The cofinal property of the Reflexive Indecomposable Banach spaces
Argyros, Spiros A.; Raikoftsalis, Theocharis
2010-01-01
It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\\ell_p$ saturated space with $1
Reflexive Operator Algebras on Banach Spaces
Merlevède, Florence; Peligrad, Costel; Peligrad, Magda
2012-01-01
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a complete Boolean algebra of projections of finite uniform multiplicity and with the direct sum property, then it is reflexive, i.e. it contains every operator that leaves invariant every closed subspace in the invariant subspace lattice of the algebra. In particular, such algebras coincide with their...
First and Second Order Convex Sweeping Processes in Reflexive Smooth Banach Spaces
In this paper we establish new characterizations of the normal cone of closed convex sets in reflexive smooth Banach spaces and then we use those results to prove the existence of solutions for first order convex sweeping processes and their variants in reflexive smooth Banach spaces. The case of second order convex sweeping processes is also studied. (author)
Let E be a real reflexive Banach space with uniformly Gateaux differentiable norm. Let K be a nonempty closed convex subset of E. Suppose that every nonempty closed convex bounded subset of K has the fixed point property for nonexpansive mappings. Let T1, T2, ..., TN be a family of nonexpansive self-mappings of K, with F := intersectioni=1N Fix(Ti) ≠ 0, F = Fix(TNTN-1... T1) = Fix(T1TN ... T2) = ... Fix(TN-1TN-2... T1TN). Let { λn} be a sequence in (0, 1) satisfying the following conditions: C1 : lim λn 0; C2 : Σ λn = ∞ . For a fixed δ element of (0, 1), define Sn : K → K by Snx := (1 - δ )x + δTnx for all x element of K where Tn = Tn mod N. For arbitrary fixed u, x0 element of K, let B := { x element of K : TNTN-1... T1x γx+(1- γ)u, for some γ > 1} be bounded and let the sequence {xn} be defined iteratively by xn+1 λn+1u + (1 - λn+1 )Sn+1xn, for n ≥ 0. Assume that lim n→∞ vertical bar vertical bar Tnxn - Tn+1 xn vertical bar vertical bar = 0. Then, {xn} converges strongly to a common fixed point of the family T1, T2, ..., TN. Convergence theorem is also proved for non-self maps. (author)
Casazza, Peter G.; Lammers, Mark C.
1999-01-01
We show that the classification problem for genus $n$ Banach spaces can be reduced to the unconditionally primary case and that the critical case there is $n=2$. It is further shown that a genus $n$ Banach space is unconditionally primary if and only if it contains a complemented subspace of genus $(n-1)$. We begin the process of classifying the genus 2 spaces by showing they have a strong decomposition property.
Multipliers of Banach valued weighted function spaces
Serap Öztop
2000-10-01
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.
Separably injective Banach spaces
Avilés, Antonio; Castillo, Jesús M F; González, Manuel; Moreno, Yolanda
2016-01-01
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines o...
$\\alpha$-minimal Banach spaces
Rosendal, Christian
2011-01-01
A Banach space with a Schauder basis is said to be $\\alpha$-minimal for some countable ordinal $\\alpha$ if, for any two block subspaces, the Bourgain embeddability index of one into the other is at least $\\alpha$. We prove a dichotomy that characterises when a Banach space has an $\\alpha$-minimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characteristic subspaces.
Albiac, Fernando
2016-01-01
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous f...
Factorization of weakly compact operators between Banach spaces and Fréchet or (LB)-spaces
Bonet Solves, José Antonio; Wright, J. D. Maitland
2012-01-01
In this note we show that weakly compact operators from a Banach space X into a complete (LB)-space E need not factorize through a reflexive Banach space. If E is a Fréchet space, then weakly compact operators from a Banach space X into E factorize through a reflexive Banach space. The factorization of operators from a Fréchet or a complete (LB)-space into a Banach space mapping bounded sets into relatively weakly compact sets is also investigated.
A pythagorean approach in Banach spaces
Gao Ji
2006-01-01
Let be a Banach space and let be the unit sphere of . Parameters , , , and , where and are introduced and studied. The values of these parameters in the spaces and function spaces are estimated. Among the other results, we proved that a Banach space with , or is uniform nonsquare; and a Banach space with , or has uniform normal structure.
Extremely strict ideals in Banach spaces
T S S R K RAO
2016-08-01
Motivated by the notion of an ideal introduced by Godefroy {\\it et al.} ({\\it Studia Math.} {\\bf 104} (1993) 13–59), in this article, we introduce and study the notion of an extremely strict ideal. For a Poulsen simplex $K$, we show that the space of affine continuous functions on $K$ is an extremely strict ideal in the space of continuous functions on $K$. For injective tensor product spaces, we prove a cancelation theorem for extremely strict ideals. We also exhibit non-reflexive Banach spaces which are not strict ideals in their fourth dual.
Fusion Frames and -Frames in Banach Spaces
Amir Khosravi; Behrooz Khosravi
2011-05-01
Fusion frames and -frames in Hilbert spaces are generalizations of frames, and frames were extended to Banach spaces. In this article we introduce fusion frames, -frames, Banach -frames in Banach spaces and we show that they share many useful properties with their corresponding notions in Hilbert spaces. We also show that -frames, fusion frames and Banach -frames are stable under small perturbations and invertible operators.
Tokarev, Eugene
2002-01-01
In the article is introduced a new class of Banach spaces that are called sub B-convex. Namely, a Banach space X is said to be B -convex if it may be represented as a direct sum l_1+ W, where W is B-convex. It will be shown that any separable sub B-convex Banach space X may be almost isometrically embedded in a separable Banach space G(X) of the same cotype as X, which has a series of properties. Namely, G(X) is an approximate envelope, i.e. any separable Banach space which is finitely repres...
Characterizing R-duality in Banach spaces
Christensen, Ole; Xiao, Xiang Chun; Zhu, Yu Can
2013-01-01
R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces.......R-duals of certain sequences in Hilbert spaces were introduced by Casazza, Kutyniok and Lammers in 2004 and later generalized to Banach spaces by Xiao and Zhu. In this paper we provide some characterizations of R-dual sequences in Banach spaces....
Existence of zeros for operators taking their values in the dual of a Banach space
Ricceri Biagio
2004-01-01
Full Text Available Using continuous selections, we establish some existence results about the zeros of weakly continuous operators from a paracompact topological space into the dual of a reflexive real Banach space.
Isometries on Banach spaces function spaces
Fleming, Richard J
2002-01-01
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...
Regularization methods in Banach spaces
Schuster, Thomas; Hofmann, Bernd; Kazimierski, Kamil S
2012-01-01
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert spaces. However, for numerous problems the reasons for using a Hilbert space setting seem to be based rather on conventions than on an approprimate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, sparsity constraints using general Lp-norms or the B
Coefficient Quantization for Frames in Banach Spaces
Casazza, P. G.; Dilworth, S. J.; Odell, E.; Schlumprecht, Th.; Zsak, Andras
2007-01-01
Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.
Banach spaces of analytic functions
Hoffman, Kenneth
2007-01-01
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc.The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the f
Simultaneous approximation in scales of Banach spaces
The problem of verifying optimal approximation simultaneously in different norms in a Banach scale is reduced to verification of optimal approximation in the highest order norm. The basic tool used is the Banach space interpolation method developed by Lions and Peetre. Applications are given to several problems arising in the theory of finite element methods
Bloch spaces on bounded symmetric domains in complex Banach spaces
DENG; Fangwen
2006-01-01
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.
On Λ-Type Duality of Frames in Banach Spaces
Renu Chugh
2013-11-01
Full Text Available Frames are redundant system which are useful in the reconstruction of certain classes of spaces. The dual of a frame (Hilbert always exists and can be obtained in a natural way. Due to the presence of three Banach spaces in the definition of retro Banach frames (or Banach frames duality of frames in Banach spaces is not similar to frames for Hilbert spaces. In this paper we introduce the notion of Λ-type duality of retro Banach frames. This can be generalized to Banach frames in Banach spaces. Necessary and sufficient conditions for the existence of the dual of retro Banach frames are obtained. A special class of retro Banach frames which always admit a dual frame is discussed.
A Gaussian Average Property for Banach Spaces
Casazza, Peter G.; Nielsen, Niels Jorgen
1996-01-01
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.
On Banach spaces without the approximation property
Reinov, Oleg I.
2002-01-01
A. Szankowski's example is used to construct a Banach space similar to that of "An example of an asymptotically Hilbertian space which fails the approximation property", P.G. Casazza, C.L. Garc\\'{\\i}a, W.B. Johnson [math.FA/0006134 ()].
Boundary Controllability of Integrodifferential Systems in Banach Spaces
K Balachandran; E R Anandhi
2001-02-01
Sufficient conditions for boundary controllability of integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle. Examples are provided to illustrate the theory.
The Topological Degree in Ordered Banach Spaces
Adrian DUMA; Ileana DUMA
2008-01-01
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this frame-work, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
Wang, Min
2016-04-01
This paper aims to establish the Tikhonov regularization method for generalized mixed variational inequalities in Banach spaces. For this purpose, we firstly prove a very general existence result for generalized mixed variational inequalities, provided that the mapping involved has the so-called mixed variational inequality property and satisfies a rather weak coercivity condition. Finally, we establish the Tikhonov regularization method for generalized mixed variational inequalities. Our findings extended the results for the generalized variational inequality problem (for short, GVIP(F, K)) in R^n spaces (He in Abstr Appl Anal, 2012) to the generalized mixed variational inequality problem (for short, GMVIP(F,φ , K) ) in reflexive Banach spaces. On the other hand, we generalized the corresponding results for the generalized mixed variational inequality problem (for short, GMVIP(F,φ ,K) ) in R^n spaces (Fu and He in J Sichuan Norm Univ (Nat Sci) 37:12-17, 2014) to reflexive Banach spaces.
Noncompact Perturbation of Sweeping Process with Delay in Banach Spaces
A. G. Ibrahim; Aladsani, F.
2013-01-01
We have proven an existence theorem concerning the existence of solutions for a functional evolution inclusion governed by sweeping process with closed convex sets depending on time and state and with a noncompact nonconvex perturbation in Banach spaces. This work extends some recent existence theorems concerning sweeping processes from Hilbert spaces setting to Banach spaces setting. Moreover, it improves some recent existence results for sweeping processes in Banach spaces.
Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces
Ruo Feng RAO
2011-01-01
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map,the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings.The main results obtained in this paper improve and extend some recent results.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
Boundedness of biorthogonal systems in Banach spaces
Hájek, Petr Pavel; Montesinos, V.
2010-01-01
Roč. 177, č. 1 (2010), s. 145-154. ISSN 0021-2172 R&D Projects: GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : M-basis * Banach spaces Subject RIV: BA - General Mathematics Impact factor: 0.630, year: 2010 http://link.springer.com/article/10.1007%2Fs11856-010-0041-x
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
Betancor, Jorge J; Rodríguez-Mesa, Lourdes
2011-01-01
In this paper we consider the space $BMO_o(\\mathbb{R},X)$ of bounded mean oscillations and odd functions on $\\mathbb{R}$ taking values in a UMD Banach space $X$. The functions in $BMO_o(\\mathbb{R},X)$ are characterized by Carleson type conditions involving Bessel convolutions and $\\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\\mathbb{R},X)$ functions hold.
Malliavin calculus and decoupling inequalities in Banach spaces
Maas, Jan
2008-01-01
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two sided L^p-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Ito chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the ...
Introduction to Banach spaces and algebras
Allan, Graham
2010-01-01
Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complexanalysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration.The text be
Unbounded operators on Banach spaces over the quaternion field
Ludkovsky, S. V.
2004-01-01
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.
The heart of the Banach spaces
Wegner, Sven-Ake
2016-01-01
Let an exact category in the sense of Quillen be given. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their famous 1982 paper, Beilinson, Bernstein and Deligne consider in this situation a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out, that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by...
BANACH CONTRACTION PRINCIPLE ON CONE RECTANGULAR METRIC SPACES
Ismat Beg
2009-08-01
Full Text Available We introduce the notion of cone rectangular metric space and prove {sc Banach} contraction mapping principle in cone rectangular metric space setting. Our result extends recent known results.
On Shrinking and Boundedly Complete Schauder Frames of Banach spaces
Liu, Rui
2009-01-01
This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will ...
Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
Jong Soo Jung
2008-01-01
Abstract Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a s...
Shenghua Wang
2013-01-01
Full Text Available We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.
Open problems in the geometry and analysis of Banach spaces
Guirao, Antonio J; Zizler, Václav
2016-01-01
This is a collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concepts of basic linear geometry, convexity, approximation, optimization, differentiability, renormings, weak compact generating, Schauder bases and biorthogonal systems, fixed points, topology and nonlinear geometry. The main purpose of this work is to help convince young researchers in Functional Analysis that the theory of Banach spaces is a fertile field of research, full of interesting open problems. Inside the Banach space area, the text should help expose young researchers to the depth and breadth of the work that remains, and to provide the perspective necessary to choose a direction for further study. Some of the problems presented herein are longstanding open problems, some are recent, some are more important and some are only "local" problems. Some would ...
On the uniqueness of minimal projections in Banach spaces
Ewa Szlachtowska; Dominik Mielczarek
2012-01-01
Let \\(X\\) be a uniformly convex Banach space with a continuous semi-inner product. We investigate the relation of orthogonality in \\(X\\) and generalized projections acting on \\(X\\). We prove uniqueness of orthogonal and co-orthogonal projections.
Some Questions Arising from the Homogeneous Banach Space Problem
Casazza, Peter G.
1992-01-01
We review the current state of the homogeneous Banach space problem. We then formulate several questions which arise naturally from this problem, some of which seem to be fundamental but new. We give many examples defining the bounds on the problem. We end with a simple construction showing that every infinite dimensional Banach space contains a subspace on which weak properties have become stable (under passing to further subspaces). Implications of this construction are considered.
Construction of generalized atomic decompositions in Banach spaces
Raj Kumar
2014-06-01
Full Text Available G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.
Metric embeddings bilipschitz and coarse embeddings into Banach spaces
Ostrovskii, Mikhail I
2013-01-01
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
Atomic decompositions of Banach-space-valued martingales
刘培德; 侯友良
1999-01-01
Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such as H_α(X) and _ρ(?)_α in the case 0<α≤1 are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.
Banach Spaces with respect to Operator-Valued Norms
Kim, Yun-Su
2008-01-01
We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products.
Additive maps preserving the reduced minimum modulus of Banach space operators
Bourhim, Abdellatif
2009-01-01
Let ${\\mathcal B}(X)$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space $X$. We prove that an additive surjective map $\\phi$ on ${\\mathcal B}(X)$ preserves the reduced minimum modulus if and only if either there are bijective isometries $U:X\\to X$ and $V:X\\to X$ both linear or both conjugate linear such that $\\phi(T)=UTV$ for all $T\\in{\\mathcal B}(X)$, or $X$ is reflexive and there are bijective isometries $U:X^*\\to X$ and $V:X\\to X^*$ both linear or both conjugate linear such that $\\phi(T)=UT^*V$ for all $T\\in{\\mathcal B}(X)$. As immediate consequences of the ingredients used in the proof of this result, we get the complete description of surjective additive maps preserving the minimum, the surjectivity and the maximum moduli of Banach space operators.
A GLIDING HUMP PROPERTY AND BANACH-MACKEY SPACES
CHARLES SWARTZ
2001-08-01
Full Text Available We consider the Banach-Mackey property for pairs of vector spaces E and E' which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and anoter measure theoretic property are Banach-Mackey pairs, i. e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given
(s, μ)-similar operators in the Banach spaces
The theory of the operator ideals formed by means of S function is developed. The problem of the construction of the operator acting from one Banach space to another whose S numbers are near to the given ones, is solved. Several conditions, sufficient for that any wholly continuous operator in the Gilbert space were transferred to the given pair of the Banach spaces without distorting too much the values of its S-numbers, are given. All the considered operators are assumed to be linear and continuous ones
Banach's space: Lviv and the Scottish cafe
D.Henderson
2004-01-01
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.
On well posedness of best simultaneous approximation problems in Banach spaces
LI; Chong
2001-01-01
［1］Pinkus, A., Uniqueness in vector-valued approximation, J. Approx. Theory, 1993, 73: 17—92.［2］Li, C., Watson, G. A., On best simultaneous approximation, J. Approx. Theory, 1997, 91: 332—348.［3］Tanimoto, S., A characterization of best simultaneous approximations, J. Approx. Theory, 1989, 59: 359—361.［4］Watson, G. A., A characterization of best simultaneous approximations, J. Approx. Theory, 1993, 75: 175—182.［5］Li, C., Watson, G. A., On best simultaneous approximation of a finite set of functions, Computer Math. Applic., 1999, 37: 1—9.［6］Stechkin, S. B., Approximation properties of sets in normed linear spaces, Rev. Roumaine Math. Pures and Appl. (in Russian), 1963, 8: 5—18.［7］Borwein, J. M., Fitzpatrick, S., Existence of nearest points in Banach spaces, Can. J. Math., 1989, 41: 702—720.［8］De Blasi, F. S., Myjak, J., On a generalized best approximation problem, J. Approx. Theory, 1998, 94: 54—72.［9］Georgiev, P. G., The strong Ekeland variational principle, the strong drop theorem and applications, J. Math. Anal. Appl., 1988, 131: 1—21.［10］Lau, K. S., Almost Chebyshev subsets in reflexive Banach spaces, Indiana Univ. Math. J., 1978, 27: 791—795.［11］Li, C., On mutually nearest and mutually furthest points in reflexive Banach spaces, J. Approx. Theory, 2000, 103: 1—17.［12］Li, C., On well posed generalized best approximation problems, J. Approx. Thory, 2000, 107: 96—108.［13］Li, C., Almost K-Chebyshev sets, Acta. Math. Sin. (in Chinese), 1990, 33: 251—259.［14］De Blasi, F. S., Myjak, J., Papini, P. L., On mutually nearest and mutually furthest points of sets in Banach spaces, J. Approx. Theory, 1992, 70: 142—155.［15］Dontchev, A., Zolezzi, T., Well Posed Optimization Problems, Lecture Notes in Math., Vol. 1543, New York: Springer-Verlag, 1993.［16］Li, C., Wang, X. H., Almost Chebyshev set with respect to bounded subsets, Science in China, Ser. A, 1997, 40: 375—383.［17］Ni, R
Riesz Isomorphisms of Tensor Products of Order Unit Banach Spaces
T S S R K Rao
2009-06-01
In this paper we formulate and prove an order unit Banach space version of a Banach–Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions in [5] and [6].
Banach spaces and descriptive set theory selected topics
Dodos, Pandelis
2010-01-01
This volume deals with problems in the structure theory of separable infinite-dimensional Banach spaces, with a central focus on universality problems. This topic goes back to the beginnings of the field and appears in Banach's classical monograph. The novelty of the approach lies in the fact that the answers to a number of basic questions are based on techniques from Descriptive Set Theory. Although the book is oriented on proofs of several structural theorems, in the main text readers will also find a detailed exposition of numerous “intermediate” results which are interesting in their own right and have proven to be useful in other areas of Functional Analysis. Moreover, several well-known results in the geometry of Banach spaces are presented from a modern perspective.
The reconstruction property in Banach spaces and a perturbation theorem
Casazza, P.G.; Christensen, Ole
2008-01-01
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 equiva...
On some impulsive fractional differential equations in Banach spaces
JinRong Wang
2010-01-01
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.
On nonlocal problems for fractional differential equations in Banach spaces
XiWang Dong
2011-01-01
Full Text Available In this paper, we study the existence and uniqueness of solutions to the nonlocal problems for the fractional differential equation in Banach spaces. New sufficient conditions for the existence and uniqueness of solutions are established by means of fractional calculus and fixed point method under some suitable conditions. Two examples are given to illustrate the results.
Improved bounds in the metric cotype inequality for Banach spaces
Giladi, Ohad; Naor, Assaf
2010-01-01
It is shown that if (X, ||.||_X) is a Banach space with Rademacher cotype q then for every integer n there exists an even integer m X we have \\sum_{j=1}^n \\Avg_x [ ||f(x+ (m/2) e_j)-f(x) ||_X^q ] n^{(1/2)+(1/q)}.
Smooth approximations of norms in separable Banach spaces
Hájek, Petr Pavel; Talponen, J.
2014-01-01
Roč. 65, č. 3 (2014), s. 957-969. ISSN 0033-5606 R&D Projects: GA ČR(CZ) GAP201/11/0345 Institutional support: RVO:67985840 Keywords : Banach space * approximation Subject RIV: BA - General Mathematics Impact factor: 0.640, year: 2014 http://qjmath.oxfordjournals.org/content/65/3/957
Multipliers of pg-Bessel sequences in Banach spaces
Abdollahpour, M. R.; Najati, A.; Gavruta, P.
2015-01-01
In this paper, we introduce (p,q)g-Bessel multipliers in Banach spaces and we show that under some conditions a (p,q)g-Bessel multiplier is invertible. Also, we show the continuous dependency of (p,q)g-Bessel multipliers on their parameters.
Banach空间中的Xd Bessel列%Sequences of Xd Bessel for a Banach space
王亚丽; 曹怀信; 张巧卫
2011-01-01
研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基.证明了当Xd为BK-空间时,(BXXd,‖·‖)是数域F上的Banach空间；当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B(X*,Xd)之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据.最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的.%Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X ate introduced and discussed. It is proved that (Bxxd || ? || ) is a Banach space when Xd is a BK-space. By de fining an operator Tf, an isometric isomorphism from Bxxd to B(X* ,Xd) is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ ent Xd frames and Xd Riesz bases for a Banach space X are the same.
Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space
Kraus, Michal
2015-01-01
We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
Consistency of Regularized Learning Schemes in Banach Spaces
Combettes, Patrick L.; Salzo, Saverio; Villa, Silvia
2014-01-01
This paper proposes a unified framework for the investigation of learning theory in Banach spaces of features via regularized empirical risk minimization. The main result establishes the consistency of such learning schemes under general conditions on the loss function, the geometry of the feature space, the regularization function, and the regularization parameters. The focus is placed on Tikhonov-like regularization with totally convex functions. This broad class of regularizers provides a ...
Integrals and Banach spaces for finite order distributions
Talvila, Erik
2011-01-01
Let $\\Bc$ denote the real-valued functions continuous on the extended real line and vanishing at $-\\infty$. Let $\\Br$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\\infty$. Define $\\acn$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\\Bc$. Similarly with $\\arn$ from $\\Br$. A type of integral is defined on distributions in $\\acn$ and $\\arn$. The multipliers are iterated integrals of functions of bounded variation. For each $n\\in\\N$, the spaces $\\acn$ and $\\arn$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\\Bc$ and $\\Br$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\\ac^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\\ar^1$ contains all finite signed Borel measure...
Some problems on ordinary differential equations in Banach spaces
Hájek, Petr Pavel; Vivi, P.
2010-01-01
Roč. 104, č. 2 (2010), s. 245-255. ISSN 1578-7303 R&D Projects: GA AV ČR IAA100190801; GA ČR GA201/07/0394 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach space * ODE * Peano's theorem Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2010 http://link.springer.com/article/10.5052%2FRACSAM.2010.16
Polynomial algebras and smooth functions in Banach spaces
D'Alessandro, Stefania; Hájek, Petr Pavel
2014-01-01
Roč. 266, č. 3 (2014), s. 1627-1646. ISSN 0022-1236 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : polynomials in Banach space Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123613004588
Weak compactness and sigma-Asplund generated Banach spaces
Fabian, Marián; Montesinos, V.; Zizler, Václav
2007-01-01
Roč. 181, č. 2 (2007), s. 125-152. ISSN 0039-3223 R&D Projects: GA AV ČR IAA1019301; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : epsilon-Asplund set * epsilon-weakly compact set * weakly compactly generated Banach space Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007
Some Properties of the Injective Tensor Product of Banach Spaces
Xiao Ping XUE; Yong Jin LI; Qing Ying BU
2007-01-01
Let X and Y be Banach spaces such that X has an unconditional basis. Then X?Y, the injective tensor product of X and Y, has the Radon-Nikodym property (respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness) if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
Tools for Malliavin calculus in UMD Banach spaces
Pronk, Matthijs
2012-01-01
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called UMD property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Ito formula for non-adapted processes.
Greedy Algorithms for Reduced Bases in Banach Spaces
DeVore, Ronald
2013-02-26
Given a Banach space X and one of its compact sets F, we consider the problem of finding a good n-dimensional space X n⊂X which can be used to approximate the elements of F. The best possible error we can achieve for such an approximation is given by the Kolmogorov width dn(F)X. However, finding the space which gives this performance is typically numerically intractable. Recently, a new greedy strategy for obtaining good spaces was given in the context of the reduced basis method for solving a parametric family of PDEs. The performance of this greedy algorithm was initially analyzed in Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) in the case X=H is a Hilbert space. The results of Buffa et al. (Modél. Math. Anal. Numér. 46:595-603, 2012) were significantly improved upon in Binev et al. (SIAM J. Math. Anal. 43:1457-1472, 2011). The purpose of the present paper is to give a new analysis of the performance of such greedy algorithms. Our analysis not only gives improved results for the Hilbert space case but can also be applied to the same greedy procedure in general Banach spaces. © 2013 Springer Science+Business Media New York.
