussed: video-filming real-time, everyday clinical practice and invi...

Iedema, Rick

2011-01-01

482

Head Stabilization by Vestibulocollic Reflexes During Quadrupedal Locomotion in Monkey  

Digital Repository Infrastructure Vision for European Research (DRIVER)

Little is known about the three-dimensional characteristics of vestibulocollic reflexes during natural locomotion. Here we determined how well head stability is maintained by the angular and linear vestibulocollic reflexes (aVCR, lVCR) during quadrupedal locomotion in rhesus and cynomolgus monkeys. Animals walked on a treadmill at velocities of 0.41.25 m/s. Head rotations were represented by Euler angles (Fick convention). The head oscillated in yaw and roll at stride frequencies (?12...

Xiang, Yongqing; Yakushin, Sergei B.; Kunin, Mikhail; Raphan, Theodore; Cohen, Bernard

2008-01-01

483

Cortical control of hering-breuer reflexes in anesthetized rats  

Directory of Open Access Journals (Sweden)

Full Text Available 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 estimated from changes in inspiratory time provoked by airway occlusion at the end of expiration. The results indicate that electrical microstimulation of the responsive sites within the insular cortex significantly weakened both expiratory-promoting and inspiratory-inhibitory reflex. Activation of the infralimbic cortex depressed expiratory-promoting reflex, but inspiratory-inhibitory reflex was enhanced. These results suggest that stimulation of the prefrontal cortex influences vagally mediated control of the respiratory phases timing and several regions of the prefrontal cortex modulate distinct sets of neurons in the network controlling inspiratory and expiratory phases of a breath cycle.

Aleksandrov VG

2009-12-01

484

HPLC analysis of closed, open, and reflex eye tear proteins  

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Full Text Available Changes in the closed, open and reflex eye tear proteins of normal subjects were compared and analysed. Tear proteins were resolved by high-performance liquid chromatography (HPLC utilising both gel filtration (P-300 SW and reverse-phase (C-18 columns and the HPLC fractions were further analysed by sodium dodecyl sulphate - polyacrylamide gel electrophoresis (SDS-PAGE under reducing and non-reducing conditions. The protein composition of the closed-eye tear was significantly different from that of the open and reflex-eye tear. Secretory IgA (sIgA was the predominant protein in closed eye tears constituting 49% of the total protein compared to 11% in reflex tears, whereas lysozyme was the predominant protein (53% in reflex tears. Levels of lactoferrin, lipocalin and lysozyme were relatively constant in both open and reflex tears. HPLC profiles of the closed-eye tears, upon continuous stimulation of lacrimal glands indicated that sIgA was significantly reduced whereas lactoferrin, lipocalin, and lysozyme were significantly increased. These results indicate that the tear composition upon waking attains that of the open eye within 4 to 5 minutes, and upon continuous stimulation this reflects the reflex-eye tear composition. It also indicates that mechanisms responsible for changes in concentration of constitutive and regulated tear protein with stimulus can be studied successfully using non-invasive methods to collect human tears.

Sitaramamma T

1998-01-01

485

Lombard reflex during PAG-induced vocalization in decerebrate cats.  

Science.gov (United States)

The Lombard reflex occurs when a speaker increases his vocal effort while speaking in the presence of ambient noise. The purpose of this study was to clarify whether the Lombard reflex can be evoked during controlled vocalization in an animal model. In decerebrate cats, repetitive electrical stimulation was applied to the midbrain periaqueductal gray (PAG) to evoke vocalization. Pure tone auditory stimulation was delivered through a loudspeaker. The activities of the laryngeal adductor muscle, diaphragm and external oblique abdominal muscle and the voice intensity were measured during PAG stimulation, in the presence and absence of the auditory stimulation. To clarify the effects of the auditory laryngeal reflex on the activity of laryngeal adductor motoneurons, the amplitude of the laryngeal reflex evoked by single shock stimulation of the superior laryngeal nerve was also measured during respiration, in the presence and absence of auditory stimulation. The sound made by the cats due to PAG-induced vocalization was augmented by exposure to auditory stimulation, and the activities of the laryngeal adductor muscle and external oblique abdominal muscle were also augmented. During respiration, auditory stimulation also increased the amplitude of the laryngeal reflex evoked in the laryngeal adductor muscle. These results demonstrate that the essential neuronal mechanisms for evoking the Lombard reflex exist within the brainstem. PMID:9527619