Some Banach spaces of Dirichlet series
Bailleul, Maxime; Lefèvre, Pascal
2013-01-01
The Hardy spaces of Dirichlet series denoted by ${\\cal H}^p$ ($p\\ge1$) have been studied in [12] when p = 2 and in [3] for the general case. In this paper we study some Lp-generalizations of spaces of Dirichlet series, particularly two families of Bergman spaces denoted ${\\cal A}^p$ and ${\\cal B}^p$. We recover classical properties of spaces of analytic functions: boundedness of point evaluation, embeddings between these spaces and "Littlewood-Paley" formulas when p = 2. We also show that the...
An approximation problem of the finite rank operator in Banach spaces
王玉文; 潘少荣
2003-01-01
By the method of geometry of Banach spaces, we have proven that a bounded linear operatorin Banach space is a compact linear one iff it can be uniformly approximated by a sequence of the finite rankbounded homogeneous operators, which reveals the essence of the counter example given by Enflo.
Adrian PETRU(S)EL; Jen-Chih YAO
2009-01-01
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
On sets minimizing their weighted length in uniformly convex separable Banach spaces
De Pauw, Thierry; Lemenant, Antoine; Millot, Vincent
2013-01-01
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show $C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity verifies a Dini growth condition.
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
Let be a normed linear space, an element of norm one, and and the local modulus of convexity of . We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open -neighbourhood of in onto a set containing the open -neighbourhood of in . It is known that . We prove that there is no universal constant such that , however, such a constant exists within the class of Hilbert spaces . If is a Hilbert space with , then .
Stability of interconnected dynamical systems described on Banach spaces
Rasmussen, R. D.; Michel, A. N.
1976-01-01
New stability results for a large class of interconnected dynamical systems (also called composite systems or large scale systems) described on Banach spaces are established. In the present approach, the objective is always the same: to analyze large scale systems in terms of their lower order and simpler subsystems and in terms of their interconnecting structure. The present results provide a systematic procedure of analyzing hybrid dynamical systems (i.e., systems that are described by a mixture of different types of equations). To demonstrate the method of analysis advanced, two specific examples are considered.
On nonautonomous second-order differential equations on Banach space
Nguyen Thanh Lan
2001-04-01
Full Text Available We show the existence and uniqueness of classical solutions of the nonautonomous second-order equation: uÃ¢Â€Â³(t=A(tuÃ¢Â€Â²(t+B(tu(t+f(t, 0Ã¢Â‰Â¤tÃ¢Â‰Â¤T; u(0=x0, uÃ¢Â€Â²(0=x1 on a Banach space by means of operator matrix method and apply to Volterra integrodifferential equations.
Iterative solutions of nonlinear equations in smooth Banach spaces
Let E be a smooth Banach space over the real field, φ not= K is contained in E closed convex and bounded, T:K → K uniformly continuous and strongly pseudo-contractive. It is proved that the Ishikawa iteration process converges strongly to the unique fixed point of T. Applications of this result to the operator equations Au=f or u+Au=f where A is a strongly accretive mapping of E into itself and under various continuity assumptions on A are also given. (author). 41 refs
Geometry and Gâteaux smoothness in separable Banach spaces
Hájek, Petr Pavel; Montesinos, V.; Zizler, Václav
2012-01-01
Roč. 6, č. 2 (2012), s. 201-232. ISSN 1846-3886 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gâteaux differentiable norms * extreme points * Radon-Nikodým property Subject RIV: BA - General Math ematics Impact factor: 0.529, year: 2012 http://oam.ele- math .com/06-15/Geometry-and-Gateaux-smoothness-in-separable-Banach-spaces
Linearization of class C1 for contractions on Banach spaces
Rodrigues, Hildebrando M.; Solà-Morales, J.
In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite-dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant manifolds, which can be interesting by itself and that was needed on the proof of our main theorem. Our results essentially generalize some classical results by P. Hartman in finite dimensions, and a result of Mora-Sola-Morales in the infinite-dimensional case. It is shown that the result can be applied to some abstract systems of semilinear damped wave equations.
Near Convexity, Near Smoothness and Approximative Compactness of Half Spaces in Banach Spaces
Zi Hou ZHANG; Yu ZHOU; Chun Yan LIU
2016-01-01
The authors discuss the dual relation of nearly very convexity and property WS.By two kinds of near convexities and two kinds of near smoothness,the authors prove a series of characterizations such that every half-space in Banach space X and every weak* half-space in the dual space X* are approximatively weakly compact and approximatively compact.They show a sufficient condition such that a Banach space X is a Asplund space.Using upper semi-continuity of duality mapping,the authors also give two characterizations of property WS and property S.
On moduli of convexity in Banach spaces
Reif Jiří
2005-01-01
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 .
FRAME MULTIRESOLUTION ANALYSIS AND INFINITE TREES IN BANACH SPACES ON LOCALLY COMPACT ABELIAN GROUPS
S. S. Panday
2004-01-01
We extend the concept of frame multiresolution analysis to a locally compact abelian group and use it to define certain weighted Banach spaces and the spaces of their antifunctionals. We define analysis and synthesis operators on these spaces and establish the continuity of their composition. Also, we prove a general result to characterize infinite trees in the above Banach spaces of antifunctionals. This paper paves the way for the study of corresponding problems associated with some other types of Banach spaces on locally compact abelian groups including modulation spaces.
Smoothness in Banach spaces. Selected problems
Fabian, Marián; Montesinos, V.; Zizler, Václav
2006-01-01
Roč. 100, č. 2 (2006), s. 101-125. ISSN 1578-7303 R&D Projects: GA ČR(CZ) GA201/04/0090; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : smooth norm * renorming * weakly compactly generated space Subject RIV: BA - General Mathematics
QUASI-LOCAL CONJUGACY THEOREMS IN BANACH SPACES
ZHANG WEIRONG; MA JIPU
2005-01-01
Let f: U(xo)() E → F be a C1 map and f'(x0) be the Frechet derivative of f at x0. In local analysis of nonlinear functional analysis, implicit function theorem, inverse function theorem, local surjectivity theorem, local injectivity theorem, and the local conjugacy theorem are well known. Those theorems are established by using the properties: f'(x0) is double splitting and R(f'(x)) ∩ N(T0+) = {0} near x0. However,in infinite dimensional Banach spaces, f'(x0) is not always double splitting (i.e., the generalized inverse of f'(x0) does not always exist), but its bounded outer inverse of f'(x0) always exists.Only using the C1 map f and the outer inverse T0# of f'(x0), the authors obtain two quasi-local conjugacy theorems, which imply the local conjugacy theorem if x0 is a locally fine point of f. Hence the quasi-local conjugacy theorems generalize the local conjugacy theorem in Banach spaces.
Homomorphisms and functional calculus on algebras on entire functions on Banach spaces
H. M. Pryimak
2015-07-01
Full Text Available The paper is devoted to study homomorphisms of algebras of entire functionson Banach spaces to a commutative Banach algebra. In particular, it is proposed amethod to construct homomorphisms vanishing on homogeneouspolynomials of degree less or equal that a fixed number $n.$
Stochastic integration in Banach spaces theory and applications
Mandrekar, Vidyadhar
2015-01-01
Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integrati...
Yan Tang
2013-01-01
Full Text Available Suppose that C is a nonempty closed convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. A viscosity iterative process is constructed in this paper. A strong convergence theorem is proved for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings. And the common element is the unique solution of certain variational inequality. The results presented in this paper extend most of the results that have been proposed for this class of nonlinear mappings.
Porous sets for mutually nearest points in Banach spaces
Chong Li
2008-01-01
Full Text Available Let \\(\\mathfrak{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 \\mathfrak{B}(X\\ we set \\(\\lambda_{EF} = \\inf \\{\\|z - x\\| : x \\in E, z \\in F \\}\\. Let \\(\\mathfrak{D}\\ denote the closure (under the maximum distance of the set of all \\((E, F \\in \\mathfrak{B}(X \\times \\mathfrak{B}(X\\ such that \\(\\lambda_{EF} \\gt 0\\. It is proved that the set of all \\((E, F \\in \\mathfrak{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 \\(\\mathfrak{D}\\.
Approximative compactness and continuity of metric projector in Banach spaces and applications
HUDZIK; Henryk; KOWALEWSKI; Wojciech; WISLA; Marek
2008-01-01
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way.It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X,then the metric projectorπC from X onto C is continuous.Under the assumption that X is midpoint locally uniformly rotund,we prove that the approximative compactness of C is also necessary for the continuity of the projectorπC by the method of geometry of Banach spaces.Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T~+,where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
On Property () in Banach Lattices, Calderón–Lozanowskiĭ and Orlicz–Lorentz Spaces
Paweł Kolwicz
2001-08-01
The geometry of Calderón–Lozanowskiĭ spaces, which are strongly connected with the interpolation theory, was essentially developing during the last few years (see [4, 9, 10, 12, 13, 17]). On the other hand many authors investigated property () in Banach spaces (see [7, 19, 20, 21, 25, 26]). The first aim of this paper is to study property () in Banach function lattices. Namely a criterion for property () in Banach function lattice is presented. In particular we get that in Banach function lattice property () implies uniform monotonicity. Moreover, property () in generalized Calderón–Lozanowskiĭ function spaces is studied. Finally, it is shown that in Orlicz–Lorentz function spaces property () and uniform convexity coincide.
In this work, we establish a sufficient condition for the controllability of the first-order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the Dhage's fixed point theorem.
张石生
2001-01-01
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results.
Approximating zero points of accretive operators with compact domains in general Banach spaces
Miyake Hiromichi
2005-01-01
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.
Exponential dichotomies for linear discrete-time systems in Banach spaces
Ioan-Lucian Popa
2012-04-01
Full Text Available In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarify the relations between these concepts.
Geometrical and Topological Properties of Bumps and Starlike Bodies in Banach Spaces
Azagra Rueda, Daniel; Jiménez Sevilla, María del Mar
2002-01-01
While the topological and geometrical properties of convex bodies in Banach spaces are quite well understood (including their topological and smooth classification), much less is known about the structure of starlike bodies. Starlike bodies are important objects in nonlinear functional analysis as they appear as level sets of $n$-homogeneous polynomials on Banach spaces. Significant progress in the study of starlike bodies has been done in the last years by the efforts of Manuel Cepedello, Ro...
Strong convergence theorems for uniformly L-Lipschitzian mappings in Banach spaces
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 {αn}n≥0 and {γn}n≥0 subset of (0, 1) be such that limn→∞ αn = 0 = limn→ ∞ γn and limn→ ∞(βn - 1)/ αn = 0, where βn Σj=0n λj and λj = 1 + αjγjL. Let Sn := (1 - αnγn)I + αnγnTn. 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 = αnu+(1 -αn) 1/ (n + 1) Σj=0n Sjxn. If φ : E → R is defined by φ (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 : φ (x) = min (u element of K) φ (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 - αn) 1/ (n + 1) Σj=0n Sjzn , n ≥ 0, under suitable conditions on the iteration parameters, converges strongly to a fixed point of T. (author)
On quasi-convex mappings of order α in the unit ball of a complex Banach space
LIU Taishun; XU Qinghua
2006-01-01
In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings.Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space Ⅹ. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.
Robert F.Allen
2014-01-01
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient condi-tions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ”computable” estimates on the operator norm.
Isometric uniqueness of a complementably universal Banach space for Schauder decompositions
Garbulińska, Joanna
2014-01-01
We present an isometric version of the complementably universal Banach space $\\mathbb{P}$ with a Schauder decomposition. The space $\\mathbb{P}$ is isomorphic to Pe{\\l}czy\\'nski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.
On well posedness of best simultaneous approximation problems in Banach spaces
无
2001-01-01
The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points in E(G) such that the best simultaneous approximation problems are not well posed is a σ-porous set in E(G) when X is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
Real-Analytic Negligibility of Points and Subspaces in Banach Spaces, with Applications
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
2002-01-01
We prove that every infinite-dimensional Banach space X having a (not necessarily equivalent) real-analytic norm is real-analytic diffeomorphic to X \\ {0}. More generally, if X is an infinite-dimensional Banach space and F is a closed subspace of X such that there is a real-analytic seminorm on X whose set of zeros is F, and X / F is infinite-dimensional, then X and X \\ F are real-analytic diffeomorphic. As an application we show the existence of real-analytic free actions of the circle and t...
Smooth negligibility of compact sets in infinite-dimensional Banach spaces, with applications
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
1998-01-01
This article deals with smooth removability of compact sets in infinite-dimensional Banach spaces. The main result states that ifX is an infinite-dimensional Banach space which has a not necessarily equivalent Cp-smooth norm and K is a compact subset of X, then X and X r K are Cp diffeomorphic. The proof relies on the construction of a “deleting path” through a nontrivial refinement of Bessaga’s incomplete-norm technique. However, norms are not at present available and the construction req...
On Best Approximations from RS-sets in Complex Banach Spaces
Chong LI
2005-01-01
The concept of an RS-set in a complex Banach Space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established.
Integrals with values in Banach spaces and locally convex spaces
Mikusinski, Piotr
2014-01-01
The purpose of this article is to present the construction and basic properties of the general Bochner integral. The approach presented here is based on the ideas from the book The Bochner Integral by J. Mikusinski where the integral is presented for functions defined on $\\mathbb{R}^N$. In this article we present a more general and simplified construction of the Bochner integral on abstract measure spaces. An extension of the construction to functions with values in a locally convex space is ...
Murthy, S; Arunkumar, M; V. Govindan
2015-01-01
In this paper, the authors introduce and investigate the general solution and generalized Ulam-Hyers stability of a generalized n-type additive-quadratic functional equation. g(x + 2y; u + 2v) + g(x 2y; u 2v) = 4[g(x + y; u + v) + g(x y; u v)] 6g(x; u) + g(2y; 2v) + g(2y;2v) 4g(y; v) 4g(y;v) Where is a positive integer with , in Banach Space and Banach Algebras using direct and fixed point methods.
The generalized hardy operator with kernel and variable integral limits in banach function spaces
Lang J; Gogatishvill A
1999-01-01
Let we have an integral operator where and are nondecreasing functions, and are non-negative and finite functions, and is nondecreasing in , nonincreasing in and for and . We show that the integral operator where and are Banach functions spaces with -condition is bounded if and only if . Where and
Bound and periodic solutions of the Riccati equation in Banach space
A. Ya. Dorogovtsev
1995-01-01
Full Text Available An abstract, nonlinear, differential equation in Banach space is considered. Conditions are presented for the existence of bounded solutions of this equation with a bounded right side, and also for the existence of stationary (periodic solutions of this equation with a stationary (periodic process in the right side.
Known results and open problems on C1 linearization in Banach spaces
Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan
2012-01-01
The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open problems that we believe that are still important for the understanding of the theory.
Common Fixed Point Theorems in Non-normal Cone Metric Spaces with Banach Algebras
HUANG Hua-ping; XU Shao-yuan; LIU Qiu-hua; MING Wei
2016-01-01
In this paper, we obtain a class of common fixed point theorems for generalized Lipschitz mappings in cone metric spaces with Banach algebras without the assumption of normality of cones. The results greatly generalize some results in the literature. Moreover, we give an example to support the main assertions.
Gu Feng
2006-01-01
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.
POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE
无
2008-01-01
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space
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)
Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces
Hai Yun ZHOU
2004-01-01
In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Fixed point iterations for quasi-contractive maps in uniformly smooth Banach spaces
Two well-known fixed point iteration methods are applied to approximate fixed points of quasi-contractive maps in real uniformly smooth Banach spaces. While our theorems generalize important known results, our method is of independent interest. (author). 25 refs
Approximate Fixed Point Theorems in Banach Spaces with Applications in Game Theory
2002-01-01
In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.
Asymptotic behaviour of the solutions of Schroedinger equation with impulse effect in a Banach space
The present paper studies the asymptotic behaviour of the solutions of linear homogeneous differential Schroedinger equation with impulse effect in a Banach space and finds a dependence between their asymptotic behaviour and the spectrum of the linear Hamiltonian operator. 6 refs
A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES
Binayak S. Choudhury
2003-01-01
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.
On common fixed points of compatible mappings in metric and Banach spaces
M. S. Khan
1988-06-01
Full Text Available We prove a number of results concerning the existence of common fixed points of a family of maps satisfying certain contractive conditions in metric and Banach spaces. Results dealing with the stucture of the set of common fixed points of such maps are also given. Our work is an improvement upon the previously known results.
Strong Convergence Theorems for Strict Pseudocontractions in Uniformly Convex Banach Spaces
Lin Wei-Wei
2010-01-01
Full Text Available The viscosity approximation methods are employed to establish strong convergence theorems of the modified Mann iteration scheme to -strict pseudocontractions in -uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm. The main result improves and extends many nice results existing in the current literature.
Some G-M-type Banach spaces and K-groups of operator algebras on them
ZHONG Huaijie; CHEN Dongxiao; CHEN Jianlan
2004-01-01
By providing several new varieties of G-M-type Banachspaces according to decomposable and compoundable properties, this paper discusses the operator structures of thesespaces and the K-theory of the algebra of the operators on these G-M-type Banach spaces throughcalculation of the K-groups of the operator ideals contained in the class of Riesz operators.
Psi-exponential dichotomy for linear differential equations in a Banach space
Atanaska Georgieva
2013-07-01
Full Text Available In this article we extend the concept psi-exponential and psi-ordinary dichotomies for homogeneous linear differential equations in a Banach space. With these two concepts we prove the existence of psi-bounded solutions of the appropriate inhomogeneous equation. A roughness of the psi-dichotomy is also considered.
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Mihaela Tomescu; Andrea Minda
2006-01-01
In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and...
Nonuniform Exponential Stability and Instability of Evolution Operators in Banach Space
Mihaela Tomescu
2006-10-01
Full Text Available In this paper is presenting a parallel between nonuniform exponential stability and nonuniform exponential instability of evolution operators in Banach spaces, beginning to present the concept of the evolution operator with nonuniform exponential decay, respectively growth, next with the concept of the nonuniform stability, respectively instability, nonuniform exponential stability, respectively instability, nonuniform integrable stability, respectively instability and relationship between this concepts.
Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces
2009-02-01
Full Text Available We study the influence of computational errors on the convergence to compact sets of orbits of nonexpansive mappings in Banach and metric spaces. We first establish a convergence theorem assuming that the computational errors are summable and then provide examples which show that the summability of errors is necessary for convergence.
ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤p＜∞) AND c0 IN BANACH SPACES
Chen Dongyang
2006-01-01
Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1 ＜ p ＜∞). Then there exists a quotient space of X which is asymptotically isometric to lq (1/p+1/q=1). Complementedasymptotically isometric copies of c0 in K(X, Y) and W(X, Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.
N. L. Braha
2005-05-01
Full Text Available In this paper we will give a characterization of 1-absolutely summing operators using μ-approximate l_1 sequences. Exactly if (x_n _1^∞ is μ-approximate l_1 , basic and normalized sequence in Banach space X then every bounded linear operator T from X into Banach space Y is 1-absolutely summing if and only if Y is isomorphic to Hilbert space.
Boulbeba Abdelmoumen; Aref Jeribi; Maher Mnif
2012-01-01
In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.
Domains of uniqueness for $C_0$-semigroups on the dual of a Banach space
Lemle, Ludovic Dan
2008-01-01
Let $({\\cal X},\\|\\:.\\:\\|)$ be a Banach space. In general, for a $C_0$-semigroup \\semi on $({\\cal X},\\|\\:.\\:\\|)$, its adjoint semigroup \\semia is no longer strongly continuous on the dual space $({\\cal X}^{*},\\|\\:.\\:\\|^{*})$. Consider on ${\\cal X}^{*}$ the topology of uniform convergence on compact subsets of $({\\cal X},\\|\\:.\\:\\|)$ denoted by ${\\cal C}({\\cal X}^{*},{\\cal X})$, for which the usual semigroups in literature becomes $C_0$-semigroups.\\\\ The main purpose of this paper is to prove th...
M. B. Ghaemi; H. Majani; Cho, Y J; Eshaghi Gordji, M.
2011-01-01
Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.
Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces
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 Hölder 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)
Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces
By making use of duality mappings, we formulate an inexact Newton–Landweber 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)
Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces
Choonkil BAAK
2006-01-01
Let X, Y be vector spaces. It is shown that if a mapping f: X → Y satisfiesf(x+y/2+z)+f(x-y/2+z)=f(x)+2f(z), (0.1)f(x+y/2+z)-f(x-y/2+z)= f(y), (0.2)or2f(x+y/2+z)=f(x)+f(y)+2f(z) (0.3)for all x, y, z ∈ X, then the mapping f: X → Y is Cauchy additive.Furthermore, we prove the Cauchy-Rassias stability of the functional equations (0.1), (0.2) and (0.3) in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebra.
Common Fixed-Point Problem for a Family Multivalued Mapping in Banach Space
Zhanfei Zuo
2011-01-01
Full Text Available It is our purpose in this paper to prove two convergents of viscosity approximation scheme to a common fixed point of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, it is the unique solution in to a certain variational inequality, where ∶=∩∞=0( stands for the common fixed-point set of the family of multivalued nonexpansive mapping {}.
Mann Type Implicit Iteration Approximation for Multivalued Mappings in Banach Spaces
Huimin He
2010-01-01
Full Text Available Let K be a nonempty compact convex subset of a uniformly convex Banach space E and let T be a multivalued nonexpansive mapping. For the implicit iterates x0∈K, xn=αnxn-1+(1-αnyn, yn∈Txn, n≥1. We proved that {xn} converges strongly to a fixed point of T under some suitable conditions. Our results extended corresponding ones and revised a gap in the work of Panyanak (2007.
Tomonari Suzuki
2006-01-01
We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
Approximating Common Fixed Points of Lipschitzian Semigroup in Smooth Banach Spaces
Saeidi Shahram
2008-01-01
Abstract Let be a left amenable semigroup, let be a representation of as Lipschitzian mappings from a nonempty compact convex subset of a smooth Banach space into with a uniform Lipschitzian condition, let be a strongly left regular sequence of means defined on an -stable subspace of , let be a contraction on , and let , , and be sequences in (0, 1) such that , for all . Let , for all . Then, under suitable hypotheses on the constants, we show that converges stron...
Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces
Yongjin Li
2013-08-01
Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.
Nonlinear Evolution Governed by Accretive Operators in Banach Spaces: Error Control and Applications
Nochetto, Ricardo H; Savare, Giuseppe
2001-01-01
Nonlinear evolution equations governed by $m$-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order $O(sqrttau)$. Applications to scalar conservation laws and degenerate parabolic equations (with or without hysteresis) in $L^1$, as well as to Hamilton-Jacobi equations in $C^...
MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES
王良龙; 王志成
2004-01-01
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces
It is proved that the Mann iteration process converges strongly to the fixed point of a strictly hemi-contractive map in real uniformly smooth Banach spaces. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets. A related result deals with the Ishikawa iteration scheme when the mapping is Lipschitzian and strictly hemi-contractive. Our theorems generalize important known results. (author). 29 refs
Suzuki Tomonari
2006-01-01
Full Text Available We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Erzakova Nina A
2004-01-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Martin Väth
2004-12-01
Full Text Available As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.
Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian
Golinski, Tomasz
2009-01-01
Using the Magri method one defines an involutive family of Hamiltonians on Banach Lie-Poisson space iR+UL_res^1 (which contains the restricted Grassmannian as a symplectic leaf) and on its complexification C+L_res^1. The hierarchy of Hamilton equations given by these Hamiltonians is investigated. The operator equations of Ricatti-type are included in this hierarchy. For a few particular cases one gives the explicit solutions.
Some s-numbers of an integral operator of Hardy type in Banach function spaces
Edmunds, D.; Gogatishvili, Amiran; Kopaliani, T.; Samashvili, N.
2016-01-01
Roč. 207, July (2016), s. 79-97. ISSN 0021-9045 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : Hardy type operators * Banach function spaces * s-numbers * compact linear operators Subject RIV: BA - General Mathematics Impact factor: 0.951, year: 2014 http://www. science direct.com/ science /article/pii/S0021904516000265
A reinterpretation of set differential equations as differential equations in a Banach space
Rasmussen, Martin; Rieger, Janosch; Webster, Kevin
2015-01-01
Set differential equations are usually formulated in terms of the Hukuhara differential, which implies heavy restrictions for the nature of a solution. We propose to reformulate set differential equations as ordinary differential equations in a Banach space by identifying the convex and compact subsets of $\\R^d$ with their support functions. Using this representation, we demonstrate how existence and uniqueness results can be applied to set differential equations. We provide a simple example,...
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Su Yongfu
2008-01-01
Full Text Available Abstract The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping and a finite family of nonexpansive mappings , respectively, in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori, 2001, Z. Opial, 1967, and others.
Yun-zhi Zou
2012-01-01
Full Text Available A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.
Hytonen, Tuomas; van Neerven, Jan; Portal, Pierre
2007-01-01
We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces. Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator (A) with certain off-diagonal bounds, such that (A) always has a bounded (H^{\\infty})-functional calculus on these spaces. This provides a new way of proving functional ...
On Linear Isometries of Banach Lattices in $\\mathcal{C}_0()$-Spaces
José M Isidro
2009-11-01
Consider the space $\\mathcal{C}_0()$ endowed with a Banach lattice-norm $\\|\\cdot p\\|$ that is not assumed to be the usual spectral norm $\\|\\cdot p\\|_∞$ of the supremum over . A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry of the Banach lattice $(\\mathcal{C}_0(),\\|\\cdot p\\|)$ induces a partition of into a family of finite subsets $S\\subset$ along with a bijection $T:→$ which preserves cardinality, and a family $[u(S):S\\in]$ of surjective linear maps $u(S):\\mathcal{C}(T(S))→\\mathcal{C}(S)$ of the finite-dimensional *-algebras $\\mathcal{C}(S)$ such that $$(U f)|_{T(S)}=u(S)(f|_S) \\quad \\forall f\\in\\mathcal{C}_0() \\quad \\forall S\\in.$$ Here we endow the space of finite sets $S\\subset$ with a topology for which the bijection and the map are continuous, thus completing the analogy with the classical result.
Casazza, Peter G.; Christensen, Ole
1995-01-01
We prove that a Hilbert space frame $\\fti$ contains a Riesz basis if every subfamily $\\ftj , J \\subseteq I ,$ is a frame for its closed span. Secondly we give a new characterization of Banach spaces which do not have any subspace isomorphic to $c_0$. This result immediately leads to an improvement of a recent theorem of Holub concerning frames consisting of a Riesz basis plus finitely many elements.
Fixed Point Theorems for Suzuki Generalized Nonexpansive Multivalued Mappings in Banach Spaces
Abkar A
2010-01-01
Full Text Available In the first part of this paper, we prove the existence of common fixed points for a commuting pair consisting of a single-valued and a multivalued mapping both satisfying the Suzuki condition in a uniformly convex Banach space. In this way, we generalize the result of Dhompongsa et al. (2006. In the second part of this paper, we prove a fixed point theorem for upper semicontinuous mappings satisfying the Suzuki condition in strictly spaces; our result generalizes a recent result of Domínguez-Benavides et al. (2009.
Convergence rates for the iteratively regularized Gauss–Newton method in Banach spaces
In this paper we consider the iteratively regularized Gauss–Newton 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. Hölder 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
Delta-semidefinite and delta-convex quadratic forms in Banach spaces
Kalton, N.; Konyagin, S. V.; Vesely, L.
2006-01-01
A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator $T\\colon X\\to X^*$ factors through a Hilbert space; (b) delta-convex (i.e., representable as a difference of two continuous convex functions) if and only if $T$ is a UMD-operator. It follows, for instance, that each quadratic form on an infinite-dimensional $...
Existence results for a class of parabolic evolution equations in Banach spaces
WangJing; XueXingmei
2003-01-01
We discuss the existence results of the parabolic evolution equation d(x(t) + g(t,x(t)))/dt + A(t)x(t) =f( t ,x(t)) in Banach spaces, where A (t) generates an evolution system and functions f, g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classieal (semi-classical) solution. We extend the cases when g(t) = 0 or A(t) = A.
Some compactness tests in Banach spaces by Cesaro means of Fourier coefficients
Öztürk, Seda
2015-09-01
Let H be a complex Banach space, T be the topological group of the unit circle with respect to the Euclidean topology, α be a strongly continuous isometric linear representation of T in H, {Fkα}k ∈ℤ be the family of Fourier coefficients with respect to α, and {σkα}k ∈ℤ be Cesaro means of the family {Fkα}k ∈ℤ . In this work, we give some compactness tests for closed subsets of H.
Oscillation and the mean ergodic theorem for uniformly convex Banach spaces
Avigad, Jeremy; Rute, Jason
2012-01-01
Let B be a p-uniformly convex Banach space, with p >= 2. Let T be a linear operator on B, and let A_n x denote the ergodic average (1 / n) sum_{i< n} T^n x. We prove the following variational inequality in the case where T is power bounded from above and below: for any increasing sequence (t_k)_{k in N} of natural numbers we have sum_k || A_{t_{k+1}} x - A_{t_k} x ||^p
ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES
WEI Wei; XIANG Xiaoling
2004-01-01
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presentedThe equations con-tain nonlinear monotone operators and a nonmonotone perturbationMoreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verifiedOur abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
Approximation of fixed points of Lipschitz pseudo-contractive mapping in Banach spaces
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
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Basic Properties of Banach Space Xμ%Banach空间Xμ的基本性质
郑列
2005-01-01
研究了Banach空间Xμ={c=(ci)i≥1:‖c‖μ=def ∞∑ i=1 iμ|Ci|∞},μ≥1.讨论了它的范数,紧性以及强收敛和弱收敛之间的关系.%Banach space Xμ= {c= (ci)i≥1: ‖c‖μ=def ∞∑ i=1 iμ|ci|∞},μ≥1. is studied. Our results relate to norm,compactness and the relation between strong convergence and weak * convergence.
Convergence theorems for a class of nonlinear maps in uniformly smooth Banach spaces
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
Hanke-Raus heuristic rule for variational regularization in Banach spaces
Jin, Qinian
2016-08-01
We generalize the heuristic parameter choice rule of Hanke-Raus for quadratic regularization to general variational regularization for solving linear as well as nonlinear ill-posed inverse problems in Banach spaces. Under source conditions formulated as variational inequalities, we obtain a posteriori error estimates in term of the Bregman distance. By imposing certain conditions on the random noise, we establish four convergence results; one relies on the source conditions and the other three do not depend on any source conditions. Numerical results are presented to illustrate the performance.
On the regularity of mild solutions to complete higher order differential equations on Banach spaces
Nezam Iraniparast
2015-09-01
Full Text Available For the complete higher order differential equation u(n(t=Σk=0n-1Aku(k(t+f(t, t∈ R (* on a Banach space E, we give a new definition of mild solutions of (*. We then characterize the regular admissibility of a translation invariant subspace al M of BUC(R, E with respect to (* in terms of solvability of the operator equation Σj=0n-1AjXal Dj-Xal Dn = C. As application, almost periodicity of mild solutions of (* is proved.
Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces
Udomene Aniefiok
2006-01-01
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 .
C0-semigroups of linear operators on some ultrametric Banach spaces
Toka Diagana
2006-01-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
A model of CT dose profiles in Banach space; with applications to CT dosimetry
Weir, Victor J.
2016-07-01
In this paper the scatter component of computed tomography dose profiles is modeled using the solution to a nonlinear ordinary differential equation. This scatter function is summed with a modeled primary function of approximate trapezoidal shape. The primary dose profile is modeled to include the analytic continuation of the Heaviside step function. A mathematical theory is developed in a Banach space. The modeled function is used to accurately fit data from a 256-slice GE Revolution scanner. A 60 cm long body phantom is assembled and used for data collection with both a pencil chamber and a Farmer-type chamber.
Local subdifferentials and multivariational inequalities in Banach and Frechet spaces
Pavlo O. Kasyanov; Valery S. Mel'nik; Anna M. Piccirillo
2008-01-01
Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudo-monotone type, connected with subdifferential maps, are considered.
On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
ZHANG; Wenjun(张文俊); LIU; Taishun(刘太顺)
2002-01-01
A class of biholomorphic mappings named "quasi-convex mapping" is introduced in the unitball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class ofstarlike mappings and contains the class of convex mappings properly, and it has the same growth and coveringtheorems as the convex mappings. Furthermore, when the Banach space is confined to Cn, the "quasi-convexmapping" is exactly the "quasi-convex mapping of type A" introduced by K. A. Roper and T. J. Suffridge.
Isomorphisms on weighed Banach spaces of harmonic and holomorphic functions
Jorda Mora, Enrique; ZARCO GARCIA, ANA MARIA
2013-01-01
For an arbitrary open subset U subset of R-d or U subset of C-d and a continuous function v : U ->]0,infinity[ we show that the space h(v0) (U) of weighed harmonic functions is almost isometric to a (closed) subspace of c(0), thus extending a theorem due to Bonet and Wolf for spaces of holomorphic functions H-v0 (U) on open sets U subset of C-d. Inspired by recent work of Boyd and Rueda, we characterize in terms of the extremal points of the dual of h(v0) (U) when h(v0) (U) is isometric to a ...
A convergence rates result for an iteratively regularized Gauss–Newton–Halley method in Banach space
The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss–Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings. (paper)
Shi-sheng ZHANG
2009-01-01
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
无
2010-01-01
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
Rongfei Lin
2013-01-01
Full Text Available Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.
Jiancai Huang
2012-01-01
Full Text Available We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.
A type (4) space in (FR)-classification
Argyros, Spiros A; Pelczar-Barwacz, Anna
2012-01-01
We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.
On Well-posed Mutually Nearest and Mutually Furthest Point Problems in Banach Spaces
Chong LI; Ren Xing NI
2004-01-01
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let K(X) denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let KG(X) denote the closure of the set {A ∈ K(X): A∩G =φ}. We prove that the set of all A ∈KG(X) (resp. A ∈ K(X)), such that the minimization (resp. maximization) problem min(A, G) (resp. max(A, G)) is well posed, contains a dense Gδ-subset of KG(X) (resp. K(X)), thus extending the recent results due to Blasi, Myjak and Papini and Li.
Models of CT dose profiles in Banach space; with applications to CT Dosimetry
Weir, Victor J
2015-01-01
This paper consists of two parts.In the first part, the scatter components of computed tomograpahy dose profiles are modeled using various functions including the solution to Riccati's differential equation. These scatter functions are combined with primary components such as a trapezoidal function and a constructed function that uses the analytic continuation of Heaviside step function. A mathematical theory is developed in Banach space. The modeled function, which is the product of the scatter and primary functions, is used to accurately fit data from the O-arm cone beam imaging system. In a second part of the paper, an approach to dosimtery is developed that shows that the results obtained from the use of a pencil shaped ion chamber is equivalent to that from a farmer chamber. This result is verified by presenting some preliminary experimental data measured in a 64 slice Siemens Sensation scanner.
A Banach space-valued ergodic theorem for amenable groups and applications
Pogorzelski, Felix
2012-01-01
In this paper we study unimodular amenable groups. The first part is devoted to results on the existence of uniform families of quasi tilings for these groups. In light of that, constructions of Ornstein and Weiss are extended by quantitative estimates for the covering properties of the corresponding decompositions. Afterwards, we apply the developed methods to obtain an abstract ergodic theorem for a class of functions mapping subsets of the group into some Banach space. Moreover, applications of this convergence result are studied: the uniform existence of the integrated density of states (IDS) for operators on amenable Cayley graphs; the uniform existence of the IDS for operators on discrete structures being quasi-isometric to some amenable group; the approximation of L2-Betti numbers on cellular CW-complexes; the existence of certain densities of clusters in a percolated Cayley graph.
Suppose E is a real uniformly smooth Banach space and K is a nonempty closed convex and bounded subset of E, T:K → K is a Lipschitz pseudo-contraction. It is proved that the Picard iterates of a suitably defined operator converges strongly to the unique fixed point of T. Furthermore, this result also holds for the slightly larger class of Lipschitz strong hemi-contractions. Related results deal with strong convergence of the Picard iterates to the unique solution of operator equations involving Lipschitz strongly accretive maps. Apart from establishing strong convergence, our theorems give existence, uniqueness and convergence-rate which is at least as fast as a geometric progression. (author). 51 refs
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
Chen Rudong
2011-01-01
Full Text Available Abstract We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011 and Lu et al. (Nonlinear Anal, 71(3-4, 1032-1041, 2009. 2000 Mathematics subject classification 47H05; 47H09; 65J15
Improved bounds in the scaled Enflo type inequality for Banach spaces
Giladi, Ohad
2010-01-01
It is shown that if (X,||.||_X) is a Banach space with Rademacher type p \\ge 1, then for every integer n there exists an even integer m X, \\Avg_{x,\\e}[||f(x+ m\\e/2)-f(x)}||_X^p] < C(p,X) m^p\\sum_{j=1}^n\\Avg_x[||f(x+e_j)-f(x)||_X^p], where the expectation is with respect to uniformly chosen x \\in Z_m^n and \\e \\in \\{-1,1\\}^n, and C(p,X) is a constant that depends on p and the Rademacher type constant of X. This improves a bound of m < Cn^{3-2/p} that was obtained in [Mendel, Naor 2007]. The proof is based on an augmentation of the "smoothing and approximation" scheme, which was implicit in [Mendel, Naor 2007].
Song, Guohui; Zhang, Haizhang
2011-01-01
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space that satisfies the linear representer theorem brings the advantage of discarding the hypothesis error from the sum automatically. Following this direction, we illustrate how reproducing kernel Banach spaces with the l1 norm can be applied to improve the learn...
Perturbations of Bessel Sequences of Order p in a Banach Space%Banach空间中P阶Bessel列的扰动
王秋芬; 曹怀信; 武海辉
2011-01-01
应用算子论方法研究Banach空间X中p(1＜P＜∞)阶Bessel列的扰动问题,对X中的任一p阶Bessel列f={fi}i∈I,定义了有界线性算子Tf:X*→lp,建立了从全体p阶Bessel列组成的Banach空间BpX(Ⅰ)到算子空间B(X*,lp)上的等距线性同构α:f→Tf,并给出了p阶Bessel列的扰动定理.%With the aid of operator theory, some perturbations of Bessel sequences of order p in a Banach space X were discussed. For a Bessel sequence f = {fi} i∈I of order p in X, we defined a bounded linear operator Tf from X* into lp and established a linear isometry isomorphism a from the space BpX (I) of all the Bessel sequences of order p in a Banach space X into the operator space B(X*,lp) defined by α(f) = Tr. In the light of operator theory, some results on perturbations of Bessel sequences of order p were given, which are helpful to the study of frames of order p for a Banach space.
Quasi-geostrophic equations with initial data in Banach spaces of local measures
Sadek Gala
2005-06-01
Full Text Available This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations $$displaylines{ partial_{t}heta+u ablaheta+( -Delta ^{gamma}heta =0 quad hbox{on }mathbb{R}^{d}imes] 0,+infty[cr heta( x,0 =heta_{0}(x, quad xinmathbb{R}^{d} }$$ where 0 less than $gammaleq 1$ is a fixed parameter and the velocity field $u=(u_{1},u_{2},dots,u_{d} $ is divergence free; i.e., $ abla u=0$. The initial data $heta_{0}$ is taken in Banach spaces of local measures (see text for the definition, such as Multipliers, Lorentz and Morrey-Campanato spaces. We will focus on the subcritical case 1/2 less than $gammaleq1$ and we analyse the well-posedness of the system in three basic spaces: $L^{d/r,infty}$, $dot {X}_{r}$ and $dot {M}^{p,d/r}$, when the solution is global for sufficiently small initial data. Furtheremore, we prove that the solution is actually smooth. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
Sokhuma, K.; A. Kaewkhao
2010-01-01
Let be a nonempty compact convex subset of a uniformly convex Banach space , and let and be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that and for all . We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary by , , where and , are sequences of positive numbers satisfying , , converges strongly to a common fixed point of and ; that is, there exists such tha...
M. Eshaghi Gordji
2009-01-01
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.
Vara Prasad KNVV
2006-01-01
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 .
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 Σn=1∞(kin - 1) in}n=1∞ be a sequence in [ε, 1 - ε ], 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 - α1n)xn + α1nT1nyn+m-2, yn+m-2 = (1 - α2n)xn + α2nT2nyn+m-3, ..., yn = (1 - αmn)xn + αmnTmnxn , 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)
Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces
Austin, Tim; Tessera, Romain
2010-01-01
Let $\\H$ denote the discrete Heisenberg group, equipped with a word metric $d_W$ associated to some finite symmetric generating set. We show that if $(X,\\|\\cdot\\|)$ is a $p$-convex Banach space then for any Lipschitz function $f:\\H\\to X$ there exist $x,y\\in \\H$ with $d_W(x,y)$ arbitrarily large and \\begin{equation}\\label{eq:comp abs} \\frac{\\|f(x)-f(y)\\|}{d_W(x,y)}\\lesssim \\left(\\frac{\\log\\log d_W(x,y)}{\\log d_W(x,y)}\\right)^{1/p}. \\end{equation} We also show that any embedding into $X$ of a ball of radius $R\\ge 4$ in $\\H$ incurs bi-Lipschitz distortion that grows at least as a constant multiple of \\begin{equation}\\label{eq:dist abs} \\left(\\frac{\\log R}{\\log\\log R}\\right)^{1/p}. \\end{equation} Both~\\eqref{eq:comp abs} and~\\eqref{eq:dist abs} are sharp up to the iterated logarithm terms. When $X$ is Hilbert space we obtain a representation-theoretic proof yielding bounds corresponding to~\\eqref{eq:comp abs} and~\\eqref{eq:dist abs} which are sharp up to a universal constant.
Lp-DICHOTOMY OF LINEAR DIFFERENTIAL EQUATIONS IN AN ARBITRARY BANACH SPACE
A. KOSSEVA; S. KOSTADINOV; K. SCHNEIDER
2003-01-01
The notion of Lp-dichotomy for linear differential equations with possibly unbounded oper-ator is introduced. By help of Banach fixed point theorem sufficient conditions for the existenceof bounded solutions of nonlinear differential equations with an Lp-dichotomous linear part areobtained.
Li Shan LIU
2001-01-01
In this paper, we will prove that Ky Fan's Theorem (Math. Z. 112(1969), 234-240) is true for1-set-contractive maps defined on a bounded closed convex subset K in a Banach space with intK ≠φ.This class of 1-set-contractive maps includes condensing maps, nonexpansive maps, semicontractivemaps, LANE maps and others. As applications of our theorems, some fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations andimprovements of the recent results obtained by many authors.
K. N. V. V. Vara Prasad
2007-01-01
Full Text Available Let E be an arbitrary real Banach space and K a nonempty, closed, convex (not necessarily bounded subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant LÃ¢Â‰Â¥1, 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 T.
Ring homomorphisms on real Banach algebras
Sin-Ei Takahasi
2003-08-01
Full Text Available Let B be a strictly real commutative real Banach algebra with the carrier space ÃŽÂ¦B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ÃÂ:AÃ¢Â†Â’B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ÃÂ(A is contained in the radical of B.
In this paper we investigate the relation between weak convergence of a sequence {μn} of probability measures on a Polish space S converging weakly to the probability measure μ and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S→X, it follows that limn∞ ∫Sf, dμn = ∫Sf, dμ —the limit one has for bounded and continuous real (or complex)—valued functions on S. This result is then applied to the stability theory of Feynman’s operational calculus where it is shown that the theory can be significantly improved over previous results.
D. A. Robbins
1994-12-01
Full Text Available We study bundles of Banach algebras ÃÂ€:AÃ¢Â†Â’X, where each fiber Ax=ÃÂ€Ã¢ÂˆÂ’1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra ÃŽÂ“(ÃÂ€ relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle ÃÂ€:AÃ¢Â†Â’X relates to the standard adjunction of identities to the fibers.
Boubakari Ibrahimou
2013-01-01
maximal monotone with and . Using the topological degree theory developed by Kartsatos and Quarcoo we study the eigenvalue problem where the operator is a single-valued of class . The existence of continuous branches of eigenvectors of infinite length then could be easily extended to the case where the operator is multivalued and is investigated.
Banach空间范数的 k-点态粗性和 k-粗性%k- pointwise roughness and k- roughness on Banach spaces
义德日胡; 苏雅拉图
2012-01-01
对 Banach 空间范数引入了 k-点态粗和 k-粗的概念，利用 Banach 空间理论的方法，给出了 x ∈ S(X)为范数的 k-粗糙点和 X 的范数是 k-粗的一些充分必要条件，证明了(k +1)-粗糙点是 k-粗糙点以及 k-粗糙点与 Fr´echet 可微性的一些结果。特别地，在 k =1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果% In this paper, the k- pointwise rough and k- rough norm on Banach space are introduced. By the method of Banach space theory, the some necessary and suﬃcient conditions of k- rough point of norm and k-rough norm of X are given respectively. We proved that (k + 1)- rough point is k- rough point and obtained some results related with k- rough point and Fr´echet differentiability. In particular, when k = 1 our results contains the results of about rough point of norm, pointwise rough norm and rough norm.
Metatext Phenomenon: Mode of Irony in Reflexive-Interpretative Space
Kuznetsova, Anna V.
2013-01-01
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...
Modification of Otolith Reflex Asymmetries Following Space Flight
Clarke, Andrew H.; Schoenfeld, Uwe; Wood, Scott J.
2011-01-01
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.
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
Raja P
2008-01-01
Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
Networks for the weak topology of Banach and Fréchet spaces
Gabriyelyan, S.; Kąkol, Jerzy; Kubiś, Wieslaw; Marciszewski, W.
2015-01-01
Roč. 432, č. 2 (2015), s. 1183-1199. ISSN 0022-247X R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : Fréchet space * space of continuous functions * locally convex space Subject RIV: BA - General Mathematics Impact factor: 1.120, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022247X15006836
One-sided interpolation of injective tensor products of Banach spaces
Michels, Carsten
2007-01-01
The Kouba formula for the complex interpolation of injective tensor products requires all spaces involved to be at least of cotype $2$. We show that this can be weakened when one side of the tensor products is fixed.
CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES
HANDEGUANG
1996-01-01
This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that erevy linear derivation of a nest algebra algN is continuous provided that one of the following conditions is satisfied:(1)0+（包含）0.(2)X-（包含于）X.(3)there exists a non-trivial idempotnet p in algN such that the range of p belongs to N, It is also proved that every additive derivation of a nest algebra is automatically linear if the underlying normed space is infinite dimemnsional.
Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line
Mu Fa CHEN
2002-01-01
Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities,spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimatesfor the optimal constants in the inequalities are presented. As a typical application, the logarithmicSobolev constant is carefully examined.
New Fixed Point Results with PPF Dependence in Banach Spaces Endowed with a Graph
Hussain, N.; S. Khaleghizadeh; P. Salimi; Akbar, F.
2013-01-01
We introduce the concept of an ${\\alpha }_{c}$ -admissible non-self-mappings with respect to ${\\eta }_{c}$ and establish the existence of PPF dependent fixed and coincidence point theorems for ${\\alpha }_{c}{\\eta }_{c}$ - $\\psi $ -contractive non-self-mappings in the Razumikhin class. As applications of our PPF dependent fixed point and coincidence point theorems, we derive some new fixed and coincidence point results for $\\psi $ -contractions whenever the range space is endowed with a graph ...
Botelho, Fabio
2014-01-01
This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
$\\sigma $ -Approximately Contractible Banach Algebras
Momeni, M; Yazdanpanah, T.; Mardanbeigi, M. R.
2012-01-01
We investigate $\\sigma $ -approximate contractibility and $\\sigma $ -approximate amenability of Banach algebras, which are extensions of usual notions of contractibility and amenability, respectively, where $\\sigma $ is a dense range or an idempotent bounded endomorphism of the corresponding Banach algebra.
娄健; 何欣枫; 何震
2009-01-01
In this paper,we introduce and study a new system of variational inclusions involving (H,η)-monotone operators in Banach space.Using the resolvent operator associated with (H,η)-monotone operators,we prove the existence and uniqueness of solutions for this new system of variational inclusions.We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the iterative sequence generated by the algorithm.
Fréchet differential of a power series in Banach algebras
Benedetto Silvestri
2010-01-01
Full Text Available We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \\(C(T : A \\mapsto [A,T]\\. Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.
Nonlinear potentials in function spaces
Rao, Murali; Vondraček, Zoran
2002-01-01
We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capa...
An inner product for a Banach-algebra
An inner product is defined on a commutative Banach algebra with an essential involution and the resultant inner product space is shown to be a topological algebra. Several conditions for its completeness are established and moreover, a decomposition theorem is proved. It is shown that every commutative Banach algebra with an essential involution has an auxiliary norm which turns it into an A*-algebra. (author). 6 refs
A Generation Condition of Integrated Bisemigroup on Banach Space%Banach空间积分双半群的生成条件
许跟起; 邵琛
2002-01-01
研究Banach空间中积分双半群的生成条件. 利用算子A的豫解算子,给出了积分双半群T(t)的生成定理. 结果表明:如果对任意的x∈X,f∈X*,以及()|λ|≤δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t), t∈R,S(t)强连续且满足积分双半群的定义.%The generation condition of integrated bisemigroup in Banach space is studied in this paper. Using the resolvent of operator A, a generation theorem of integrated bisemigroup T(t) is proved. The result is showed that if ()|λ|≤δ,λ∈ρ(A), and satisfy 〈∈Lp(R), for all x∈X, f∈X*, then there exists a family operators S(t), t∈R, which is strongly continuous and satisfies the definition of integrated bisemigroup.