Nonaka, S; Takahashi, R; Enomoto, K; Katada, A; Unno, T

1997-12-01

486

HPV Reflex Testing in Menopausal Women  

Science.gov (United States)

Objective. To determine the frequency of high risk (HR) HPV and intraepithelial neoplasia following ASCUS pap cytology screens in menopausal women. Study Design. Following IRB approval, we performed a retrospective review of all cases of ASCUS pap tests, HPV results, and relevant clinical-pathologic data in women age 50 or over from November 2005 to January 2007 within a tertiary care center. Statistical analyses were performed in EXCEL. Results. 344 patients were analyzed for a total of 367 screening pap tests. 25.29% (87/344) patients were HR HPV positive, with greater percentages of HR HPV cases occurring in women age 6574. Within HR HPV cases, 79.3% (69/87) underwent colposcopy. 27.5% (19/69) biopsy proven lesions were discovered, including cervical, vulvar or vaginal (intraepithelial neoplasia). Within the negative HR HPV group 3.1% (8/257) patients were diagnosed with dysplasia or carcinoma. Within both HR HPV positive and negative groups, patients with no prior history of lower genital tract lesions or cancer were identified. Conclusion. Reflex HPV testing plays an important role in ASCUS triage in menopausal women. Pap test screening and HPV testing should not be limited to women of reproductive age as they may aid in the diagnosis of intraepithelial neoplasia in women of older age. PMID:21559191

Ko, Emily M.; Tambouret, Rosemary; Wilbur, David; Goodman, Annekathryn

2011-01-01

487

Impaired Sacculocollic Reflex in Lateral Medullary Infarction  

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Full Text Available Objective: The aim of this study was to determine saccular dysfunction by measuring cervical vestibular-evoked myogenic potentials (cVEMP and to correlate abnormality of cVEMP with results of other vestibular function tests in lateral medullary infarction (LMI. Methods: We recorded cVEMP in 21 patients with LMI documented on MRI. cVEMP was induced by a short tone burst and was recorded in contracting sternocleidomastoid muscle while patients turned their heads forcefully to the contralateral side against resistance. Patients also underwent video-oculographic recording of spontaneous, gaze-evoked and head-shaking (HSN nystagmus, evaluation of ocular tilt reaction (OTR, measurement of the subjective visual vertical (SVV tilt, bithermal caloric tests and audiometry. Results: Nine patients (43% showed abnormal cVEMP, unilateral in seven and bilateral in two. The cVEMP abnormalities included decreased p13-n23 amplitude in four, delayed p13/n23 responses in five, and both decreased and delayed responses in two. The abnormal cVEMP was ipsilesional in five, contralesional in two, and bilateral in two. The prevalence of OTR/SVV tilt, spontaneous nystagmus, and HSN did not differ between the patients with normal and abnormal cVEMP. Conclusion: cVEMP was abnormal in approximately half of the patients with LMI. The abnormal cVEMP indicates damage to the descending sacculocollic reflex pathway or disruption of commissural modulation between the vestibular nuclei.

SeonhyeKim

2011-02-01

488

Vestibuloocular reflex of rhesus monkeys after spaceflight  

Science.gov (United States)

The vestibuloocular reflex (VOR) of two rhesus monkeys was recorded before and after 14 days of spaceflight. The gain (eye velocity/head velocity) of the horizontal VOR, tested 15 and 18 h after landing, was approximately equal to preflight values. The dominant time constant of the animal tested 15 h after landing was equivalent to that before flight. During nystagmus induced by off-vertical axis rotation (OVAR), the latency, rising time constant, steady-state eye velocity, and phase of modulation in eye velocity and eye position with respect to head position were similar in both monkeys before and after flight. There were changes in the amplitude of modulation of horizontal eye velocity during steady-state OVAR and in the ability to discharge stored activity rapidly by tilting during postrotatory nystagmus (tilt dumping) after flight: OVAR modulations were larger, and tilt dumping was lost in the one animal tested on the day of landing and for several days thereafter. If the gain and time constant of the horizontal VOR exchange in microgravity, they must revert to normal soon after landing. The changes that were observed suggest that adaptation to microgravity had caused alterations in way that the central nervous system processes otolith input.