Banach Algebras Associated to Lax Pairs
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
Spectral synthesis for Banach Algebras II
Feinstein, J. F.; Somerset, D. W. B.
1999-01-01
This paper continues the study of spectral synthesis and the topologies $\\tau_{\\infty}$ and $\\tau_r$ on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C$^*$-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of $\\tau_{\\infty}$. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of $\\tau_r$.
Fundamental aspects of vector-valued Banach limits
Garcia-Pacheco, F. J.; Perez-Fernandez, F. J.
2016-04-01
This paper is divided into four parts. In the first we study the existence of vector-valued Banach limits and show that a real Banach space with a monotone Schauder basis admits vector-valued Banach limits if and only if it is 1-complemented in its bidual. In the second we prove two vector-valued versions of Lorentz' intrinsic characterization of almost convergence. In the third we show that the unit sphere in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X) cannot be obtained via compositions of surjective linear isometries with vector-valued Banach limits. In the final part we show that if X enjoys the Krein-Milman property, then the set of vector-valued Banach limits is a face of the unit ball in the space of all continuous linear operators from \\ell_∞(X) to X which are invariant under the shift operator on \\ell_∞(X).
From a special class of systems has been used the linear homogeneous differential equations with impulse effect in Minkowski space field theory with time dependent boundary conditions, i.e. those of moving mirrors. The field theoretical approach for studing the properties of the vacuum starts from an analysis of the behaviour of local field quantities in Minkowski space with uniformly moving mirrors. For the impulsive moving mirror model is the real process of interaction between the quantum field and the external mirror a subject to disturbances in its evolution acting in time very short compared with the entire duration of the process. The stability of the process in the stability of the vacuum state energy. 7 refs
Zhang Peiguo
2011-01-01
Full Text Available Abstract By obtaining intervals of the parameter λ, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. MSC: 34B15; 34B16.
2008-01-01
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (Ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A : there exists an element p in S such that Xp(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit ball S*(1) = {f ∈ S* : Xf* 1} of the random conjugate space (S*,X*) of (S,X) is compact under the random weak star topology on (S*,X*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {An : n ∈ N} of at most countably many μ-atoms from E∩A such that E =∪n∞=1 An and for each element F in E∩A, there is an H in the σ-algebra generated by {An : n ∈ N} satisfying μ(F △H) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding classical case. Further, Banach-Bourbaki-Kakutani-mulian (briefly, BBKS) theorem in a complete random normed module is established as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S : Xp 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E∩A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James theorem and
GUO TieXin
2008-01-01
Let(Ω,A,μ)be a probability space,K the scalar field R of real numbers or C of complex numbers,and(S,X)a random normed space over K with base(Ω,A,μ).Denote the support of(S,X)by E,namely E is the essentiaI supremum of the ser {A∈A:there exists an element p in S such that Xp(ω)＞0 for almost all ω in A}. In this paper,Banach-Alaoglu theorem in a random normed space is first established as follows:The random closed unit ball S*(1)={f∈S*:X*f≤1}of the random conjugate space(S*,x*)of(S,X)is compact under the random weak star topology on (S*,X*)iff E∩A=:{E∩A|A∈A}is essentially purely μ-atomic(namely,there exists a disjoint family{An:n∈N}of at most countably many μ-atoms from E∩A such that E=∪∞n=1 An and for each element F in E∩A,there is an H in the σ-algebra generated by{An:n∈N)satisfying μ(F△H)=0),whose proof forces us to provide a key topological skill,and thus is much more involved than the corresponding classical case.Further,Banach-Bourbaki-Kakutani-Smulian(briefly,BBKS)theorem in a complete random normed module is established as follows:If(S,X)is a complete random normed module,then the random closed unit ball S(1)={p∈S:Xp≤1}of(S,X)is compact under the random weak topology on(S,X)iff both(S,X)is random reflexive and E∩A is essentially purely μ-atomic.Our recent work shows that the famous classical James theorem still holds for an arbitrary complete random normed module,namely a complete random normed module is random reflexive iff the random norm of an arbitrary almost surely bounded random linear functional on it is attainable on its random closed unit ball,but this paper shows that the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they possess extremely simple stratification structure,namely their supports are essentially purely μ-atomic.Combining the James theorem and BBKS theorem in complete random normed modules leads directly to an interesting
Moduli and Characteristics of Monotonicity in Some Banach Lattices
Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
-, - (2010), s. 852346. ISSN 1687-1812 R&D Projects: GA AV ČR IAA100190804; GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach lattice * characteristics of monotonicity * Orlicz function space * Orlicz sequence space Subject RIV: BA - General Mathematics http://www. fixed pointtheoryandapplications.com/content/2010/1/852346
Derivations into Duals of Ideals of Banach Algebras
M E Gorgi; T Yazdanpanah
2004-11-01
We introduce two notions of amenability for a Banach algebra $\\mathcal{A}$. Let be a closed two-sided ideal in $\\mathcal{A}$, we say $\\mathcal{A}$ is -weakly amenable if the first cohomology group of $\\mathcal{A}$ with coefficients in the dual space * is zero; i.e., $H^1(\\mathcal{A},I^*) =\\{0\\}$, and, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the -weak amenability of a Banach algebra $\\mathcal{A}$ for some special closed two-sided ideal .
张育梅; 程毅; 王靖华
2012-01-01
利用同伦方法证明了一类发展方程反周期解在Banach空间中的存在性和唯一性.先构造同伦方程,再对方程做先验估计.最后通过定义解算子,运用拓扑度方法,给出了发展方程反周期解存在的充分条件.%We proved the existence and uniqueness of a class of evolution equation in Banach space using homotopy methods. We constructed a homotopy equation and made α priori, estimate to this equation. Under the definition solution operator conditions, a sufficient condition of existence of solutions was obtained by means of topological degree method.
赵吕慧子; 孙经先
2011-01-01
The definition of a class of new operators, convex-power 1-set-contraction operators in Banach spaces is giv en , and the existence of fixed points of this class of operators is studied. By using methods of approximation by opera tors, the fixed point theorems of Rothe and Altman type convex-power 1-set-contraction operators is obtained, which generalize fixed point theorems of 1-set-contraction operators.%在Banach空间中给出了一类新算子——凸幂1集压缩算子的定义,研究了这类新算子不动点的存在性问题,利用算子逼近的方法,获得了Rothe及Altman型凸幂1集压缩算子的不动点定理,推广了1集压缩算子的不动点定理.
Stability of functional equations in Banach algebras
Cho, Yeol Je; Rassias, Themistocles M; Saadati, Reza
2015-01-01
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the l...
Abbas NAJATI
2009-01-01
In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equation f(x+y/2+z)-g(x-y/2+z)=h(y).This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soe., 72, 297-300 (1978).
Several complex variables and Banach algebras
This paper aims to present certain applications of the theory of holomorphic functions of several complex variables to the study of commutative Banach algebras. The material falls into the following sections: (A) Introcution to Banach algebras (this will not presuppose any knowledge of the subject); (B) Groups of differential forms (mainly concerned with setting up a useful language); (C) Polynomially convex domains. (D) Holomorphic functional calculus for Banach algebras; (E) Some applications of the functional calculus. (author)
Approximately -Jordan Homomorphisms on Banach Algebras
Karimi T
2009-01-01
Full Text Available Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b to each approximate -Jordan homomorphism between two commutative Banach algebras there corresponds a unique -ring homomorphism near to for all .
Erratum to: “Polynomial algebras on classical Banach spaces”
D'Alessandro, Stefania; Hájek, Petr Pavel; Johanis, M.
2015-01-01
Roč. 207, č. 2 (2015), s. 1003-1012. ISSN 0021-2172 R&D Projects: GA ČR(CZ) GAP201/11/0345; GA MŠk(CZ) 7AMB12FR003 Institutional support: RVO:67985840 Keywords : Banach space * polynomial algebra Subject RIV: BA - General Mathematics Impact factor: 0.787, year: 2014 http://link.springer.com/article/10.1007%2Fs11856-015-1155-y
Segal algebras in commutative Banach algebras
INOUE, Jyunji; TAKAHASI, Sin-Ei
2014-01-01
The notion of Reiter's Segal algebra in commutative group algebras is generalized to a notion of Segal algebra in more general classes of commutative Banach algebras. Then we introduce a family of Segal algebras in commutative Banach algebras under considerations and study some properties of them.
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) proposes to develop an advanced reflexive structure system to increase the survivability of aerostructures. This reflexive...
刘玉波; 张凤敏; 苟长义
2009-01-01
首先证明了取值于Banach空间上强连续的向量值函数是可积分的;然后用初等方法证明了向量值函数的柯西积分公式和高阶导数公式;最后讨论了取值于lp(p≥1)空间上的向量值函数解析、可积、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式,并且给出了有限维赋范线性空间上的向量值函数连续、解析、可积、柯西定理、柯西积分公式和高阶导数公式与其各分量函数的关系和表示形式.%The strongly continuous vector valued functions in Banach space are proved integrable. The Cauchy integral for-mula and higher.derivative formula of vector-valued functions are proved using the elementary method. The relationship be-tween vector valued functions in the space of lp (p≥1) and their componential functions about analyticity, integrability, the Cauchy integral formula and higher derivative formula are discussed. And the relationship between vector valued functions in finite dimensional normed linear space and their componential functions about continuity, analyticity, integrability, Cauchys theorem, the Cauchy integral formula and higher derivative formula are also given.
The Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game
Fishman, Lior; Reams, Vanessa; Simmons, David
2015-01-01
We introduce two new mathematical games, the Banach-Mazur-Schmidt game and the Banach-Mazur-McMullen game, merging well-known games. We investigate the properties of the games, as well as providing an application to Diophantine approximation theory, analyzing the geometric structure of certain Diophantine sets.
Aileen Collier
2016-05-01
Full Text Available Background: There is international consensus of the need for improved palliative and end-of-life care in hospital settings. What is less clear is how such improvements might be realised in practice. Research and practice improvement methodologies need to acknowledge the relational, spiritual, moral and ethical as well as physical dimensions of death and dying if improvements in care are to be achieved. Aims and objectives: The aim of this article is to explore the potential of video-reflexive ethnography as a practice development methodology to improve care of people with a life-limiting illness in the hospital setting. Methods: The study used video-reflexive ethnography and was underpinned by an indigenous research ethical framework. Findings: Study findings highlight the potential of video-reflexive ethnography as a practice development methodology. The reach of video extended internally and externally beyond immediate practice research sites to make hospital dying tangible. The research acted as a disruptive innovation, foregrounding peoples’ (patients and families expertise as well as that of healthcare workers. For some patient and family participants, the research offered a visual legacy. Conclusions: The theories underpinning video-reflexive ethnography and practice development are closely aligned; the former has potential as a practice development methodology to promote person-centred palliative and end-of-life care. The underpinning philosophical, ethical and values framework through which it is applied, along with the skills and aptitude of facilitation, are critical if its potential is to be realised. Implications for practice development: The delivery of person-centred end-of-life care may be facilitated by: Healthcare workers seeing themselves and those they care for differently Healthcare organisations seeing their employees as well as patients and families differently Researchers also being prepared to see themselves differently
An elementary approach to a lattice-valued Banach-Stone Theorem
Jinxi Chen
2007-01-01
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} $.
Peterka, Robert J.
1993-01-01
Recent studies have identified significant correlations between space motion sickness susceptibility and measures of disconjugate torsional eye movements recorded during parabolic flights. These results support an earlier proposal which hypothesized that an asymmetry of otolith function between the two ears is the cause of space motion sickness. It may be possible to devise experiments that can be performed in the 1 g environment on earth that could identify and quantify the presence of asymmetric otolith function. This paper summarizes the known physiological and anatomical properties of the otolith organs and the properties of the torsional vestibulo-ocular reflex which are relevant to the design of a stimulus to identify otolith asymmetries. A specific stimulus which takes advantage of these properties is proposed.
Wood, Scott J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, less than 20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. One result of this study will be to characterize the variability (gain, asymmetry) in both otolith-ocular responses and motion perception during variable radius centrifugation, and measure the time course of post-flight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved
Banach function algebras and certain polynomially norm-preserving maps
Hosseini, Maliheh; Sady, Fereshteh
2012-01-01
Let $A$ and $B$ be Banach function algebras on compact Hausdorff spaces $X$ and $Y$, respectively. Given a non-zero scalar $\\alpha$and $s,t\\in \\Bbb N$ we characterize the general form of suitable powers of surjective maps $T, T': A \\longrightarrow B$ satisfying $\\|(Tf)^s (T'g)^t-\\alpha\\|_Y=\\|f^s g^t-\\alpha \\|_X$, for all $f,g \\in A$, where $\\|\\cdot \\|_X$ and $\\|\\cdot \\|_Y$ denote the supremum norms on $X$ and $Y$, respectively. A similar result is given for the case where $T...
Eventually and asymptotically positive semigroups on Banach lattices
Daners, Daniel; Glück, Jochen; Kennedy, James B.
2016-09-01
We develop a theory of eventually positive C0-semigroups on Banach lattices, that is, of semigroups for which, for every positive initial value, the solution of the corresponding Cauchy problem becomes positive for large times. We give characterisations of such semigroups by means of spectral and resolvent properties of the corresponding generators, complementing existing results on spaces of continuous functions. This enables us to treat a range of new examples including the square of the Laplacian with Dirichlet boundary conditions, the bi-Laplacian on Lp-spaces, the Dirichlet-to-Neumann operator on L2 and the Laplacian with non-local boundary conditions on L2 within the one unified theory. We also introduce and analyse a weaker notion of eventual positivity which we call "asymptotic positivity", where trajectories associated with positive initial data converge to the positive cone in the Banach lattice as t → ∞. This allows us to discuss further examples which do not fall within the above-mentioned framework, among them a network flow with non-positive mass transition and a certain delay differential equation.
Spectral theory of linear operators and spectral systems in Banach algebras
Müller, Vladimir
2003-01-01
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed. The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book. The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem. This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach alg...
Tensor products of commutative Banach algebras
Shobha Madan
1982-09-01
Full Text Available Let A1, A2 be commutative semisimple Banach algebras and A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚A2 be their projective tensor product. We prove that, if A1Ã¢ÂŠÂ—Ã¢ÂˆÂ‚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.
Admissibility of Linear Systems in Banach Spaces
GUO Fa-ming
2005-01-01
In this paper, infinite-time p-admissibility of unbounded operators is introduced and the Co-semigroup characterization of the infinite-time p-admissibility of unbounded observation operators is given. Moreover, the analogous result for the infinite-time p-admissibility of unbounded control operators is presented.
... area into the arm may be present (these nerves are called brachial plexus). A Moro reflex in an older infant, child, or adult is ... be done to examine the child's muscles and nerves. Diagnostic ... absent reflex, may include: Shoulder x-ray Tests for disorders ...
(2-1)-Ideal amenability of triangular banach algebras
S Etemad; M Ettefagh
2015-05-01
Let $\\mathcal{A}$ and $\\mathcal{B}$ be two unital Banach algebras and let $\\mathcal{M}$ be an unital Banach $\\mathcal{A}$, $\\mathcal{B}$-module. Also, let $\\mathcal{T}=\\left[\\begin{smallmatrix} \\mathcal{A} & \\mathcal{M}\\\\ & \\mathcal{B}\\end{smallmatrix}\\right]$ be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435–1452) have studied the -weak amenability of triangular Banach algebras. In this paper, we investigate (2-1)-ideal amenability of $\\mathcal{T}$ for all ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2-1)-ideal amenability of $\\mathcal{T}$ depends on (2-1)-ideal amenability of Banach algebras $\\mathcal{A}$ and $\\mathcal{B}$.
Multipliers of Weighted Semigroups and Associated Beurling Banach Algebras
S J Bhatt; P A Dabhi; H V Dedania
2011-11-01
Given a weighted discrete abelian semigroup $(S,)$, the semigroup $M_(S)$ of -bounded multipliers as well as the Rees quotient $M_(S)/S$ together with their respective weights $\\overline{}$ and $\\overline{}_q$ induced by are studied; for a large class of weights , the quotient $\\ell^1(M_(S),\\overline{})/\\ell^1(S,)$ is realized as a Beurling algebra on the quotient semigroup $M_(S)/S$; the Gel’fand spaces of these algebras are determined; and Banach algebra properties like semisimplicity, uniqueness of uniform norm and regularity of associated Beurling algebras on these semigroups are investigated. The involutive analogues of these are also considered. The results are exhibited in the context of several examples.
A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences
Loaiza Ossa, Gabriel Ignacio; Quiceno Echavarría, Héctor Román
2013-01-01
For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears ...
Sifat Aljabar Banach Komutatif dan Elemen Identitas pada Kelas D(K
Malahayati Malahayati
2013-11-01
Full Text Available The first Baire class of bounded functions on separable metric spaces K denoted by B1(k. One of the most important subclass of B1(k is D(K, by D(K is denoted the class of all functions on K which are differences of bounded semicontinuous functions. In this paper we proved that D(K is abelian Banach algebra and identity element
Diederichsen, Louise; Krogsgaard, Michael; Voigt, Michael;
2002-01-01
long latency (300 ms) excitatory reflex has been found when nerves in the capsule were stimulated electrically during shoulder surgery. In addition, when the anterior-inferior capsule was excited in conscious humans with modest amplitude electrical stimuli during muscle activity, a strong inhibition...... likely that the joint receptors have a more distinct role for the kinaestethic sense than muscle receptors. In cats a direct reflex from the afferents innervating the shoulder to the muscles around the shoulder has been presented. The reflex had an extremely short latency (2.7-3.1 ms). In man, a very...... was found with an average latency of 33 ms. Stimulation of the sensory nerves in the coracoacromial ligament has also been found to modify muscle activity strongly. Even though our understanding of the control of shoulder motion is incomplete, it is clear that sensory inputs can strongly modify muscle...
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras
Hirasawa Go
2005-01-01
Full Text Available We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to .
Reflexive Aero Structures for Enhanced Survivability Project
National Aeronautics and Space Administration — Cornerstone Research Group Inc. (CRG) will develop an advanced reflexive structure technology system to increase the survivability of future systems constructed of...
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, 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.
On $\\phi$-ergodic property of Banach modules
Nemati, Mehdi
2015-01-01
Let ${\\mathcal A}$ be a Banach algebra and let $\\phi$ be a non-zero character on ${\\mathcal A}$. We introduce the notion of $\\phi$-ergodic property for a Banach right ${\\mathcal A}$-module $X$. This concept considerably generalizes the existence of $\\phi$-means of norm one on ${\\mathcal A}^*$. We also show that the $\\phi$-ergodic property of $X$ is related to some other properties such as a Hahn-Banach type extension property and the existence of $\\phi$-means of norm one on ...
Very Smooth Points of Spaces of Operators
T S S R K Rao
2003-02-01
In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is an -ideal in the space of bounded operators, a very smooth operator attains its norm at a unique vector (up to a constant multiple) and ( ) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon–Nikodým property. We give an example of a smooth Banach space without any very smooth points.
Ideal Amenability of Banach Algebras on Locally Compact Groups
M Eshaghi Gordji; S A R Hosseiniun
2005-08-01
In this paper we study the ideal amenability of Banach algebras. Let $\\mathcal{A}$ be a Banach algebra and let be a closed two-sided ideal in $\\mathcal{A}, \\mathcal{A}$ is -weakly amenable if $H^1(\\mathcal{A},I^∗)=\\{0\\}$. Further, $\\mathcal{A}$ is ideally amenable if $\\mathcal{A}$ is -weakly amenable for every closed two-sided ideal in $\\mathcal{A}$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, <20 cm radius), the effects of stimulus frequency (0.15 - 0.6 Hz) are examined on eye movements and motion perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual
Wood, S. J.; Clarke, A. H.; Rupert, A. H.; Harm, D. L.; Clement, G. R.
2009-01-01
Two joint ESA-NASA studies are examining changes in otolith-ocular reflexes and motion perception following short duration space flights, and the operational implications of post-flight tilt-translation ambiguity for manual control performance. Vibrotactile feedback of tilt orientation is also being evaluated as a countermeasure to improve performance during a closed-loop nulling task. METHODS. Data is currently being collected on astronaut subjects during 3 preflight sessions and during the first 8 days after Shuttle landings. Variable radius centrifugation is utilized to elicit otolith reflexes in the lateral plane without concordant roll canal cues. Unilateral centrifugation (400 deg/s, 3.5 cm radius) stimulates one otolith positioned off-axis while the opposite side is centered over the axis of rotation. During this paradigm, roll-tilt perception is measured using a subjective visual vertical task and ocular counter-rolling is obtained using binocular video-oculography. During a second paradigm (216 deg/s, perception. A closed-loop nulling task is also performed with and without vibrotactile display feedback of chair radial position. PRELIMINARY RESULTS. Data collection is currently ongoing. Results to date suggest there is a trend for perceived tilt and translation amplitudes to be increased at the low and medium frequencies on landing day compared to pre-flight. Manual control performance is improved with vibrotactile feedback. DISCUSSION. One result of this study will be to characterize the variability (gain, asymmetry) in both otolithocular responses and motion perception during variable radius centrifugation, and measure the time course of postflight recovery. This study will also address how adaptive changes in otolith-mediated reflexes correspond to one's ability to perform closed-loop nulling tasks following G-transitions, and whether manual control performance can be improved with vibrotactile feedback of orientation.
Modern methods in topological vector spaces
Wilansky, Albert
2013-01-01
Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect
Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra
Yang-Hi Lee
2013-01-01
Full Text Available We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY
TaoChangli; LuShijie; ChenPeixin
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales
MA Tao; LIU Peide
2006-01-01
The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0 ＜ r≤ 1.Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.
The Classical Integral Operators in Weighted Lorentz Spaces with Variable Exponent.
D.M. Israfilov; N.P. Tuzkaya
2006-01-01
In this paper the Lorentz spaces with variable exponent are introduced. These Banach function spaces are defined on the base of variable Lebesgue spaces. Boundedness of classical integral operators are proved in variable Lorentz spaces.
Approximately Linear Mappings in Banach Modules over a C*-algebra
Choonkil PARK; Jian Lian CUI
2007-01-01
Let X and Y be vector spaces. The authors show that a mapping f: X → Y satisfies the functional equation 2df(∑2dj=1(-1)j+1xj/2d)=∑2dj=1(-1)j+1f(xj) with f(0) = 0 if and only if the mapping f: X → Y is Cauchy additive, and prove the stability of the functional equation (++) in Banach modules over a unital C*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C*-algebras, Poisson C*-algebras or Poisson JC*-algebras. As an application, the authors show that every almost homomorphism h: A → B of A into B is a homomorphism when h((2d-1)nuy) = h((2d-1)nu)h(y) or h((2d-1)nuoy) = h((2d-1)nu)oh(y) for all unitaries u ∈ A, all y ∈ A, n= 0, 1, 2,....Moreover, the authors prove the stability of homomorphisms in C*-algebras, Poisson C*-algebras or Poisson JC*-algebras.
Ratner, Helene
through reflexivity in order to change their practices. Reflexivity is thus imbued with a sense of optimism: awareness about how practice is constructed is seen to improve the possibilities for changing it (Ratner 2012). Despite this optimism, “implementing” reflexivity proves difficult as risks of...
The smooth Banach submanifold B*(E,F) in B(E,F)
无
2009-01-01
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for B*(E,F)={T ∈ B+(E,F):dimN(T)=codimR(T)= ∞} without the characteristic numbers,dimN(A) ,codimR(A) ,index(A) and Rank(A) of the equivalent classes above,it is very diffcult to find which class of operators in B*(E,E) forms a smooth submanifold of B(E,F) . Fortunately,we find that B*(E,F) is just a smooth submanifold of B(E,F) with the tangent space TAB*(E,F)={T ∈ B(E,F) :T N(A) -R(A) } for each A ∈ B*(E,F) . Thus the geometric construction of B+(E,F) is obtained,i.e.,B+(E,F) is a smooth Banach submanifold of B(E,F) ,which is the union of the previous smooth submanifolds disjoint from each other. Meanwhile we give a smooth submanifold S(A) of B(E,F) ,modeled on a fixed Banach space and containing A for any A ∈ B+(E,F) . To end these,results on the generalized inverse perturbation analysis are generalized. Specially,in the case E=F=Rn,it is obtained that the set Σr of all n × n matrices A with Rank(A)=r < n is an arcwise connected and smooth hypersurface(submanifold) in B(Rn) with dimΣr=2nr-r2. Then a new geometrical construction of B(Rn) ,analogous to B+(E,F) ,is given besides its analysis and algebra constructions known well.
The Socle and Finite Dimensionality of some Banach Algebras
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
de Jeu, Marcel
2012-01-01
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers. In this paper, we study spectral synthesis for the closed ideals of this associated algebra in two versions, one modeled after C(X), and one modeled after the group algebra of the integers. We identify the closed ideals which are equal to (what is the analogue of) the kernel of their hull, and determine when this holds for all closed ideals, i.e., when spectral synthesis holds. In both models, this is the case precisely when the homeomorphism has no periodic points.
Lectures given at the Banach Center and C.I.M.E. Joint Summer School
Lachowicz, Mirosław
2008-01-01
The aim of this volume that presents Lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex systems in the natural sciences, with a special attention to Biology and Medicine. Mastering complexity implies sharing different tools requiring much higher level of communication between different mathematical and scientific schools, for solving classes of problems of the same nature. Today more than ever, one of the most important challenges derives from the need to bridge parts of a system evolving at different time and space scales, especially with respect to computational affordability. As a result the content has a rather general character; the main role is played by stochastic processes, positive semigroups, asymptotic analysis, kinetic theory, continuum theory and game theory.
Emotionally Colorful Reflexive Games
Tarasenko, Sergey
2011-01-01
This study addresses the matter of reflexive control of the emotional states by means of Reflexive Game Theory (RGT). It is shown how to build a bridge between RGT and emotions. For this purpose the Pleasure-Arousal-Dominance (PAD) model is adopted. The major advantages of RGT are its ability to predict human behavior and unfold the entire spectra of reflexion in the human mind. On the other hand, PAD provides ultimate approach to model emotions. It is illustrated that emotions are reflexive processes and, consequently, RGT fused with PAD model is natural solution to model emotional interactions between people. The fusion of RGT and PAD, called Emotional Reflexive Games (ERG), inherits the key features of both components. Using ERG, we show how reflexive control can be successfully applied to model human emotional states. Up to date, EGR is a unique methodology capable of modeling human reflexive processes and emotional aspects simultaneously.
SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD ∑r OF B(E,F) AND A DIMENSION FORMULA IN B(IRn,IRm)
Jipu Ma
2008-01-01
Given two Banach spaces E, F, let B(E, F) be the set of all bounded linear oper-ators from E into F, ∑r the set of all operators of finite rank r in B(E, F), and ∑#r the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submani-fold in B(E, F) with given expression of its tangent space at each A ∈∑r. In this paper, the equality ∑#r = 1 is proved. Consequently, the following theorem is obtained: for any non-negative integer r, ∑r is a smooth and path connected Banach submanifold in B(E, F) with the tangent space TA∑r={B∈B(E,F): BN(A) R(A)} at each A∈∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = IRn and F = IRm, then ∑r is a smooth and path connected submanifold of B(IRn,IRm) and its dimension is dim ∑r = (m + n)r- r2 for each r, 0 ≤ r < min{n,m}.
Regular norm and the operator semi-norm on a non-unital Banach Algebra
Orenstein, Adam
2014-01-01
We show that if $\\mathfrak{A}$ is a commutative complex non-unital Banach Algebra with norm $\\|\\cdot\\|$, then $\\|\\cdot\\|$ is regular on $\\mathfrak{A}$ if and only if $\\|\\cdot\\|_{op}$ is a norm on $\\mathfrak{A}\\oplus \\mathbb{C}$ and $\\mathfrak{A}\\oplus\\mathbb{C}$ is a commutative complex Banach Algebra with respect to $\\|\\cdot\\|_{op}$.
Convergence Rates in the Law of Large Numbers for Arrays of Banach Valued Martingale Differences
Shunli Hao
2013-01-01
Full Text Available We study the convergence rates in the law of large numbers for arrays of Banach valued martingale differences. Under a simple moment condition, we show sufficient conditions about the complete convergence for arrays of Banach valued martingale differences; we also give a criterion about the convergence for arrays of Banach valued martingale differences. In the special case where the array of Banach valued martingale differences is the sequence of independent and identically distributed real valued random variables, our result contains the theorems of Hsu-Robbins-Erdös (1947, 1949, and 1950, Spitzer (1956, and Baum and Katz (1965. In the real valued single martingale case, it generalizes the results of Alsmeyer (1990. The consideration of Banach valued martingale arrays (rather than a Banach valued single martingale makes the results very adapted in the study of weighted sums of identically distributed Banach valued random variables, for which we prove new theorems about the rates of convergence in the law of large numbers. The results are established in a more general setting for sums of infinite many Banach valued martingale differences. The obtained results improve and extend those of Ghosal and Chandra (1998.
Convexity and w*-compactness in Banach spaces
Granero, A. S.; Hájek, Petr Pavel; Santalucía, V. M.
2004-01-01
Roč. 328, č. 4 (2004), s. 625-631. ISSN 0025-5831 R&D Projects: GA ČR GA201/01/1198; GA AV ČR IAA1019205 Institutional research plan: CEZ:AV0Z1019905 Keywords : krein theorem * weak compactness Subject RIV: BA - General Mathematics Impact factor: 0.790, year: 2004
Stability of stationary and periodic solutions equations in Banach space
A. Ya. Dorogovtsev
1997-01-01
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.
Existence theorems for functional differential equations in Banach spaces
Sghir, A
2009-01-01
This paper concernes with the study of existence theorems for a general class of functional differential equations of the form u'(t)=f(t,u circ g(t,cdot)).The obtained results generalize the retarded functional differential equations [5], [6], [8] and cover singular functional differential equations [1], [3], [4], [7], [9], [12].
On the topological classification of starlike bodies in Banach spaces
Azagra Rueda, Daniel; Dobrowolski, Tadeusz
2003-01-01
Starlike bodies are interesting in nonlinear analysis because they are strongly related to polynomials and smooth bump functions, and their topological and geometrical properties are therefore worth studying. In this note we consider the question as to what extent the known results on topological classification of convex bodies can be generalized for the class of starlike bodies, and we obtain two main results in this line, one which follows the traditional Bessaga-Klee scheme for the classif...
Tools for analysis of Dirac structures on banach spaces
Iftime, Orest V.; Sandovici, Adrian; Golo, Goran
2005-01-01
Power-conserving and Dirac structures are known as an approach to mathematical modeling of physical engineering systems. In this paper connections between Dirac structures and well known tools from standard functional analysis are presented. The analysis can be seen as a possible starting framework
Reflexive intensification in Spanish: Toward a complex reflexive?
Pedersen, Johan
2005-01-01
Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo......Spanish, intensifier, intensification, reflexive pronouns, anaphor, reanalysis, grammaticalization, sí, mismo...
Vestibular reflexes of otolith origin
Wilson, Victor J.
1988-01-01
The vestibular system and its role in the maintenance of posture and in motion sickness is investigated using cats as experimental subjects. The assumption is that better understanding of the physiology of vestibular pathways is not only of intrinsic value, but will help to explain and eventually alleviate the disturbances caused by vestibular malfunction, or by exposure to an unusual environment such as space. The first project deals with the influence on the spinal cord of stimulation of the vestibular labyrinth, particularly the otoliths. A second was concerned with the properties and neural basis of the tonic neck reflex. These two projects are related, because vestibulospinal and tonic neck reflexes interact in the maintenance of normal posture. The third project began with an interest in mechanisms of motion sickness, and eventually shifted to a study of central control of respiratory muscles involved in vomiting.
The compactum of a semi-simple commutative Banach algebra
Abduliah H. Al-Moajil
1984-12-01
Full Text Available Let A be a commutative semi-simple Banach algebra such that the set consisting of finite sums of elements from minimal left ideals coincides with that of finite sums of elements from minimal right ideals. Let S(A (the socle of A denote this set. Let C(A denote the set of elements x in A such that the map aÃ¢Â†Â’xax is compact. It is shown that C(A is the norm closure of S(A.
Mario Cardano
2014-01-01
Full Text Available This essay deals with a relevant and controversial topic – objectivity in ethnographic research. More specifically, I would like to examine how reflexive procedures, more precisely “reflexive account”, can increase the robustness of results gained through an ethnographic research. The essay is organized in five parts. I will start by giving a preliminary definition of the two key concepts which are at the center of the analysis – objectivity and reflexivity. I will then give a brief description of the epistemological framework in which the proposed conceptions of objectivity and reflexivity are located. Thirdly, I move on to consider the epistemic status of ethnographic research, and will emphasize that ethnographies are not just “theory-laden”, as many writers have stated, but also “praxis” or “procedure laden”. In other words, I will stress that it is not only theories which are inevitably embedded in research, influencing how observations can be made; much the same can also be said of the concrete research practices which contribute to determine the experience of the ethnographer and its representation in a text. Fourthly, I will discuss why it is useful to employ reflexive practices, and then immediately afterwards will illustrate the ways in which reflexive descriptions can contribute to greater objectivity of ethnographic accounts. In conclusion, I will discuss a number of objections which have been raised against this use of reflexivity.
Petrov, S.
2000-08-20
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.
Krogsgaard, Michael R; Dyhre-Poulsen, Poul; Fischer-Rasmussen, Torsten
2002-01-01
The idea of muscular reflexes elicited from sensory nerves of the cruciate ligaments is more than 100 years old, but the existence of such reflexes has not been proven until the recent two decades. First in animal experiments, a muscular excitation could be elicited in the hamstrings when the...... anterior cruciate ligament (ACL) was pulled, and tension in the ligament caused activity of the gamma motor neurones of the muscles around the knee. Impulses from the sensory nerves in ACL were activated during motion of the knee, in particular overstretching and combined extension and rotation. In humans...... isokinetic muscle work, and also during dynamic activity (gait). This inhibitory reflex subjectively resembledgiving way. The latency of the reflex was short in animals (about 3 ms) and long in humans (60-120 ms), probably caused by differences in the experimental setup and between species. The long latency...
Simplified and Equivalent Characterizations of Banach Limit Functional and Strong Almost Convergence
You, Chao
2009-01-01
In this paper, we give simplified and equivalent characterizations of Banach limit functional, which is the minimum requirement to characterize strong almost convergence. With this machinery, we show that Hajdukovic's quasi-almost convergence is equivalent to strong almost convergence.
Convolution and Involution on Function Spaces of Homogeneous Spaces
Farashahi, Arash Ghaani
2012-01-01
Let $G$ be a locally compact group and also let $H$ be a compact subgroup of $G$. It is shown that, if $\\mu$ is a relatively invariant measure on $G/H$ then there is a well-defined convolution on $L^1(G/H,\\mu)$ such that the Banach space $L^1(G/H,\\mu)$ becomes a Banach algebra. We also find a generalized definition of this convolution for other $L^p$-spaces. Finally, we show that various types of involutions can be considered on $G/H$.
Vela Velupillai, K.
2014-01-01
The Hahn-Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using nonconstructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn-Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented...
Reflexive functors in Algebraic Geometry
Sancho, Pedro
2015-01-01
Reflexive functors of modules naturally appear in Algebraic Geometry. In this paper we define a wide and elementary family of reflexive functors of modules, closed by tensor products and homomorphisms, in which Algebraic Geometry can be developed.
The Reflexivity of Explicit Performatives
Cristina Corredor
2010-03-01
Full Text Available The aim of this contribution is to propose a natural implementation of the reflexive-referential theory advanced by Perry 2001 that aims at accounting for the reflexive character of explicit performative utterances. This is accomplished by introducing a reflexive-performative constraint on explicit performatives.
Sweeney, Mary M.; Urcuioli, Peter J.
2010-01-01
A recent theory of pigeons' equivalence-class formation (Urcuioli, 2008) predicts that reflexivity, an untrained ability to match a stimulus to itself, should be observed after training on two "mirror-image" symbolic successive matching tasks plus identity successive matching using some of the symbolic matching stimuli. One group of pigeons was…
Approximately
Karimi T; Kaboli Gharetapeh S; Gordji MEshaghi
2009-01-01
Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresp...
Remark on Regularity of Continuous Operators on AL-Spaces
冯勋省; 陈滋利
2004-01-01
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
Mentalis muscle related reflexes.
Gündüz, Ayşegül; Uyanık, Özlem; Ertürk, Özdem; Sohtaoğlu, Melis; Kızıltan, Meral Erdemir
2016-05-01
The mentalis muscle (MM) arises from the incisive fossa of the mandible, raises and protrudes the lower lip. Here, we aim to characterize responses obtained from MM by supraorbital and median electrical as well as auditory stimuli in a group of 16 healthy volunteers who did not have clinical palmomental reflex. Reflex activities were recorded from the MM and orbicularis oculi (O.oc) after supraorbital and median electrical as well as auditory stimuli. Response rates over MM were consistent after each stimulus, however, mean latencies of MM response were longer than O.oc responses by all stimulation modalities. Shapes and amplitudes of responses from O.oc and MM were similar. Based on our findings, we may say that MM motoneurons have connections with trigeminal, vestibulocochlear and lemniscal pathways similar to other facial muscles and electrophysiological recording of MM responses after electrical and auditory stimulation is possible in healthy subjects. PMID:26721248
Reducibility of invertible tuples to the principal component in commutative Banach algebras
Mortini, Raymond; Rupp, Rudolf
2015-10-01
Let A be a complex, commutative unital Banach algebra. We introduce two notions of exponential reducibility of Banach algebra tuples and present an analogue to the Corach-Suárez result on the connection between reducibility in A and in C(M(A)). Our methods are of an analytical nature. Necessary and sufficient geometric/topological conditions are given for reducibility (respectively reducibility to the principal component of Un(A)) whenever the spectrum of A is homeomorphic to a subset of {C}n.
Functional calculus and *-regularity of a class of Banach algebras II
Leung, Chi-Wai; Ng, Chi-Keung
2006-10-01
In this article, we define a natural Banach *-algebra for a C*-dynamical system (A,G,[alpha]) which is slightly bigger than L1(G;A) (they are the same if A is finite-dimensional). We will show that this algebra is *-regular if G has polynomial growth. The main result in this article extends the two main results in [C.W. Leung, C.K. Ng, Functional calculus and *-regularity of a class of Banach algebras, Proc. Amer. Math. Soc., in press].
Reflexive functors of modules in Commutative Algebra
J. Navarro; Sancho, C.; Sancho, P.
2012-01-01
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.
Reflexive functors of modules in Commutative Algebra
Navarro, J; Sancho, P
2012-01-01
Reflexive functors of modules are ubiquitous in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors.
Stability of a Bi-Additive Functional Equation in Banach Modules Over a C⋆-Algebra
Won-Gil Park
2012-01-01
Full Text Available We solve the bi-additive functional equation f(x+y,z−w+f(x−y,z+w=2f(x,z−2f(y,w and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.
On solvability of some quadratic functional-integral equation in Banach algebra
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)
Common fixed points for Banach operator pairs from the set of best approximations
Ćirić, L.; Hussain, N.; F. Akbar; Ume, J. S.
2009-01-01
The existence of common fixed point results for a Banach operator pair under certain generalized $\\varphi$-contractions is established. As applications, the corresponding invariant best approximation results are proved. Our results unify and generalize various known results to the more general class of noncommuting mappings.
Central limit theorem for the Banach-valued weakly dependent random variables
The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked
绝对平均有界数列空间Aab(K)%Absolutely Average Bounded Number Sequence Space Aab(K)
马凤红; 罗成; 孙凤龙
2011-01-01
Based on the absolutely average convergence of a number sequence,the concept of absolutely average bounded number sequence is given.Space Aab (K) is defined as absolutely average bounded number sequences over the real or complex scalar field K ,which is a space between space 1∞ of bounded number sequences and space Ab (K) of approxmatively bounded number sequences.Moreover,that an equivalent condition of a number sequence is absolutely average bounded is given,and space Aab(K) is a non-separable , non-reflexive Banach space which has neither the Krern-Mil 'man property nor Radon-Nikodym property are proved.%提出了绝对平均有界数列的概念,并由此定义了实(或复)数域K上绝对平均有界的数列空间Aab(K),这是一个介于有界数列空间l∞和近似有界数列空间Ab(K)之间的空间.给出了数列绝对平均有界性的等价条件,证明了空间Aab(K)是不可分的、不自反的、不具有Kre(r)n-Mil'man性质和Radon-Nikod(y)m性质的Banach空间.
The Intuitionistic Fuzzy Normed Space of Coefficients
Bilalov, B. T.; S. M. Farahani; Guliyeva, F. A.
2012-01-01
Intuitionistic fuzzy normed space is defined using concepts of $t$ -norm and $t$ -conorm. The concepts of fuzzy completeness, fuzzy minimality, fuzzy biorthogonality, fuzzy basicity, and fuzzy space of coefficients are introduced. Strong completeness of fuzzy space of coefficients with regard to fuzzy norm and strong basicity of canonical system in this space are proved. Strong basicity criterion in fuzzy Banach space is presented in terms of coefficient operator.
Survey on nonlocal games and operator space theory
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states
Survey on nonlocal games and operator space theory
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Survey on nonlocal games and operator space theory
Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Dentocardiac Reflex: an Allegedly New Subform of the Trigeminocardiac Reflex
Amr Abdulazim; Ashkan Rashad; Behnam Bohluli; Bernhard Schaller; Fatemeh Momen-Heravi; Pooyan Sadr-Eshkevari
2011-01-01
Trigeminocardiac reflex (TCR) is currently defined as a sudden bradycardia and decrease in mean arterial blood pressure by 20% during the manipulation of the branches of trigeminal nerve. TCR, especially during the last decade has been mostly studied in the course of neurosurgical procedures which are supposed to elicit the central subtype of TCR. Previously the well-known oculocardiac reflex was also considered as a subtype of TCR. Recently, surgeons dealing with the other branches of the fi...
The Sociology of Lesbian and Gay Reflexivity or Reflexive Sociology?
Brian Heaphy
2008-01-01
This article is concerned with sociological conceptualisations of lesbian and gay sexualities as reflexive forms of existence, and identifies core problems with these. Our sociological narratives about lesbian and gay reflexivity tend to be partial in two senses. First, they talk about and envision only very particular - and relatively exclusive â€“ experience, and fail to adequately account for the significance of difference and power in shaping diverse lesbian and gay experiences. Second, t...
Management of Reflex Anoxic Seizures
J Gordon Millichap
2013-10-01
Full Text Available Investigators at the Roald Dahl EEG Unit, Alder Hey Children’s NHS Foundation, Liverpool, UK, review the definition, pathophysiology, clinical presentation, and management of reflex anoxic seizures (RAS in children.
Reflex Sympathetic Dystrophy in Children
Adnan Ayvaz
2013-01-01
Reflex sympathetic dystrophy (chronic regional pain syndrome) isn’t frequently encountered in practical pediatrics and childhood. Reflex sympathetic dystrophy syndrome (RSD) is a disorder characterized by widespread localized pain, often along with swelling, discoloration, trophic changes and autonomic abnormalities such as vasomotor disorders. Its etio-pathogenesis hasn’t been completely determined.The disease can form in an area innerved by a partially damaged nerve...
[Reflex sympathetic dystrophy].
Oliveira, Marta; Manuela, Manuela; Cantinho, Guilhermina
2011-01-01
Reflex Sympathetic Dystrophy is rare in pediatrics. It is a complex regional pain syndrome, of unknown etiology, usually post-traumatic, characterized by dysfunctions of the musculoskeletal, vascular and skin systems: severe persistent pain of a limb, sensory and vascular alterations, associated disability and psychosocial dysfunction. The diagnosis is based in high clinical suspection. In children and adolescents there are aspects that are different from the adult ones. Excessive tests may result in worsening of the clinical symptoms. Bone scintigraphy can help. Pain treatment is difficult, not specific. Physical therapies and relaxation technics give some relief. Depression must be treated. This syndrome includes fibromyalgia and complex regional pain syndrome type I. We present a clinical report of an adolescent girl, referred for pain, cold temperature, pallor and functional disability of an inferior limb, all signals disclosed by a minor trauma. She had been diagnosed depression the year before. The bone scintigraphy was a decisive test. The treatment with gabapentin, C vitamin, physiotherapy and pshycotherapy has been effective. PMID:22713207
On Fixed-point theorems in Intuitionistic Fuzzy metric Space
Samanta, T K; Jebril, Iqbal H
2010-01-01
In this paper, first we have established two sets of sufficient conditions for a mapping to have unique fixed point in a intuitionistic fuzzy metric space and then we have redefined the contraction mapping in a intuitionistic fuzzy metric space and thereafter we proved the Banach Fixed Point theorem.
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2013-01-01
We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is...
A note on mutiplication operators on Köthe-Bochner spaces
S. S. Khurana
2012-01-01
Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g x) =g x for everyg Î L¥, f Î E(X), x Î X, x* Î X*.
Bessel and Grüss Type Inequalities in Inner Product Modules over Banach -Algebras
Dragomir SS
2011-01-01
Full Text Available We give an analogue of the Bessel inequality and we state a simple formulation of the Grüss type inequality in inner product -modules, which is a refinement of it. We obtain some further generalization of the Grüss type inequalities in inner product modules over proper -algebras and unital Banach -algebras for -seminorms and positive linear functionals.
Dentocardiac Reflex: an Allegedly New Subform of the Trigeminocardiac Reflex
Amr Abdulazim
2011-05-01
Full Text Available Trigeminocardiac reflex (TCR is currently defined as a sudden bradycardia and decrease in mean arterial blood pressure by 20% during the manipulation of the branches of trigeminal nerve. TCR, especially during the last decade has been mostly studied in the course of neurosurgical procedures which are supposed to elicit the central subtype of TCR. Previously the well-known oculocardiac reflex was also considered as a subtype of TCR. Recently, surgeons dealing with the other branches of the fifth cranial nerve have become more interested in this reflex. Some noteworthy points have been published discussing new aspects of the trigeminocardiac reflex (TCR in simple oral surgical procedures. Arakeri et al. have reviewed the similarities and differences between TCR, vasovagal response (VVR, and syncope. They have also explained a new possible pathway for the reflex during the simple extraction of upper first molars. The present paper aims to briefly discuss these recently presented points. Although the discussed concepts are noteworthy and consistent our preliminary results of our yet to be published studies, it seemed timely for us to discuss some possible shortcomings that may affect the results of such assessments.
Casazza, Peter G
1989-01-01
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).
[The oculocardiac reflex in blepharoplasties].
Rippmann, V; Scholz, T; Hellmann, S; Amini, P; Spilker, G
2008-08-01
The oculocardiac reflex (OCR) is a well-known phenomenon in ophthalmic surgery, but is rarely described in aesthetic blepharoplasty surgery. It was first mentioned in 1908 by Ascher and Dagnini. Since then, ophthalmologists and anaesthesiologists have regarded the onset of the oculocardiac reflex as a significant intraoperative problem, which is undermined by several case reports that describe dysrhythmias which have haved caused morbidity and death. Per definition the OCR is caused by ocular manipulation and involves intraoperative bradycardia by a change of 20 beats/minute compared to the preoperative heart rate or any dysrhythmia during the manipulation via a trigeminal-vagal-mediated reflex arc. Having operated on a 48-year-old, healthy woman in our clinic, who underwent a cardiac arrest during the blepharoplasty procedure, followed by a successful resuscitation, we investigated the onset of the OCR in our blepharoplasty patients within the last 3 years. The onset of the OCR was noted in 22 of 110 (20 %) blepharoplasty patients, mainly affecting younger, low-weighted patients operated under local anaesthesia. Awareness and treatment of this potentially life-threatening oculocardiac reflex are necessary. In most cases the onset of the reflex may be avoided by a gentle operation technique and by refraining from severe traction to the muscle or fat pad. The best treatment of a profound bradycardia caused by the OCR is to release tension to the muscle or fat pad in order to permit the heart rate to return to normal. Intraoperative monitoring is of utmost importance. PMID:18716987
The isometric extension of “into” mappings on unit spheres of AL-spaces
2008-01-01
In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.
Garbulińska, Joanna
2011-01-01
We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word "almost", we get the notion of a strong Gurarii space. There exists a unique (up to isometry) separable Gurarii space, however strong Gurarii spaces cannot be separable. The structure of the class of non-separable Gurarii spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In particular, we characterize non-separable Gurarii spaces in terms of skeletons of separable subspaces, we construct a non-separable Gurarii space with a projectional resolution of the identity and we show that no strong Gurarii space can be weakly Lindel\\"of determined.
Stereotype locally convex spaces
Akbarov, S S
2000-08-31
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
Akbarov, S. S.
2000-08-01
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.
Stereotype locally convex spaces
We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis
Reflexivity in the research process: psychoanalytic observations
Brown, J. C.
2006-01-01
This paper highlights what psychoanalysis can add to discussions of reflexivity, by specifically describing how reflexivity is conceptualized and fostered on psychoanalytic observation methods courses at the Tavistock Clinic, London. It is demonstrated that this psychological form of reflexivity is relevant to empirical and conceptual work and shown that it shares interesting parallels with debates about reflexivity in social research methods, while also being able to contribute to discussion...