Cohen, Bernard; Kozlovskaia, Inessa; Raphan, Theodore; Solomon, David; Helwig, Denice; Cohen, Nathaniel; Sirota, Mikhail; Iakushin, Sergei

1992-01-01

489

Stability of the Jensen--type functional equation in ternary Banach algebras: An alternative fixed point approach  

CERN Document Server

Using fixed point methods, we prove the generalized Hyers--Ulam--Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen--type functional equation

Gordji, M Eshaghi

2009-01-01

490

Soleus stretch reflex modulation during gait in humans.  

Science.gov (United States)

1. The modulation of the short-latency stretch reflex during walking at different walking speeds was investigated and compared with the stretch reflex during standing in healthy human subjects. 2. Ankle joint stretches were applied by a system able to rotate the human ankle joint during treadmill walking in any phase of the step cycle. The system consisted of a mechanical joint attached to the subject's ankle joint and connected to a motor placed beside the treadmill by means of bowden wires. The weight of the total system attached to the leg of the subject was 900 g. 3. The short-latency soleus stretch reflex was modulated during a step. In the stance phase, the amplitude equaled that found during standing at matched soleus background electromyogram (EMG). In the transition from stance to swing, the amplitude was 0 in all subjects. In late swing, the stretch reflex amplitude increased to 45 +/- 27% (mean +/- SD) of the maximal amplitude in the stance phase (stretch amplitude 8 degrees, stretch velocity 250 degrees/s). 4. The onset (42 +/- 3.2 ms) and peak latencies (59 +/- 2.5 ms) of the stretch reflex did not depend on the phase in the step cycle at which the reflex was elicited. 5. When the ankle joint is rotated, a change in torque can be measured. The torque measured over the first 35 ms after stretch onset (nonreflex torque) was at a maximum during late stance, when the leg supported a large part of the body's weight, and at a minimum during the swing phase. At heel contact the nonreflex torque was 50% of its maximal value. 6. During the stance phase the maximal EMG stretch reflex had a phase lead of approximately 120 ms with respect to the maximal background EMG and a phase lead of approximately 250 ms with respect to the maximal nonreflex torque. 7. The constant latency of the stretch reflex during a step implied that the ankle extensor muscle spindles are always taut during walking. 8. The relatively high amplitude of the stretch reflex in late swing and at heel contact made it likely that the stretch reflex contributed to the activation of the ankle extensor muscles in early stance phase. PMID:8871224

Sinkjaer, T; Andersen, J B; Larsen, B

1996-08-01

491

Space  

Science.gov (United States)

This unit begins by introducing students to the historical motivation for space exploration. They learn about the International Space Station, including current and futuristic ideas that engineers are designing to propel space research. Then they learn about the physical properties of the Moon, and think about what types of products engineers would need to design in order for humans to live on the Moon. Lastly, students learn some descriptive facts about asteroids, such as their sizes and how that relates to the potential danger of an asteroid colliding with the Earth.

Integrated Teaching And Learning Program

492

Nonlocal Controllability for the Semilinear Fuzzy Integrodifferential Equations in -Dimensional Fuzzy Vector Space  

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Full Text Available We study the existence and uniqueness of solutions and controllability for the semilinear fuzzy integrodifferential equations in -dimensional fuzzy vector space by using Banach fixed point theorem, that is, an extension of the result of J. H. Park et al. to -dimensional fuzzy vector space.