Educating the Reflexive Practitioner
Marc J. Neveu
2012-09-01
wearing any clothes.Notwithstanding such issues, I do believe the studio holds the potentialto be an empowering learning experience. The intention of this article is to question the mode of instruction in an architectural studio. I’ve structured the paper in three parts. First, I will briefly describe the findingsof the study made by the Carnegie Foundation for the Advancementof Teaching known as the Boyer Report.2 To develop and support the findings of the Boyer Report, I introduce the work of the educator Donald Schön. Though I see much merit in the Boyer Report, and Schön’sproposals, I argue that a more nuanced approach is required. I will recommend, therefore, in the second section of this paper that a meansof architectural education as based on the Socratic method may be amore productive approach. My reading of the Socratic method is basedprimarily on early Socratic dialogues and I will specifically use Charmidesto illustrate the issues that I believe are relevant to studio pedagogy.3 From my analysis of Charmides I will, in the third section of the essay,describe how the Socratic method is beneficial to studio pedagogy threeways: reflexive, non-propositional, and finally how Socrates’ approachmay indeed be practical. This last section will be illustrated with a studentproject. It is my conjecture that the Socratic method offers insight intocurrent discussions of educational theory, namely student-centered,project-based learning.
TRANSIENT RELEASE REFLEXES IN CATONIC SCHIZOPHRENIA
Damodaran, Saji S.; Sinha, Vinod K.
1994-01-01
This case report describes the presence of grasp reflex and palmomental reflex as a state dependant phenomenon in a 23 year old patient with catatonic schizophrenia. A transitory disturbance of frontal lobe function is proposed as the probable mechanism. The need to study the release reflexes as an effort to delineate a neurological “sub group” of schizophrenia is suggested.
The reflexive case study method
Rittenhofer, Iris
2015-01-01
This paper extends the international business research on small to medium-sized enterprises (SME) at the nexus of globalization. Based on a conceptual synthesis across disciplines and theoretical perspectives, it offers management research a reflexive method for case study research of postnational...
Reflexivity in Narratives on Practice
Jakobsen, Helle Nordentoft; Olesen, Lektor Birgitte Ravn
Previous research has shown how reflexivity is a precondition for knowledge co-production through productive dialogue in organisational contexts because it entails a re-ordering, re-arranging and re-designing of what one knows and therefore creates new angles of vision. In this paper, we draw on...
On prime and semiprime rings with generalized derivations and non-commutative Banach algebras
MOHD ARIF RAZA; NADEEM UR REHMAN
2016-08-01
Let $R$ be a prime ring of characteristic different from 2 and $m$ a fixed positive integer. If $R$ admits a generalized derivation associated with a nonzero deviation $d$ such that $[F(x), d(y)]_m = [x, y]$ for all $x$, $y$ in some appropriate subset of $R$, then $R$ is commutative. Moreover, we also examine the case $R$ is a semiprime ring. Finally, we apply the above result to Banach algebras, and we obtain a non-commutative version of the Singer--Werner theorem.
Lakshmi Narayan Mishra
2016-04-01
Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.
THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES
LIU SHANGPING; LI BINGREN
2005-01-01
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
In some symmetric spaces monotonicity properties can be reduced to the cone of rearrangements
Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav
2016-01-01
Roč. 90, č. 1 (2016), s. 249-261. ISSN 0001-9054 Institutional support: RVO:67985840 Keywords : symmetric space s * K-monotone symmetric Banach space s * strict monotonicity * lower local uniform monotonicity Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2014 http://link.springer.com/article/10.1007%2Fs00010-015-0379-6
Reflexive fatherhood in everyday life
Westerling, Allan
2015-01-01
This article looks at fathering practices in Denmark, using the findings from a research project on everyday family life in Denmark. It takes a social psychological perspective and employs discursive psychology and theories about reflexive modernisation. It shows how fathers orient towards intimacy....... Through this analysis and discussion, the article offers a way to understand the complexities of fathering in everyday life from the perspective of fathers....
Topological centers of module actions and cohomological groups of Banach Algebras
Azar, Kazem Azem Haghnejad
2010-01-01
In this paper, first we study some Arens regularity properties of module actions. Let $B$ be a Banach $A-bimodule$ and let ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$ be the topological centers of the left module action $\\pi_\\ell:~A\\times B\\rightarrow B$ and the right module action $\\pi_r:~B\\times A\\rightarrow B$, respectively. We investigate some relationships between topological center of $A^{**}$, ${Z}_1({A^{**}})$ with respect to the first Arens product and topological centers of module actions ${Z}^\\ell_{B^{**}}(A^{**})$ and ${Z}^\\ell_{A^{**}}(B^{**})$. On the other hand, if $A$ has Mazure property and $B^{**}$ has the left $A^{**}-factorization$, then $Z^\\ell_{A^{**}}(B^{**})=B$, and so for a locally compact non-compact group $G$ with compact covering number $card(G)$, we have $Z^\\ell_{M(G)^{**}}{(L^1(G)^{**})}= {L^1(G)}$ and $Z^\\ell_{L^1(G)^{**}}{(M(G)^{**})}= {M(G)}$. By using the Arens regularity of module actions, we study some cohomological groups properties of Banach algebra and we...
We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the A∞-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras
Reflexivity, social transformation, and counter culture
Cox, Laurence
1997-01-01
This paper attempts to identify how reflexivity works within the local rationalities of social movement milieux that, it is argued, represent an important source of the development of reflexivity in contemporary lifeworlds. In interviews in the Dublin counter culture, reflexivity appears above all as the institutionalisation of autonomy, the creation of new social forms for self-determined purposes. A starting point is strategies of distancing from the taken-for-granted assumptions of in...
The emergence of reflexive global labour law
Rogowski, Ralf
2015-01-01
The article introduces the main tenets of reflexive labour law and uses this perspective to interpret core trends in global labour law. It suggests a conceptual distinction between international and global labour law and identifies a transformation in the global labour law regime related to processes of reflexivity and constitutionalisation. The first part of the article analyses reflexivity within the International Labour Organization (ILO) in relation to its policy of defining labour standa...
Star product realizations of kappa-Minkowski space
Durhuus, Bergfinnur; Sitarz, Andrzej
2011-01-01
We define a family of star products and involutions associated with $\\kappa$-Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on $\\kappa$-Minkowski space. Furthermore, we ...
Isometric Reflection Vectors and Characterizations of Hilbert Spaces
Donghai Ji
2014-01-01
Full Text Available A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere SX of a Banach space X has nonempty interior in SX, then X is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.
The trigeminocardiac reflex – a comparison with the diving reflex in humans
Lemaitre, Frederic; Chowdhury, Tumul; Schaller, Bernhard
2015-01-01
The trigeminocardiac reflex (TCR) has previously been described in the literature as a reflexive response of bradycardia, hypotension, and gastric hypermotility seen upon mechanical stimulation in the distribution of the trigeminal nerve. The diving reflex (DR) in humans is characterized by breath-holding, slowing of the heart rate, reduction of limb blood flow and a gradual rise in the mean arterial blood pressure. Although the two reflexes share many similarities, their relationship and esp...
Arakeri′s Reflex: an Alternative Pathway for Dento-Cardiac Reflex Mediated Syncope
Veena Arali; Shailaja Reddy; C G Raghuram; Gururaj Arakeri
2010-01-01
Introduction: Dentocardiac reflex, a variant of trigeminocardiac reflex elicited specifically during tooth extraction procedures in den-tal/maxillofacial surgery and is believed to cause syncope with an afferent link mediated by posterior superior alveolar nerve. Another variant of trigeminocardiac reflex which is also of interest to the oral and maxillofacial surgeon is oculocardiac reflex which can be triggered by direct or indirect manipulation of eye globe or muscles around it.The hypothe...
Sunder, V S
2016-01-01
The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators. .
Dinda, Bivas; Jebril, Iqbal H
2011-01-01
In this paper intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are introduced. Intuitionistic fuzzy Banach contraction theorem for M-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Elelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy {\\psi}-{\\phi}-contractive mappings are proved.
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
An Existence Result for Nonlinear Fractional Differential Equations on Banach Spaces
Cabada Alberto
2009-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problem for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of noncompactness.
The fixed point theorems of 1-set-contractive operators in Banach space
Wang Shuang
2011-01-01
Full Text Available Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10
Chang Shih-sen
2008-01-01
Full Text Available Abstract In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007, Liu (1996, Osilike (2004, Su and Li (2006, Gu (2007, Xu and Ori (2001.
Mouffak Benchohra; Fatima-Zohra Mostefai
2012-01-01
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Zhiqun Xue
2008-03-01
Full Text Available The purpose of this paper is to compare convergence speed of the Picard and Mann iterations on one hand, Krasnoselskij and Ishikawa iterations on the other hand, for the class of Zamfirescu operators. The results improve corresponding results of (Berinde 2004 and (Babu and Vara Prasad 2006.
k-接近一致光滑Bananch空间%k-Nearly Uniformly Smooth Banach Spaces
王翠玲; 魏文展; 周玲丽
2006-01-01
定义k-接近一致光滑模,利用其给出k-接近一致光滑(k-NUS)空间的概念,证明k-接近一致光滑空间与k-接近一致凸空间是对偶概念,同时引入具有w*k性质的空间,给出k-接近一致光滑空间的一个特征刻画,并讨论(k+1)-接近一致光滑空间与接近一致光滑和k-一致光滑(kUS)空间的关系.
NEW FIXED POINT THEOREMS FOR P1-COMPACT MAPPINGS IN BANACH SPACES
无
2007-01-01
F.E. Browder and W. V. Petryshyn[1] defined the topological degree for Aproper mappings and then W. V. Petryshyn[2] studied a class of A-proper mappings, namely,P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn[2], we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder's theorem, Rothe's theorem, Altman's theorem,Petryshyn's theorem, etc.
2008-01-01
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
LIU WeiDong; FU KeAng; ZHANG LiXin
2008-01-01
In this paper, we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables. As an interesting application, we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
CONCEPTS OF DICHOTOMY FOR SKEW-EVOLUTION SEMIFLOWS IN BANACH SPACES
Mihail Megan
2011-01-01
Full Text Available In this paper we investigate some dichotomy concepts for skew-evolution semiflows in Banachspaces.Our main objective is to estab-lish relations between these concepts.We motivate our approach byillustrative examples.
On H–Dichotomy for Skew-Evolution Semiflows in Banach Spaces
Stoica Codruţa
2012-04-01
Full Text Available The aim of this paper is to define and characterize a particular case of dichotomy for skew-evolution semiflows, called the H–dichotomy, as a useful tool in describing the behaviors for the solutions of evolution equations that describe phenomena from engineering or economics. The paper emphasizes also other asymptotic properties, as ω–growth and ω–decay, H–stability and H–instability, as well as the classic concept of exponential dichotomy.
ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE
宋光兴
2003-01-01
By using partial order method, the existence, uniqueness and iterative ap-proximation of solutions for a class of systems of nonlinear operator equations in Banachspace are discussed. The results obtained in this paper extend and improve recent results.
On the mild solutions of higher-order differential equations in Banach spaces
Nguyen Thanh Lan
2003-01-01
Full Text Available For the higher-order abstract differential equation u(n(t=Au(t+f(t, t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E with respect to the above-mentioned equation in terms of solvability of the operator equation AX−Xn=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
Axon reflexes in human cold exposed fingers
Daanen, H.A.M.; Ducharme, M.B.
2000-01-01
Exposure of fingers to severe cold induces cold induced vasodilation (CIVD). The mechanism of CIVD is still debated. The original theory states that an axon reflex causes CIVD. To test this hypothesis, axon reflexes were evoked by electrical stimulation of the middle fingers of hands immersed in wat
Ferro, Leonardo
2013-01-01
El objetivo principal de esta disertación es el estudio de la teoría de las álgebras de Lie–Jordan Banach y su papel en el marco de la mecánica clásica y cuántica y sus aplicaciones en diferentes ámbitos de las matemáticas. La investigación algebraica de los fundamentos de la física surgió de la búsqueda de una formulación “excepcional” para la mecánica cuántica, que finalmente culminó en la formulación de las álgebras de Jordan y las posteriores C∗–álgebras.............
An improvement of dimension-free Sobolev imbeddings in r spaces
Fiorenza, A.; Krbec, Miroslav; Schmeisser, H.-J.
2014-01-01
Roč. 267, č. 1 (2014), s. 243-261. ISSN 0022-1236 R&D Projects: GA ČR GAP201/10/1920 Institutional support: RVO:67985840 Keywords : imbedding theorem * small Lebesgue space * rearrangement-invariant Banach Subject RIV: BA - General Mathematics Impact factor: 1.322, year: 2014 http://www.sciencedirect.com/science/article/pii/S0022123614001724
Reflexive Learning through Visual Methods
Frølunde, Lisbeth
2014-01-01
methods are exemplified through two university classroom cases about collaborative idea generation processes. The visual methods and materials in the cases are photo elicitation using photo cards, and modeling with LEGO Serious Play sets. Why. The goal is to encourage the reader, whether student or...... professional, to facilitate with visual methods in a critical, reflective, and experimental way. The chapter offers recommendations for facilitating with visual methods to support playful, emergent designerly processes. The chapter also has a critical, situated perspective. Where. This chapter offers case...... vignettes that refer to design-oriented workshops where student groups generate ideas, such as for a campaign. The cases are set at Roskilde University. How. There are recommendations on how to facilitate workshops and develop your own practice as a reflexive facilitator. Some of the typical facilitation...
[Research progress of rectoanal inhibitory reflex].
Yin, Shuhui; Zhao, Ke
2015-12-01
The understanding of rectoanal inhibitory reflex (RAIR) is progressing for the latest 100 years. From the discovery of its important role in diagnosis of Hirschsprung's disease to all aspects of its development, reflex pathways, neural regulation and physiological functions, there have been more in-depth explorations. It is now recognized that a number of other diseases also have a more specific performance of RAIR. It has become an important and indispensable part to anorectal manometry. Research progress of rectoanal inhibitory reflex is reviewed in this article. PMID:26704013
Latencies of Reflex Discharges in Some Oro-facial Reflexes of the Frog
NOMURA, HIROMICHI; Suzuki, Hirokazu
1987-01-01
Unitary reflex discharges were recorded from the branches of the trigeminal nerve innervating the submental and masseter muscles following electrical stimulation of the lingual branch of the glossopharyngeal nerve, the maxillary branch of the trigeminal nerve and the mandibular branch of the facial nerve. Reflex discharges were effectively elicited by repetitive electrical stimulation of afferent nerves, but the number of reflex impulses as well as the latencies varied from discharge to disch...
The legacy of care as reflexive learning
García, Marta Rodríguez; Moya, Jose Luis Medina
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through constant comparisons of the categories. Results: the results demonstrate that the tutors' use of reflexive strategies such as didactic questioning, didactic empathy and pedagogical silence contributes to encourage the students' reflection and significant learning. Conclusions: reflexive practice is key to tutors' training and students' learning. PMID:27305180
Entrepreneurship Teaching Conducted as Strategic Reflexive Conversation
Kristiansson, Michael
The paper intends exploring and ascertaining whether the concept of strategic reflexive conversation can profitably be applied to entrepreneurship. As a start, a process of conceptualisation is undertaken, which is instrumental in placing the notion of strategic reflexive conversation into a...... knowledge management perspective. Strategic reflexive conversation is presented in an enhanced and updated version, which is contrasted to entrepreneurship through reflection. The findings indicate and it can be concluded that, with some important reservations, strategic reflexive conversation can...... advantageously, and on a pilot basis, be applied to entrepreneurship in practical environments and within the framework of entrepreneurship-centred teaching. The present theoretical investigation is solely of an introductory nature and steps are considered that can lead to the planning of additional exploratory...
Demanding Reflexivity: Lazy Ozzie and Other Stories.
McCormack, David
2007-01-01
One of the orthodoxies of supervising research within the framework of a radical approach to adult education is that you 'demand' a reflexive approach. That is, you ask that the researcher adopt a paradigm of research that does not pretend scientific validity, one that recognises that the researcher's own assumptions, experiences and subjectivity constitute the major source of colour in the canvas he or she is painting. Reflexivity in research involves developing 'critical literacy' by not...
The legacy of care as reflexive learning
García, Marta Rodríguez; Moya, Jose Luis Medina
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through const...
The legacy of care as reflexive learning
Marta Rodríguez García; Jose Luis Medina Moya
2016-01-01
Abstract Objective: to analyze whether the tutor's use of reflexive strategies encourages the students to reflect. The goal is to discover what type of strategies can help to achieve this and how tutors and students behave in the practical context. Method: a qualitative and ethnographic focus was adopted. Twenty-seven students and 15 tutors from three health centers participated. The latter had received specific training on reflexive clinical tutoring. The analysis was developed through c...
The passive of reflexive verbs in Icelandic
Hlíf Árnadóttir
2011-10-01
Full Text Available The Reflexive Passive in Icelandic is reminiscent of the so-called New Passive (or New Impersonal in that the oblique case of a passivized object NP is preserved. As is shown by recent surveys, however, speakers who accept the Reflexive Passive do not necessarily accept the New Passive, whereas conversely, speakers who accept the New Passive do also accept the Reflexive Passive. Based on these results we suggest that there is a hierarchy in the acceptance of passive sentences in Icelandic, termed the Passive Acceptability Hierarchy. The validity of this hierarchy is confirmed by our diachronic corpus study of open access digital library texts from Icelandic journals and newspapers dating from the 19th and 20th centuries (tímarit.is. Finally, we sketch an analysis of the Reflexive Passive, proposing that the different acceptability rates of the Reflexive and New Passives lie in the argument status of the object. Simplex reflexive pronouns are semantically dependent on the verbs which select them, and should therefore be analyzed as syntactic arguments only, and not as semantic arguments of these verbs.
Brauer-Thrall for totally reflexive modules
Christensen, Lars Winther; Rahmati, Hamidreza; Striuli, Janet; Wiegand, Roger
2010-01-01
Let R be a commutative noetherian local ring that is not Gorenstein. It was recently discovered that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R,m) with m^3=0 are commonly regarded as the structurally simplest rings to admit diverse categorical and homological characteristics. For such rings we obtain conclusive results about the category of totally reflexive modules, modeled on the Brauer-Thrall conjectures. Starting from a non-free cyclic totally reflexive module, we construct a family of indecomposable totally reflexive R-modules that contains, for every n in N, a module that is minimally generated by n elements. Moreover, if the residue field R/m is algebraically closed, then we construct for every n in N an infinite family of indecomposable and pairwise non-isomorphic totally reflexive R-mo...
The Spaces of Functions of Two Variables of Bounded κΦ-Variation in the Sense of Schramm-Korenblum
A. Azócar
2015-01-01
Full Text Available The purpose of this paper is twofold. Firstly, we introduce the concept of bounded κΦ-variation in the sense of Schramm-Korenblum for real functions with domain in a rectangle of R2. Secondly, we study some properties of these functions and we prove that the space generated by these functions has a structure of Banach algebra.
Functional calculus on real interpolation spaces for generators of $C_{0}$-groups
Haase, Markus; Rozendaal, Jan
2014-01-01
We study functional calculus properties of $C_{0}$-groups on real interpolation spaces, using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded $H^{\\infty}_{1}$-calculus on real interpolation spaces. Additional results are derived from this.
Bastiaanse, Catharina Maria
2003-01-01
This thesis describes six studies on the influence of active movements and body loading on reflex responses. To measure those influences healthy subjects were asked to walk with different loadings (e.g. a backpack) or with different active movements (e.g. arm swing) while different reflex responses
A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES
Peyman SALIMI; Pasquale VETRO
2014-01-01
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.
Sampling and Galerkin reconstruction in reproducing kernel spaces
Cheng, Cheng; Jiang, Yingchun; Sun, Qiyu
2014-01-01
In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin met...
Functional Analysis: Entering Hilbert Space
Hansen, Vagn Lundsgaard
In the second edition, I have expanded the material on normed vector spaces and their operators presented in Chapter 1 to include proofs of the Open Map-ping Theorem, the Closed Graph Theorem and the Hahn-Banach The orem. The material on operators between normed vector spaces is further expanded in...... operators between Hilbert spaces. Fredholm operators are of interest far beyond mathematical analysis, they also play a significant role in theoretical physics, differential geometry and topology with the famous Index Theorem proved by Michael Atiyah and Isadore Singer in 1963 as a highlight. With the...... addition of the new material on normed vector spaces and their operators, the book can hopefully serve as a general introduction to functional analysis viewed as a theory of infinite dimensional linear spaces and linear operators acting on them....
Results on the Existence and Convergence of Best Proximity Points
Abkar Ali
2010-01-01
Full Text Available We first consider a cyclic -contraction map on a reflexive Banach space and provide a positive answer to a question raised by Al-Thagafi and Shahzad on the existence of best proximity points for cyclic -contraction maps in reflexive Banach spaces in one of their works (2009. In the second part of the paper, we will discuss the existence of best proximity points in the framework of more general metric spaces. We obtain some new results on the existence of best proximity points in hyperconvex metric spaces as well as in ultrametric spaces.
Human investigations into the exercise pressor reflex
Secher, Niels H; Amann, Markus
2012-01-01
. The importance of the exercise pressor reflex for tight cardiovascular regulation during dynamic exercise is supported by studies using pharmacological blockade of lower limb muscle afferent nerves. These experiments show attenuation of the increase in BP and cardiac output when exercise is performed......During exercise, neural input from skeletal muscles reflexly maintains or elevates blood pressure (BP) despite a maybe fivefold increase in vascular conductance. This exercise pressor reflex is illustrated by similar heart rate (HR) and BP responses to electrically induced and voluntary exercise....... The lack of an increase in BP during exercise with paralysed legs manifests, although electrical stimulation of muscles enhances lactate release and reduces muscle glycogen. Thus, the exercise pressor reflex enhances sympathetic activity and maintains perfusion pressure by restraining abdominal blood...
Visual reflex seizures induced by complex stimuli.
Zifkin, Benjamin G; Inoue, Yushi
2004-01-01
Visual reflex seizures induced by complex stimuli may be triggered by patterned and flashing displays that are now ubiquitous. The seizures may be clinically generalized, but unilateral and bilateral myoclonic attacks also may be triggered, especially in patients with juvenile myoclonic epilepsy, and recently, clearly focal reflex occipital lobe seizures have been described. Some seizure-triggering properties of video displays can be identified, such as perceived brightness, pattern, flicker frequency, and color. Knowledge of these is useful in planning individual treatment and in designing regulations for screen content of television broadcasts or for other video displays. Some subjects will also be sensitive to cognitive or action-programming activation, especially when playing video games, and this can increase the chance of seizure triggering. Nonspecific factors such as sleep deprivation, prolonged exposure, and drug or alcohol use also may play a role in reflex seizure occurrence. PMID:14706042
Polarized neutron reflectometer 'Reflex-P'
Korneev, D A; Yaradajkin, S P
2002-01-01
About 10 years ago the idea of a new spectrometer 'Reflex' at the IBR-2 reactor was formulated. According to the initial idea, the spectrometer was projected as a combination of two reflectometers. One of them is the spectrometer with polarized neutrons and another one with nonpolarized neutrons. At present half of the project has been executed. On the 9th beam of the IBR-2 reactor the polarized branch of the spectrometer 'Reflex-P' is successfully working. This paper is devoted to the description of main parameters of this spectrometer and development perspectives.
Reflex control for safe autonomous robot operation
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
复指数函数系在Lpα空间中的完备性%Completeness of Complex Exponential System in Space
闫峰; 邓冠铁
2008-01-01
A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space Lpα = {f : f∞-∞ |f(t)e-α(t)|pdt ∞}, where 1 ≤ p + ∞and α(t) is a nonnegative continuous function on R.
Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces
Laowang W; Panyanak B
2010-01-01
Suppose that is a nonempty closed convex subset of a complete CAT(0) space with the nearest point projection from onto . Let be a nonexpansive nonself mapping with . Suppose that is generated iteratively by , , , where and are real sequences in for some . Then -converges to some point in . This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.
On the moduli and characteristic of monotonicity in Orlicz-Lorentz function spaces
Foralewski, P.; Hudzik, H.; Kaczmarek, R.; Krbec, Miroslav; Wojtowicz, M.
2013-01-01
Roč. 20, č. 4 (2013), s. 955-970. ISSN 0944-6532 R&D Projects: GA ČR GAP201/10/1920 Institutional research plan: CEZ:AV0Z10190503 Keywords : Kothe space * Banach lattice * Orlicz-Lorentz space Subject RIV: BA - General Mathematics Impact factor: 0.592, year: 2013 http://www.heldermann.de/JCA/JCA20/JCA204/jca20052.htm
Fixed Point Results for Multivalued Maps in Metric Spaces with Generalized Inwardness Conditions
Frigon M
2010-01-01
Full Text Available We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize recent results of Azé and Corvellec, Maciejewski, and Uderzo for contractions and directional contractions. Finally, we present local fixed point theorems and continuation principles for generalized inward contractions.