Park JinHan

2009-01-01

493

Regional cerebral perfusion in cardiovascular reflex syncope  

International Nuclear Information System (INIS)

Little is known about the regional cerebral perfusion in subjects with presyncope or syncope, and the impact that autonomic nervous dysfunction has on it. Seven subjects with cardiovascular vasodepressor reflex syncope were studied. A baseline test was performed with the patients standing in the 70 upright position, while the passive head-up tilt table test with and without isoprenaline infusion was employed for provocation. Regional cerebral perfusion was assessed by means of single-photon emission tomography with technetium-99m labelled V-oxo-1,2-N,N1-ethylenedylbis-l-cysteine diethylester (baseline, and during blood pressure decline in the provocation test) and the autonomic nervous function by means of spectral analysis of heart rate variability (baseline, and before blood pressure decline in the provocation test). Every subject showed an abrupt decline in blood pressure in the provocation test (five with presyncope and two with syncope). The systolic and diastolic blood pressures decreased significantly (P<0.001) between the baseline and the provocation study time points (radiopharmaceutical injection and lowest systolic blood pressure). Mean cerebral perfusion as average count densities decreased upon provocation as compared with baseline (19063 vs 30790 counts/voxel, respectively, P=0.013). Hypoperfusion was most pronounced in the frontal lobe. These results suggest that cerebral perfusion decreases markedly during presyncope or syncope with systy during presyncope or syncope with systemic blood pressure decline in subjects with cardiovascular vasodepressor syncope. Furthermore, the autonomic nervous function remains unchanged before the systemic blood pressure decline. (orig.). With 3 figs., 2 tabs

494

Regional cerebral perfusion in cardiovascular reflex syncope  

Energy Technology Data Exchange (ETDEWEB)

Little is known about the regional cerebral perfusion in subjects with presyncope or syncope, and the impact that autonomic nervous dysfunction has on it. Seven subjects with cardiovascular vasodepressor reflex syncope were studied. A baseline test was performed with the patients standing in the 70 upright position, while the passive head-up tilt table test with and without isoprenaline infusion was employed for provocation. Regional cerebral perfusion was assessed by means of single-photon emission tomography with technetium-99m labelled V-oxo-1,2-N,N{sub 1}-ethylenedylbis-l-cysteine diethylester (baseline, and during blood pressure decline in the provocation test) and the autonomic nervous function by means of spectral analysis of heart rate variability (baseline, and before blood pressure decline in the provocation test). Every subject showed an abrupt decline in blood pressure in the provocation test (five with presyncope and two with syncope). The systolic and diastolic blood pressures decreased significantly (P<0.001) between the baseline and the provocation study time points (radiopharmaceutical injection and lowest systolic blood pressure). Mean cerebral perfusion as average count densities decreased upon provocation as compared with baseline (190{+-}63 vs 307{+-}90 counts/voxel, respectively, P=0.013). Hypoperfusion was most pronounced in the frontal lobe. These results suggest that cerebral perfusion decreases markedly during presyncope or syncope with systemic blood pressure decline in subjects with cardiovascular vasodepressor syncope. Furthermore, the autonomic nervous function remains unchanged before the systemic blood pressure decline. (orig.). With 3 figs., 2 tabs.

Toeyry, J.P. [Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio (Finland); Kuikka, J.T. [Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio (Finland); Laensimies, E.A. [Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio (Finland)

1997-02-01

495

Measurement of the Achilles tendon reflex for the diagnosis of lumbosacral root compression syndromes.  

Digital Repository Infrastructure Vision for European Research (DRIVER)

The Hoffmann reflex and the Achilles tendon reflex were measured in a group of 194 subjects suspected of having a lumbosacral root compression syndrome. The Achilles tendon reflex was elicited manually with a metal hammer. There was a high correlation between the H-M interval and the Achilles tendon reflex-M interval. The usefulness of the Achilles tendon reflex was evaluated in a selected sub-group of 61 patients with proven L5 or S1 root compression. Neither the H-reflex nor the Achilles te...

Rico, R. E.; Jonkman, E. J.

1982-01-01

496

Spectral calculus and Lipschitz extension for barycentric metric spaces  

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The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT(0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is a...