Cones and gauges in complex spaces : Spectral gaps and complex Perron-Frobenius theory
Rugh, Hans Henrik
2006-01-01
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch's Theorem to complex integral operators, a Krein-Rutman Theorem to compact and quasi-compact complex operators and a Ruelle-Perron-Frobeni...
Monitoring of head injury by myotatic reflex evaluation
Cozens, J; Miller, S; Chambers, I.; Mendelow, A
2000-01-01
OBJECTIVES—(1) To establish the feasibility of myotatic reflex measurement in patients with head injury. (2) To test the hypothesis that cerebral dysfunction after head injury causes myotatic reflex abnormalities through disordered descending control. These objectives arise from a proposal to use reflex measurements in monitoring patients with head injury. METHODS—The phasic stretch reflex of biceps brachii was elicited by a servo-positioned tendon hammer. Antagonist i...
Brainstem reflexes and brainstem auditory evoked responses in Huntington's chorea.
Bollen, E; Arts, R.J.; Roos, R A; van der Velde, E A; Buruma, O J
1986-01-01
Blink reflex, corneal reflex, jaw reflex, exteroceptive suppression in masseter muscles and brainstem auditory evoked potentials were measured in 20 patients with Huntington's chorea and 12 controls. A significantly increased latency of the second component of the homolateral and heterolateral blink reflex was found in the patient group as compared with the controls. The other investigations revealed no significant differences between patients and controls except for some facilitation of the ...
Prevalence of family history in patients with reflex syncope
Holmegard, Haya N; Benn, Marianne; Kaijer, Michelle Nymann; Haunsø, Stig; Mehlsen, Jesper
2013-01-01
Reflex syncope is defined by a rapid transient loss of consciousness caused by global cerebral hypoperfusion resulting from vasodilatation and/or bradycardia attributable to inappropriate cardiovascular reflexes. A hereditary component has been suggested, but prevalence of family history may differ...... among subtypes of reflex syncope, as these have different autonomic responses and pathogeneses may be diverse. The present study aimed to assess the prevalence of a positive family history of syncope and cardiovascular characteristics in patients with cardioinhibitory and vasodepressor reflex syncope...
Anatomy and neuro-pathophysiology of the cough reflex arc
Polverino Mario; Polverino Francesca; Fasolino Marco; Andò Filippo; Alfieri Antonio; De Blasio Francesco
2012-01-01
Abstract Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the...
On weakly Radon-Nikod\\'ym compact spaces
Martínez-Cervantes, Gonzalo
2015-01-01
A compact space is said to be weakly Radon-Nikod\\'ym if it is homeomorphic to a weak*-compact subset of the dual of a Banach space not containing an isomorphic copy of $\\ell_1$. In this work we provide an example of a continuous image of a Radon-Nikod\\'ym compact space which is not weakly Radon-Nikod\\'ym. Moreover, we define a superclass of the continuous images of weakly Radon-Nikod\\'ym compact spaces and study its relation with Corson compacta and weakly Radon-Nikod\\'ym compacta.
Juliana Spelta Valbuza
2011-10-01
Full Text Available Obstructive sleep apnea (OSA has high prevalence and may cause serious comorbities. The aim of this trial was to show if simple noninvasive methods such as gag reflex and palatal reflex are prospective multivariate assessments of predictor variables for OSA. METHOD: We evaluate gag reflex and palatal reflex, of fifty-five adult patients, and their subsequent overnight polysomnography. RESULTS: Forty-one participants presented obstructive sleep apnea. The most relevant findings in our study were: [1] absence of gag reflex on patients with severe obstructive apnea (p=0.001; [2] absence of palatal reflex on moderate obstructive apnea patients (p=0.02. CONCLUSION: Gag reflex and palatal reflex, a simple noninvasive test regularly performed in a systematic neurological examination can disclose the impact of the local neurogenic injury associated to snoring and/or obstructive sleep apnea syndrome.
Vestibulospinal control of reflex and voluntary head movement
Boyle, R.; Peterson, B. W. (Principal Investigator)
2001-01-01
Secondary canal-related vestibulospinal neurons respond to an externally applied movement of the head in the form of a firing rate modulation that encodes the angular velocity of the movement, and reflects in large part the input "head velocity in space" signal carried by the semicircular canal afferents. In addition to the head velocity signal, the vestibulospinal neurons can carry a more processed signal that includes eye position or eye velocity, or both (see Boyle on ref. list). To understand the control signals used by the central vestibular pathways in the generation of reflex head stabilization, such as the vestibulocollic reflex (VCR), and the maintenance of head posture, it is essential to record directly from identified vestibulospinal neurons projecting to the cervical spinal segments in the alert animal. The present report discusses two key features of the primate vestibulospinal system. First, the termination morphology of vestibulospinal axons in the cervical segments of the spinal cord is described to lay the structural basis of vestibulospinal control of head/neck posture and movement. And second, the head movement signal content carried by the same class of secondary vestibulospinal neurons during the actual execution of the VCR and during self-generated, or active, rapid head movements is presented.
Biological Motion Cues Trigger Reflexive Attentional Orienting
Shi, Jinfu; Weng, Xuchu; He, Sheng; Jiang, Yi
2010-01-01
The human visual system is extremely sensitive to biological signals around us. In the current study, we demonstrate that biological motion walking direction can induce robust reflexive attentional orienting. Following a brief presentation of a central point-light walker walking towards either the left or right direction, observers' performance…
Madonna as a symbol of reflexive modernisation
M. van den Berg; C.L. ter Hoeven
2013-01-01
The communication of social and cultural tensions embodied in the symbol Madonna explain the unparalleled public and scientific fascination for this cultural phenomenon. These tensions can be seen as communications of reflexive modernisation, in which modernisation has produced its own counterforce.
A reflexive perspective in problem solving
Chio, José Angel
2013-01-01
Full Text Available The objective of this paper is to favour the methodological process of reflexive analysis in problem solving in the general teaching methods that concentrates in strengthening the dimensional analysis, to gain a greater preparation of the students for the solution of mathematical problems.
The reflexive self and culture: a critique.
Adams, Matthew
2003-06-01
This article attempts to engage with a tendency in the theorization of social change and self-identity, evident in the work of a number of contemporary social theorists, to place an extended process of reflexivity at the heart of modern identity. As symptomatic of 'neo-modern' accounts of selfhood, critical readings of Giddens, Beck, Castells and some aspects of social theory more generally, and their account of modern reflexivity's relationship to culture, are assessed. In light of these criticisms, ways in which culture might still play an important part in the shaping of identity are considered. The relationship between language, culture and reflexivity, drawing from philosophy, sociology and G. H. Mead's own brand of social psychology, are all utilized in establishing a critique of the role Giddens and others designate for culture in the constitution of the contemporary self. By potentially repositioning self-identity in its connection to culture, the overall bearing of reflexivity upon the processes of self-identity is thus questioned. It is argued that a culturally-situated, yet fluid and multifarious account of self-identity is a necessary analytical and normative alternative. PMID:12945868
Reflectivity, Reflexivity and Situated Reflective Practice
Malthouse, Richard; Roffey-Barentsen, Jodi; Watts, Mike
2014-01-01
This paper describes an aspect of reflective practice referred to as situated reflective practice. The overarching theory is derived from social theories of structuration and reflexivity. In particular, from Giddens' theory of structuration, which sees social life as an interplay of agency and structure. Discussion of the research reported…
Smirnov, V A [Moscow State Pedagogical University, Moscow (Russian Federation); Kuznetsova, S V; Mayorova, I V
1998-08-31
We consider the following problem: how can one apply the methods employed for describing the cohomology of algebras and based on the use of the A{sub {infinity}}-structures of Stasheff to describe the cohomology of Banach algebras and locally convex algebras.
New Molecular Knowledge Towards the Trigemino-Cardiac Reflex as a Cerebral Oxygen-Conserving Reflex
N. Sandu
2010-01-01
Full Text Available The trigemino-cardiac reflex (TCR represents the most powerful of the autonomous reflexes and is a subphenomenon in the group of the so-called “oxygen-conserving reflexes”. Within seconds after the initiation of such a reflex, there is a powerful and differentiated activation of the sympathetic system with subsequent elevation in regional cerebral blood flow (CBF, with no changes in the cerebral metabolic rate of oxygen (CMRO2 or in the cerebral metabolic rate of glucose (CMRglc. Such an increase in regional CBF without a change of CMRO2 or CMRglc provides the brain with oxygen rapidly and efficiently. Features of the reflex have been discovered during skull base surgery, mediating reflex protection projects via currently undefined pathways from the rostral ventrolateral medulla oblongata to the upper brainstem and/or thalamus, which finally engage a small population of neurons in the cortex. This cortical center appears to be dedicated to transduce a neuronal signal reflexively into cerebral vasodilatation and synchronization of electrocortical activity; a fact that seems to be unique among autonomous reflexes. Sympathetic excitation is mediated by cortical-spinal projection to spinal preganglionic sympathetic neurons, whereas bradycardia is mediated via projections to cardiovagal motor medullary neurons. The integrated reflex response serves to redistribute blood from viscera to the brain in response to a challenge to cerebral metabolism, but seems also to initiate a preconditioning mechanism. Previous studies showed a great variability in the human TCR response, in special to external stimuli and individual factors. The TCR gives, therefore, not only new insights into novel therapeutic options for a range of disorders characterized by neuronal death, but also into the cortical and molecular organization of the brain.
Voluntary and reflex cough and the expiration reflex; implications for aspiration after stroke
Widdicombe, J G; Addington, W.R.; Fontana, G.A.; Stephens, R.E.
2011-01-01
Abstract Aspiration is a common result of stroke, and may lead to lung infections and pneumonia. Cough may prevent this aspiration and thus prevent the pneumonia. We review the four types of cough usually used to assess aspiration risk: voluntary cough (VC), reflex cough (RC), the laryngeal expiration reflex (LER), and cough on swallow (CoS). VC is easy to test but starts with an inspiration that may cause aspiration, and is controlled by cortico-brainstem pathways that may not be ...
Feminist Politics as Reflexive Citizenship
Nikos Katrivesis
2008-11-01
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.
Beraneck, Mathieu; Bojados, Mickael; Le Séac'h, Anne; Jamon, Marc; Vidal, Pierre-Paul
2012-01-01
The vestibular organs consist of complementary sensors: the semicircular canals detect rotations while the otoliths detect linear accelerations, including the constant pull of gravity. Several fundamental questions remain on how the vestibular system would develop and/or adapt to prolonged changes in gravity such as during long-term space journey. How do vestibular reflexes develop if the appropriate assembly of otoliths and semi-circular canals is perturbed? The aim of present work was to evaluate the role of gravity sensing during ontogeny of the vestibular system. In otoconia-deficient mice (ied), gravity cannot be sensed and therefore maculo-ocular reflexes (MOR) were absent. While canals-related reflexes were present, the ied deficit also led to the abnormal spatial tuning of the horizontal angular canal-related VOR. To identify putative otolith-related critical periods, normal C57Bl/6J mice were subjected to 2G hypergravity by chronic centrifugation during different periods of development or adulthood (Adult-HG) and compared to non-centrifuged (control) C57Bl/6J mice. Mice exposed to hypergravity during development had completely normal vestibulo-ocular reflexes 6 months after end of centrifugation. Adult-HG mice all displayed major abnormalities in maculo-ocular reflexe one month after return to normal gravity. During the next 5 months, adaptation to normal gravity occurred in half of the individuals. In summary, genetic suppression of gravity sensing indicated that otolith-related signals might be necessary to ensure proper functioning of canal-related vestibular reflexes. On the other hand, exposure to hypergravity during development was not sufficient to modify durably motor behaviour. Hence, 2G centrifugation during development revealed no otolith-specific critical period. PMID:22808156
Mathieu Beraneck
Full Text Available The vestibular organs consist of complementary sensors: the semicircular canals detect rotations while the otoliths detect linear accelerations, including the constant pull of gravity. Several fundamental questions remain on how the vestibular system would develop and/or adapt to prolonged changes in gravity such as during long-term space journey. How do vestibular reflexes develop if the appropriate assembly of otoliths and semi-circular canals is perturbed? The aim of present work was to evaluate the role of gravity sensing during ontogeny of the vestibular system. In otoconia-deficient mice (ied, gravity cannot be sensed and therefore maculo-ocular reflexes (MOR were absent. While canals-related reflexes were present, the ied deficit also led to the abnormal spatial tuning of the horizontal angular canal-related VOR. To identify putative otolith-related critical periods, normal C57Bl/6J mice were subjected to 2G hypergravity by chronic centrifugation during different periods of development or adulthood (Adult-HG and compared to non-centrifuged (control C57Bl/6J mice. Mice exposed to hypergravity during development had completely normal vestibulo-ocular reflexes 6 months after end of centrifugation. Adult-HG mice all displayed major abnormalities in maculo-ocular reflexe one month after return to normal gravity. During the next 5 months, adaptation to normal gravity occurred in half of the individuals. In summary, genetic suppression of gravity sensing indicated that otolith-related signals might be necessary to ensure proper functioning of canal-related vestibular reflexes. On the other hand, exposure to hypergravity during development was not sufficient to modify durably motor behaviour. Hence, 2G centrifugation during development revealed no otolith-specific critical period.
Variable Lebesgue spaces and hyperbolic systems
2014-01-01
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some mor...
Stick balancing with reflex delay in case of parametric forcing
Insperger, Tamas
2011-04-01
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.
Ingrid Hötte Ambrogi
2011-08-01
Full Text Available Pensar a ação docente requer analisar as condições objetivas nas quais elas ocorrem. O espaço das instituições escolares é um dos elementos de sustentação da práxis pedagógica e sua organização indica inúmeros elementos, tais como: coerência teórica e prática, condições objetivas para efetivar as propostas em relação ao número de crianças e o projeto pedagógico, entre outros. Portanto, quando se propõe a utilização de linguagens artísticas, os resultados das explorações infantis vinculam-se à organização dos espaços em relação ao projeto a ser efetivado. Ana Lúcia Goulart de Faria, Mayumi W. Souza Lima, Rollo May e Ana Mae Barbosa são alguns dos autores que dão sustentação teórica para nossas reflexões e indicam que a preparação do espaço vinculado à proposta para a ação das crianças potencializa seu processo de experimentação de troca e gera satisfação diante de suas criações.Taking the teaching attitude into consideration requires an analysis of the objective conditions in which it occurs. The space is are one of the elements which sustain the pedagogical praxis and their organization indicates several elements, such as theoretical and practical coherence, objective conditions to foster the proposals as to the number of children and the pedagogical project, among others. Therefore, when we propose the use of artistic languages, the result of the children's projects is linked to the organization of the spaces in which these projects are performed. Ana Lúcia Goulart de Faria, Mayumi W. Souza Lima, Rollo May, Ana Mae Barbosa are some of the authors who give us the theoretical framework for our reflections and point out that the preparation of the places for the children's action enhances their process for experimenting exchanges and generates satisfaction to these children towards their creations.
Elements of mathematics topological vector spaces
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).
Proximunalty in Orlicz-bochner Function Spaces
M. Khandaqji; Khalil, R; D. Hussein
2003-01-01
A (closed) subspace $ Y$ of a Banach space $ X$ is called proximinal if for every $ x\\in X$ there exists some $ y\\in Y$ such that $ \\|x-y\\|\\le\\|x-z\\|$ for $ z\\in Y$. It is the object of this paper is to study the proximinality of $ L^\\Phi(I,Y)$ in $ L^\\Phi(I,X)$ for some class of Young's functions $ \\Phi$, where $ I$ is the unit interval. We prove (among other results) that if $ Y$ is a separable proximinal subspace of $ X$, then $ L^\\Phi(I,Y)$ is proximinal in $ L^\\Phi(I,X)$.
Assessment and reflexivity in family therapy training.
Neden, Jeanette
2007-01-01
Educational contexts can be both enriched and impoverished by our relationship with learning and our 'identity stories' as learners influence how we construct contexts for learning. Keenoy et al. (2007) describe identity as a 'transient bridging concept' between the individual and society which is constructed through 'reflexive processes of naming, labelling, classifying and associating symbolic artefacts and social actors in a dialogical process of social definition and redefinition'. Can me...
Frequency dependence of vestibuloocular reflex thresholds
Haburcakova, Csilla; Lewis, Richard F.; Merfeld, Daniel M.
2011-01-01
How the brain processes signals in the presence of noise impacts much of behavioral neuroscience. Thresholds provide one way to assay noise. While perceptual thresholds have been widely investigated, vestibuloocular reflex (VOR) thresholds have seldom been studied and VOR threshold dynamics have never, to our knowledge, been reported. Therefore, we assessed VOR thresholds as a function of frequency. Specifically, we measured horizontal VOR thresholds evoked by yaw rotation in rhesus monkeys, ...
Reflectivity, reflexivity and situated reflective practice
Malthouse, R; Roffey-Barentsen, J; Watts, DM
2014-01-01
This paper describes an aspect of reflective practice referred to as ‘Situated Reflective Practice’ (SRP). The overarching theory is derived from social theories of structuration and reflexivity. In particular, from Giddens’s (1984) theory of structuration, this sees social life as interplay of agency and structure. Discussion of the research reported here centres on the nature of such situated reflection, considers related literature and presents the data collected in a recent small-scale st...
Axially evoked postural reflexes: influence of task
Govender, Sendhil; Dennis, Danielle L.; Colebatch, James G.
2014-01-01
Postural reflexes were recorded in healthy subjects (n = 17) using brief axial accelerations and tap stimuli applied at the vertebra prominens (C7) and manubrium sterni. Short latency (SL) responses were recorded from the soleus, hamstrings and tibialis anterior muscles and expressed as a percentage of the background EMG prior to stimulus onset. In the majority of postural conditions tested, subjects were recorded standing erect and leaning forward with their feet together. The SL response wa...
ABNORMAL CARDIOVASCULAR REFLEXES IN PATIENTS WITH ACHALASIA
戈峰; 李泽坚; 柯美云
1994-01-01
Using 3 non-invasive tests,abnormalities of cardiovascular reflex function were found in 7 of 15 patients with achalasia.Abnormalities of heart rate responses to the Valsalva maneuver,deep breathing ,and standing were moted in patients with autonomic neuropathy defect.The findings are consistent with the hypothesis that an abnormality of vagal function may contribute to the pathogenesis of achalasia.
Ruscheweyh, Ruth; Kreusch, Annette; Albers, Christoph; Sommer, Jens; Marziniak, Martin
2011-11-01
Distraction from pain reduces pain perception, and imaging studies have suggested that this may at least partially be mediated by activation of descending pain inhibitory systems. Here, we used the nociceptive flexor reflex (RIII reflex) to directly quantify the effects of different distraction strategies on basal spinal nociception and its temporal summation. Twenty-seven healthy subjects participated in 3 distraction tasks (mental imagery, listening to preferred music, spatial discrimination of brush stimuli) and, in a fourth task, concentrated on the painful stimulus. Results show that all 3 distraction tasks reduced pain perception, but only the brush task also reduced the RIII reflex. The concentration-on-pain task increased both pain perception and the RIII reflex. The extent of temporal summation of pain perception and the extent of temporal summation of the RIII reflex were not affected by any of the tasks. These results suggest that some, but not all, forms of pain reduction by distraction rely on descending pain inhibition. In addition, pain reduction by distraction seems to preferentially affect mechanisms of basal nociceptive transmission, not of temporal summation. PMID:21925793
The swallowing reflex and its significance as an airway defensive reflex
Takashi eNishino
2013-01-01
Full Text Available Swallowing function, in humans, is very complex. Swallowing plays, not only an important role in food digestion, but also a major role in preventing the entrance of food and/or other materials into the lower respiratory tract. To achieve this, precise coordination is necessary between breathing and swallowing since the pharynx serves as a common pathway for both respiration and digestion. The swallowing reflex consists of afferent pathways, central integration, and efferent pathways. Any defect or disorder along reflex arc can cause a potential delay or impairment in swallow function. The swallowing reflex can be modulated not only by pathological factors but also by physiological factors. Among these, timing of swallows in relation to the phase of respiration may be the most important factor that determines the occurrence of pulmonary aspiration, since phases of inspiration and the expiration-inspiration transition are the most vulnerable for pulmonary aspiration.
Diadic Baire space and continuity of weakly quasi-continuous maps(in Ukrainian
O. V. Maslyuchenko
2011-07-01
Full Text Available We introduce some diadic analogue of the Choquet game and a class of diadic Baire spaces which is a subclass of Baire spaces and is wider then the class Choquet spaces. We prove that for any diadic Baire space X, a Banach space Y, a countable Asplund∗ norming set E⊆Y∗ and for every map φ:X→Y, such that zφ is quasi-continuous for any z∈E, the discontinuity point set C(φ is residual.
An experimental study of artificial murine bladder reflex arc established by abdominal reflex
WANG Jin-wu; ZHAO Yu-wu; HOU Chun-lin; NI Wei-feng; RUI Bi-yu; GUO Shang-chun; ZHENG Xian-you; DAI Ke-rong
2011-01-01
Background The neurogenic bladder dysfunction caused by spinal cord injury is difficult to treat clinically. The aim of this research was to establish an artificial bladder reflex arc in rats through abdominal reflex pathway above the level of spinal cord injury, reinnervate the neurogenic bladder and restore bladder micturition.Methods The outcome was achieved by intradural microanastomosis of the right T13 ventral root to S2 ventral root with autogenous nerve grafting, leaving the right T13 dorsal root intact. Long-term function of the reflex arc was assessed from nerve electrophysiological data and intravesical pressure tests during 8 months postoperation. Horseradish peroxidase (HRP) tracing was performed to observe the effectiveness of the artificial reflex.Results Single stimulus (3 mA, 0.3 ms pulses, 20 Hz, 5-second duration) on the right T13 dorsal root resulted in evoked action potentials, raised intravesical pressures and bladder smooth muscle, compound action potential recorded from the right vesical plexus before and after the spinal cord transaction injury between L5 and S4 segmental in 12 Sprague-Dawley rats. There were HRP labelled cells in T13 ventral horn on the experimental side and in the intermediolateral nucleus on both sides of the L6-S4 segments after HRP injection. There was no HRP labelled cell in T13 ventral horn on the control side.Conclusion Using the surviving somatic reflex above the level of spinal cord injury to reconstruct the bladder autonomous reflex arc by intradural microanastomosis of ventral root with a segment of autologous nerve grafting is practical in rats and may have clinical applications for humans.
Nice Surjections on Spaces of Operators
T S S R K Rao
2006-11-01
A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on $\\mathcal{K}(X, Y)$ for Banach spaces , . We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for $\\mathcal{L}(X, Y)$ thereby proving an analogue of the result from [9] for $L^p(1 < p ≠ 2 < ∞)$ spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from [8].
Electrophysiological observations on the human pudendo-anal reflex.
Varma, J S; Smith, A N; McInnes, A
1986-01-01
A reproducible electrophysiological technique is described to determine the latency of reflex contraction of the external anal sphincter in response to stimulation of the dorsal genital nerve: the pudendo-anal reflex. This was studied in 38 asymptomatic control subjects and 20 women with neurogenic faecal incontinence, supplemented by determination of the mean motor unit potential duration (MUPD) of the external anal sphincter and anorectal manometry. The reflex latency in the control group w...
Characteristics of Glottic Closure Reflex in a Canine Model
Kim, Young-Ho; Kang, Ju Wan; Kim, Kwang-Moon
2009-01-01
Purpose The most important function of the larynx is airway protection which is provided through a polysynaptic reflex closure triggered by the receptors in the glottic and supraglottic mucosa, evoking the reflex contraction of the laryngeal muscles especially by strong adduction of vocal cords. Based on the hypotheses that central facilitation is essential for this bilateral adductor reflex and that its disturbance can result in weakened laryngeal closure, we designed this study to elucidate...
Cardiovascular regulation by skeletal muscle reflexes in health and disease
Murphy, Megan N.; Mizuno, Masaki; Mitchell, Jere H.; Smith, Scott A
2011-01-01
Heart rate and blood pressure are elevated at the onset and throughout the duration of dynamic or static exercise. These neurally mediated cardiovascular adjustments to physical activity are regulated, in part, by a peripheral reflex originating in contracting skeletal muscle termed the exercise pressor reflex. Mechanically sensitive and metabolically sensitive receptors activating the exercise pressor reflex are located on the unencapsulated nerve terminals of group III and group IV afferent...
Can Treadmill Perturbations Evoke Stretch Reflexes in the Calf Muscles?
Sloot, Lizeth H.; van den Noort, Josien C; van der Krogt, Marjolein M.; Bruijn, Sjoerd M.; Jaap Harlaar
2015-01-01
Disinhibition of reflexes is a problem amongst spastic patients, for it limits a smooth and efficient execution of motor functions during gait. Treadmill belt accelerations may potentially be used to measure reflexes during walking, i.e. by dorsal flexing the ankle and stretching the calf muscles, while decelerations show the modulation of reflexes during a reduction of sensory feedback. The aim of the current study was to examine if belt accelerations and decelerations of different intensiti...