Mendel, Manor; Naor, Assaf

2013-01-01

497

PLB-spaces of holomorphic functions with logarithmic growth conditions  

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Countable projective limits of countable inductive limits, called PLB-spaces, of weighted Banach spaces of continuous functions have recently been investigated by Agethen, Bierstedt and Bonet. In a previous article, the author extended their investigation to the case of holomorphic functions and characterized when spaces over the unit disc w.r.t. weights whose decay, roughly speaking, is neither faster nor slower than that of a polynomial are ultrabornological or barrelled. ...

Wegner, Sven-ake

2014-01-01

498

Reflex control of inflammation by sympathetic nerves, not the vagus.  

Science.gov (United States)

We investigated a neural reflex that controls the strength of inflammatory responses to immune challenge - the inflammatory reflex. In anaesthetized rats challenged with intravenous lipopolysaccharide (LPS, 60?gkg(-1)), we found strong increases in plasma levels of the key inflammatory mediator tumour necrosis factor ? (TNF?) 90min later. Those levels were unaffected by previous bilateral cervical vagotomy, but were enhanced approximately 5-fold if the greater splanchnic sympathetic nerves had been cut. Sham surgery had no effect, and plasma corticosterone levels were unaffected by nerve sections, so could not explain this result. Electrophysiological recordings demonstrated that efferent neural activity in the splanchnic nerve and its splenic branch was strongly increased by LPS treatment. Splenic nerve activity was dependent on inputs from the splanchnic nerves: vagotomy had no effect on the activity in either nerve. Together, these data demonstrate that immune challenge with this dose of LPS activates a neural reflex that is powerful enough to cause an 80% suppression of the acute systemic inflammatory response. The efferent arm of this reflex is in the splanchnic sympathetic nerves, not the vagi as previously proposed. As with other physiological responses to immune challenge, the afferent pathway is presumptively humoral: the present data show that vagal afferents play no measurable part. Because inflammation sits at the gateway to immune responses, this reflex could play an important role in immune function as well as inflammatory diseases. PMID:24421357

Martelli, D; Yao, S T; McKinley, M J; McAllen, R M

2014-04-01

499

Plasticity of the human otolith-ocular reflex  

Science.gov (United States)

The eye movement response to earth vertical axis rotation in the dark, a semicircular canal stimulus, can be altered by prior exposure to combined visual-vestibular stimuli. Such plasticity of the vestibulo-ocular reflex has not been described for earth horizontal axis rotation, a dynamic otolith stimulus. Twenty normal human subjects underwent one of two types of adaptation paradigms designed either to attenuate or enhance the gain of the semicircular canal-ocular reflex prior to undergoing otolith-ocular reflex testing with horizontal axis rotation. The adaptation paradigm paired a 0.2 Hz sinusoidal rotation about a vertical axis with a 0.2 Hz optokinetic stripe pattern that was deliberately mismatched in peak velocity. Pre- and post-adaptation horizontal axis rotations were at 60 degrees/s in the dark and produced a modulation in the slow component velocity of nystagmus having a frequency of 0.17 Hz due to putative stimulation of the otolith organs. Results showed that the magnitude of this modulation component response was altered in a manner similar to the alteration in semicircular canal-ocular responses. These results suggest that physiologic alteration of the vestibulo-ocular reflex using deliberately mismatched visual and semicircular canal stimuli induces changes in both canal-ocular and otolith-ocular responses. We postulate, therefore, that central nervous system pathways responsible for controlling the gains of canal-ocular and otolith-ocular reflexes are shared.

Wall, C. 3rd; Smith, T. R.; Furman, J. M.

1992-01-01

500

GENERALIZED ULAM-HYERS STABILITIES OF QUARTIC DERIVATIONS ON BANACH ALGEBRAS  

Scientific Electronic Library Online (English)

Full Text Available SciELO Chile | Language: English Abstract in english Let A , B be two rings. A mapping ? : A ? B is called quartic derivation, if ? is a quartic function satisfies ?(ab) = a4?(b) + ?(a)b4 for all a, b ? A. The main purpose of this paper to prove the generalized Hyers-Ulam-Rassias stability of the quartic derivations on Banach algebras. [...

M, Eshaghi Gordji; N, Ghobadipour.

2010-12-01