The Role of Transformational Leadership in Enhancing Team Reflexivity
Schippers, M.C.; Hartog, den, JI Jerry; Koopman, P.L.; Knippenberg, van, D.
2007-01-01
textabstractTeam reflexivity, or the extent to which teams reflect upon and modify their functioning, has been identified as a key factor in the effectiveness of work teams. As yet, however, little is known about the factors that play a role in enhancing team reflexivity, and it is thus important to develop theorizing around the determinants of reflexivity. From an applied perspective, leadership is a very relevant factor. The current study is a first step in the development of such a theory,...
Skew polynomial rings over abelian and idempotent reflexive rings
Louzari, Mohamed
2015-01-01
Let $R$ be a ring and $\\sigma$ an endomorphism of $R$. In this note, we study skew polynomial rings and skew power series rings over idempotent reflexive rings and abelian rings. Also, we introduce the concept of right (resp., left) $\\sigma$-idempotent reflexive rings which generalizes right (resp., left) idempotent reflexive rings and $\\sigma$-abelian rings. Certain results are obtained as corollaries from our results.
Cortical control of hering-breuer reflexes in anesthetized rats
Aleksandrov VG; Mercuriev VA; Ivanova TG; Tarasievich AA; Aleksandrova NP
2009-01-01
Abstract It had been hypothesized that the regions of prefrontal cortex which are involved in respiratory control can modulate Hering-Breuer reflexes evoked by vagal input from pulmonary stretch receptors. In the present study, experiments were performed on urethane anesthetized spontaneously breathing Wistar rats. The expiratory-promoting reflex was evaluated from changes in expiratory time immediately after airway occlusion at the end of inspiration. The inspiratory-inhibitory reflex was es...
Cholesteric Liquid Crystal Based Reflex Color Reflective Displays
Khan, Asad
2012-02-01
Bistable color cholesteric liquid crystal displays are unique LCDs that exhibit high reflectivity, good contrast, extremely low power operation, and are amenable to versatile roll-to-roll manufacturing. The display technology, now branded as Reflex has been in commercialized products since 1996. It has been the subject of extensive research and development globally by a variety of parties in both academic and industrial settings. Today, the display technology is in volume production for applications such as dedicated eWriters (Boogie Board), full color electronic skins (eSkin), and displays for smart cards. The flexibility comes from polymerization induced phase separation using unique materials unparalleled in any other display technology. The blend of monomers, polymers, cross linkers, and other components along with nematic liquid crystals and chiral dopants is created and processed in such ways so as to enable highly efficient manufactrable displays using ultra thin plastic substrates -- often as thin as 50μm. Other significant aspects include full color by stacking or spatial separation, night vision capability, ultra high resolution, as well as active matrix capabilities. Of particular note is the stacking approach of Reflex based displays to show full color. This approach for reflective color displays is unique to this technology. Owing to high transparency in wavelength bands outside the selective reflection band, three primarily color layers can be stacked on top of each other and reflect without interfering with other layers. This highly surprising architecture enables the highest reflectivity of any other reflective electronic color display technology. The optics, architecture, electro-topics, and process techniques will be discussed. This presentation will focus on the physics of the core technology and color, it's evolution from rigid glass based displays to flexible displays, development of products from the paradigm shifting concepts to consumer
Anatomy and neuro-pathophysiology of the cough reflex arc
Polverino Mario
2012-06-01
Full Text Available Abstract Coughing is an important defensive reflex that occurs through the stimulation of a complex reflex arc. It accounts for a significant number of consultations both at the level of general practitioner and of respiratory specialists. In this review we first analyze the cough reflex under normal conditions; then we analyze the anatomy and the neuro-pathophysiology of the cough reflex arc. The aim of this review is to provide the anatomic and pathophysiologic elements of evaluation of the complex and multiple etiologies of cough.
Supercyclicity with Respect to a Sequence on Special Sequence Spaces
S. Foroutan, and B. Yousef
2007-06-01
Full Text Available Let {β(n}∞ n=−∞ be a sequence of positive numbers such that β(0 = 1 and let 1 < p < ∞. We consider the space of all formal Laurent series f(z = P∞ n=−∞ ˆf(nz n such that X∞ n=−∞ | ˆf(n| pβ(n p < ∞. We investigate the supercyclicity with respect to a sequence on the Banach spaces of formal Laurent series
Raven, Glenda
2006-01-01
In this article, the author argues for a central and critical role for "reflexivity in research" with the aim of developing and strengthening not only everyone's understanding of what everyone does in environmental education research, but also how, and why everyone does it. In a narrative account of methodological issues that occurred within, and…
Reflexive regulation of CSR to promote sustainability
Buhmann, Karin
2011-01-01
This article discusses Corporate Social Responsibility (CSR) from the perspective of governmental regulation as a measure to promote public policy interests through public-private regulation intended to influence firms’ self-regulation. Presenting a ‘government case’ for CSR, the connection between...... and the EU CSR Alliance. Focusing on human rights based in international law, it analyses the patterns of negotiation in the MSF and the background for the launch of the CSR Alliance. It shows that analysing public-private regulation of CSR from the perspective of reflexive law theory assists us in...
Olyaei G; Akbari M; Esfandiarpoor F
2000-01-01
The purpose of the this study was to investigate the effect of direct current on montoneuron reflex exitability. Thirty six subjects (18 males, 18 females) 19.36 years of age ( x= 24.06, SD= 3.63) participated in this study. The reflex excitability of soleus motoneruons was assessed by measuring the amount of change in the peak to peak ampitude of the H-reflex before and after direct current was applied to the skin over the sural nerve. Reflex recordings were taken before and after direct cur...
E.C. Vasquez
1997-04-01
Full Text Available The maintenance of arterial pressure at levels adequate to perfuse the tissues is a basic requirement for the constancy of the internal environment and survival. The objective of the present review was to provide information about the basic reflex mechanisms that are responsible for the moment-to-moment regulation of the cardiovascular system. We demonstrate that this control is largely provided by the action of arterial and non-arterial reflexes that detect and correct changes in arterial pressure (baroreflex, blood volume or chemical composition (mechano- and chemosensitive cardiopulmonary reflexes, and changes in blood-gas composition (chemoreceptor reflex. The importance of the integration of these cardiovascular reflexes is well understood and it is clear that processing mainly occurs in the nucleus tractus solitarii, although the mechanism is poorly understood. There are several indications that the interactions of baroreflex, chemoreflex and Bezold-Jarisch reflex inputs, and the central nervous system control the activity of autonomic preganglionic neurons through parallel afferent and efferent pathways to achieve cardiovascular homeostasis. It is surprising that so little appears in the literature about the integration of these neural reflexes in cardiovascular function. Thus, our purpose was to review the interplay between peripheral neural reflex mechanisms of arterial blood pressure and blood volume regulation in physiological and pathophysiological states. Special emphasis is placed on the experimental model of arterial hypertension induced by N-nitro-L-arginine methyl ester (L-NAME in which the interplay of these three reflexes is demonstrable
Liang Yue; Yang He
2011-01-01
Abstract The paper deals with the existence of positive solutions for Neumann boundary value problems of nonlinear second-order integro-differential equations - u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) = u ′ ( 1 ) = θ and u ″ ( t ) + M u ( t ) = f ( t , u ( t ) , ( S u ) ( t ) ) , 0 < t < 1 , u ′ ( 0 ) ...
The paper studies a class of set-values operators with emphasis on properties of their adjoints and existence of eigenvalues and eigenvectors of infinite-dimensional convex closed set-valued operators. Sufficient conditions for existence of eigenvalues and eigenvectors of set-valued convex closed operators are derived. These conditions specify possible features of control problems. The results are applied to some constrained control problems of infinite-dimensional systems described by discrete-time inclusions whose right-hand-sides are convex closed set- valued functions. (author). 8 refs
Banach空间中的∞阶Bessel序列%Bessel sequence of order ∞ in a Banach space
虞志坚; 曹怀信
2001-01-01
在Banach空间中引入了∞阶Bessel序列与 Bessel算子的概念,研究了它们的一系列重要性质,并给出了一个序列成为∞阶Bessel序列的若干充分必要条件,证明了全体∞阶Bessel序列之集构成一个Banach空间.
Bessel sequences of order 1 in a Banach space%Banach空间中的1阶Bessel序列
虞志坚; 曹怀信
2005-01-01
在Banach空间X中引入了1阶Bessel序列与Bessel算子的概念,证明了X上的全体1阶Bessel序列构成一个Banach空间;对X上的任意1阶Bessel序列f={fn}n∈∧,引入了算子Tf:X*→l1,给出一个序列成为1阶Bessel序列的若干充分必要条件;引入(1,∞)阶对偶对的概念,证明了(f,g*)成为X×X*中的(1,∞)阶对偶对当且仅当Tf*Tg*|x=IX.
Monitoring of head injury by myotatic reflex evaluation
Cozens, J; Miller, S.; Chambers, I.; Mendelow, A
2000-01-01
OBJECTIVES—(1) To establish the feasibility of myotatic reflex measurement in patients with head injury. (2) To test the hypothesis that cerebral dysfunction after head injury causes myotatic reflex abnormalities through disordered descending control. These objectives arise from a proposal to use reflex measurements in monitoring patients with head injury. METHODS—The phasic stretch reflex of biceps brachii was elicited by a servo-positioned tendon hammer. Antagonist inhibition was evoked by vibration to the triceps. Using surface EMG, the amplitude of the unconditioned biceps reflex and percentage antagonist inhibition were measured. After standardisation in 16 normal adult subjects, the technique was applied to 36 patients with head injury across the range of severity. Objective (1) was addressed by attempting a measurement on each patient without therapeutic paralysis; three patients were also measured under partial paralysis. Objective (2) was addressed by preceding each of the 36 unparalysed measurements with an assessment of cerebral function using the Glasgow coma scale (GCS); rank correlation was employed to test a null hypothesis that GCS and reflex indices are unrelated. RESULTS—In normal subjects, unconditioned reflex amplitude exhibited a positive skew requiring logarithmic transformation. Antagonist inhibition had a prolonged time course suggesting presynaptic mechanisms; subsequent measurements were standardised at 80 ms conditioning test interval (index termed "TI80"). Measurements were obtained on all patients, even under therapeutic paralysis (objective (1)). The unconditioned reflex was absent in most patients with GCS less than 5; otherwise it varied little across the patient group. TI80 fell progressively with lower GCS, although patients' individual GCS could not be inferred from single measurements. Both reflex indices correlated with GCS (p<0.01), thereby dismissing the null hypothesis (objective (2)).
Gorini, C.; Jameson, H. S.; Mendelowitz, D.
2009-01-01
Stimulation of the trigeminal nerve evokes a dramatic decrease in heart rate and blood pressure, and this reflex has generally been termed the trigeminocardiac reflex. A subset of the trigeminocardiac reflex is the diving reflex in which the nasal mucosa is stimulated with water or air-borne chemical irritants. Activation of the diving reflex evokes a pronounced bradycardia, mediated by increased parasympathetic cardiac activity, and is the most powerful autonomic reflex. However, exaggeratio...
Generalizations of the Lax-Milgram Theorem
Dimosthenis Drivaliaris
2007-05-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
Generalizations of the Lax-Milgram Theorem
Yannakakis Nikos
2007-01-01
Full Text Available We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular, we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all bounded linear functionals of the latter. We also give two applications to singular differential equations.
Reflex switch experiments with capacitor bank drivers
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
Bourdieu and Science Studies: Toward a Reflexive Sociology
Hess, David J.
2011-01-01
Two of Bourdieu's fundamental contributions to science studies--the reflexive analysis of the social and human sciences and the concept of an intellectual field--are used to frame a reflexive study of the history and social studies of science and technology as an intellectual field in the United States. The universe of large, Ph.D.-granting…
The Role of Transformational Leadership in Enhancing Team Reflexivity
M.C. Schippers (Michaéla); D.N. den Hartog (Deanne); P.L. Koopman (Paul); D.L. van Knippenberg (Daan)
2007-01-01
textabstractTeam reflexivity, or the extent to which teams reflect upon and modify their functioning, has been identified as a key factor in the effectiveness of work teams. As yet, however, little is known about the factors that play a role in enhancing team reflexivity, and it is thus important to
Voluntary Control of the Near Reflex: A Case Report
Serpil Akar
2014-03-01
Full Text Available Spasm of the near reflex is a rare disorder that involves intermittent and variable episodes of esotropia, pseudomyopia, and pupillary myosis. It is usually functional in origin and is seen mainly in young patients. Treatment options for spasm of the near reflex have had variable success. In instances where the etiology of spasm of the near reflex was suspected to be hysteria, psychotherapy has proven beneficial. We report the case of an 11-year-old girl who had functional spasm of the near reflex. The symptoms persisted for two years. Symptomatic relief was achieved by cycloplegia and spectacle correction (added plus lenses at near. The patient also underwent psychological counseling. In our case, the functional spasm of the near reflex spontaneously resolved after 2 years. (Turk J Ophthalmol 2014; 44: 161-3
Effects of Bed Rest on Conduction Velocity of the Triceps Surae Stretch Reflex and Postural Control
Reschke, M. F.; Wood, S. J.; Cerisano, J. M.; Kofman, I. S.; Fisher, E. A.; Esteves, J. T.; Taylor, L. C.; DeDios, Y. E.; Harm, D. L.
2011-01-01
Despite rigorous exercise and nutritional management during space missions, astronauts returning from microgravity exhibit neuromuscular deficits and a significant loss in muscle mass in the postural muscles of the lower leg. Similar changes in the postural muscles occur in subjects participating in long-duration bed rest studies. These adaptive muscle changes manifest as a reduction in reflex conduction velocity during head-down bed rest. Because the stretch reflex encompasses both the peripheral (muscle spindle and nerve axon) and central (spinal synapse) components involved in adaptation to calf muscle unloading, it may be used to provide feedback on the general condition of neuromuscular function, and might be used to evaluate the effectiveness of countermeasures aimed at preserving muscle mass and function during periods of unloading. Stretch reflexes were measured on 18 control subjects who spent 60 to 90 days in continuous 6 deg head-down bed rest. Using a motorized system capable of rotating the foot around the ankle joint (dorsiflexion) through an angle of 10 degrees at a peak velocity of about 250 deg/sec, a stretch reflex was recorded from the subject's left triceps surae muscle group. Using surface electromyography, about 300 reflex responses were obtained and ensemble-averaged on 3 separate days before bed rest, 3 to 4 times in bed, and 3 times after bed rest. The averaged responses for each test day were examined for reflex latency and conduction velocity (CV) across gender. Computerized posturography was also conducted on these same subjects before and after bed rest as part of the standard measures. Peak-to-peak sway was measured during Sensory Organization Tests (SOTs) to evaluate changes in the ability to effectively use or suppress visual, vestibular, and proprioceptive information for postural control. Although no gender differences were found, a significant increase in reflex latency and a significant decrease in CV were observed during the bed
The swallowing reflex and its significance as an airway defensive reflex
TakashiNishino
2013-01-01
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 ...
The swallowing reflex and its significance as an airway defensive reflex
Nishino, Takashi
2013-01-01
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 defe...
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)
Reflexivity, description and the analysis of social settings
Rodney Watson
2005-01-01
Full Text Available The concept of 'reflexivity' has become an often-intoned mantra in contemporary social science, particulary, perhaps, sociology. This article, however, argues that the 'blanket use' of 'reflexivity' glosses over and confuses many different actual definitions and understandings of the concept - not least because the concept operates differently as a move within each of the divergent analytic 'games' that compose the overall discipline. One (among many other crucial distinctions is that between 'stipulative' and 'essential' reflexivity - the former originating in part in G.H.Mead's notions of the 'I' and the 'Me', and extended within current theories of reflexive modernity. This concept has been wrenched by professional social scientist from its mundane moorings and has been 'elevated' into an analytic technique of self interrogation. By contrast, 'essential' reflexivity, as adduced by ethnomethodological sociologists, remains resolutely emplaced in the domain of lay society-members' ordinary sense-making practices: it here refers to the reciprocal, back-and-forth determinations of sense of members' mundane descriptions of their specific circumstances and of the circumstances they describe - description and circumstance reflect upon each other during the sense-making practices. A brief example of essential reflexivity is given- reflexive formulations in ordinary conversations.
Khinchin's Inequality, Dunford-Pettis and Compact Operators on the Space ([0, 1], )
Dumitru Popa
2007-02-01
We prove that if , are Banach spaces, a compact Hausdorff space and :(,) → is a bounded linear operator, and if is a Dunford–Pettis operator the range of the representing measure $G()\\subseteq D P(X, Y)$ is an uniformly Dunford–Pettis family of operators and $\\|G\\|$ is continuous at $\\emptyset$. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space $C([0,1],X)$ with values in $c_0$ or $l_p,(1≤ p < ∞)$ be Dunford–Pettis and/or compact operators, in which, Khinchin’s inequality plays an important role.
The Effects of Attention on the Trigeminal Blink Reflex.
Schicatano, Edward J
2016-04-01
During top-down processing, higher cognitive processes modulate lower sensory processing. The present experiment tested the effects of directed attention on trigeminal reflex blinks in humans (n = 8). In separate sessions, participants either attended to blink-eliciting stimuli or were given no attentional instructions during stimulation of the supraorbital branch of the trigeminal nerve. Attention to blink-eliciting stimuli significantly increased reflex blink amplitude and duration and shortened blink latency compared with the no attention condition. These results suggested that higher processes such as attention can modify the trigeminal blink reflex circuit. PMID:27166326
The functional and pragmatic features of assonance phraseological reflexes
Shkapenko T.
2014-09-01
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.
On $\\mathfrak{I}$-reconstruction Property
Vashisht, L. K.; Khattar, Geetika
2013-01-01
Reconstruction property in Banach spaces introduced and studied by Casazza and Christensen in [1]. In this paper we introduce reconstruction property in Banach spaces which satisfy $\\mathfrak{I}$-property. A characterization of reconstruction property in Banach spaces which satisfy $\\mathfrak{I}$-property in terms of frames in Banach spaces is obtained. Banach frames associated with reconstruction property are discussed.
Watt, D. G.; Money, K. E.; Tomi, L. M.
1986-01-01
Reflex responses that depend on human otolith organ sensitivity were measured before, during and after a 10 day space flight. Otolith-spinal reflexes were elicited by means of sudden, unexpected falls. In weightlessness, "falls" were achieved using elastic cords running from a torso harness to the floor. Electromyographic (EMG) activity was recorded from gastrocnemius-soleus. The EMG response occurring in the first 100-120 ms of a fall, considered to be predominantly otolith-spinal in origin, decreased in amplitude immediately upon entering weightlessness, and continued to decline throughout the flight, especially during the first two mission days. The response returned to normal before the first post-flight testing session. The results suggest that information coming from the otolith organs is gradually ignored by the nervous system during prolonged space flight, although the possibility that otolith-spinal reflexes are decreased independent of other otolith output pathways cannot be ruled out.
Watt, D. G. D.; Money, K. E.; Tomi, L. M.
1986-01-01
Reflex responses that depend on human otolith organ sensitivity were measured before, during and after a 10 day space flight. Otolith-spinal reflexes were elicited by means of sudden, unexpected falls. In weightlessness, 'falls' were achieved using elastic cords running from a torso harness to the floor. Electromyographic (EMG) activity was recorded from gastrocnemius-soleus. The EMG response occurring in the first 100-120 ms of a fall, considered to be predominantly otolith-spinal in origin, decreased in amplitude immediately upon entering weightlessness, and continued to decline throughout the flight, especially during the first two mission days. The response returned to normal before the first post-flight testing session. The results suggest that information coming from the otolith organs is gradually ignored by the nervous system during prolonged space flight, although the possibility that otolith-spinal reflexes are decreased independent of other otolith output pathways cannot by ruled out.
Spinal Reflexes During Postural Control Under Psychological Pressure.
Tanaka, Yoshifumi
2015-07-01
This study investigated the effect of psychological pressure on spinal reflex excitability. Thirteen participants performed a balancing task by standing on a balance disk with one foot. After six practice trials, they performed one nonpressure and one pressure trial involving a performance-contingent cash reward or punishment. Stress responses were successfully induced; state anxiety, mental effort, and heart rates all increased under pressure. Soleus Hoffmann reflex amplitude in the pressure trial was significantly smaller than in the nonpressure trial. This modification of spinal reflexes may be caused by presynaptic inhibition under the control of higher central nerve excitation under pressure. This change did not prevent 12 of the 13 participants from successfully completing the postural control task under pressure. These results suggest that Hoffmann reflex inhibition would contribute to optimal postural control under stressful situations. PMID:25587695
Nasal reflexes: implications for exercise, breathing, and sex.
Baraniuk, James N; Merck, Samantha J
2008-04-01
Nasal patency, with both congestion and decongestion, is affected in a wide variety of reflexes. Stimuli leading to nasal reflexes include exercise; alterations of body position, pressure, and temperature; neurologic syndromes; and dentistry. As anticipated, the vagal and trigeminal systems are closely integrated through nasobronchial and bronchonasal reflexes. However, perhaps of greater pathophysiologic importance are the naso-hypopharyngeal-laryngeal reflexes that become aggravated during sinusitis. None other than Sigmund Freud saw deeply beyond the facial adornment and recognized the deeper sexual tensions that can regulate nasal functions and psychoanalytical status. Wine, women, and song are linked with airflow through the nose-the nose, which by any other name would still smell as sweetly. PMID:18417057
On the gastrocecal inhibitory reflex in the rat.
Lee,Zai-Liu
1981-11-01
Full Text Available In rats anesthetized with urethane, the effects of distention of the stomach upon cecal motility and neural mechanisms which generate this effect were studied. Cecal motility was inhibited which generate this effect were studied. Cecal motility was inhibited when the pars glandularis of the stomach was distended by pressure ranging from 25 to 30 cm H2O. This inhibitory reflex was not affected by bilateral cervical vagotomy, but completely abolished following bilateral severance of the greater splanchnic nerves or after intravenous administration of guanethidine. After transection of the spinal cord at the level of the 5th thoracic segment the inhibitory reflex remained intact, but was abolished following pithing of the 6th thoracic segment and below. It may be concluded that the afferent and efferent path of the gastrocecal inhibitory reflex mainly pass through the greater splanchnic nerves and the reflex center is located in thoracic segments caudal to the 6th thoracic segment.
Reconsidering reflexivity: introducing the case for intellectual entrepreneurship.
Cutcliffe, John R
2003-01-01
In this article, the author reconsiders reflexivity and attempts to examine some unresolved issues by drawing particular attention to the relationship between reflexivity and certain related phenomena/processes: the researcher's a priori knowledge, values, beliefs; empathy within qualitative research; the presence and influence of the researcher's tacit knowledge, and May's "magic" in method. Given the limitations of some reflexive activity identified in this article, the author introduces the case for greater intellectual entrepreneurship within the context of qualitative research. He suggests that excessive emphasis on reflexive activity might inhibit intellectual entrepreneurship. Wherein intellectual entrepreneurship implies a conscious and deliberate attempt on the part of academics to explore the world of ideas boldly; to take more risks in theory development and to move away from being timid researchers. PMID:12564268
Short-duration spaceflight impairs human carotid baroreceptor-cardiac reflex responses
Fritsch, Janice M.; Charles, John B.; Bennett, Barbara S.; Jones, Michele M.; Eckberg, Dwain L.
1992-01-01
The effect of a spaceflight on the vagally mediated baroreceptor-cardiac reflex responses of humans were investigated by measuring the responses (provoked by neck pressure changes) in supine position and the heart rate and blood pressure in the supine and standing positions in 16 astronauts before and after 4- to 5-day long Space Shuttle missions. The results showed that exposures to spaceflight resulted in reduced baseline levels of the vagal-cardiac outflow and the vagally mediated responses to changes of the arterial baroreceptor input and that these changes contribute to postflight reductions of astronauts' ability to maintain standing arterial pressures.
Rudrashish Haldar; Jasleen Kaur; Sukhminder Jit Singh Bajwa
2015-01-01
Nasocardiac reflex is a relatively less discussed variant of trigeminovagal reflex where the afferent arc of the reflex is represented by any of the branches of the trigeminal nerves, and the efferent arc is via the vagus nerve. Elicitation of this reflex is commonly seen during surgical manipulation and is manifested as bradycardia or even asystole. We report a case where nasocardiac reflex was unusually observed in a patient when aspiration and injection were done through a nasogastric tube.
Critical Evaluation of a Program to Foster Reflexive Antiracism
Hayley Franklin; Yin Paradies; Emma Kowal
2014-01-01
This paper documents the evaluation of a three-day program entitled: Race, Culture, Indigeneity and the Politics of Disadvantage, which was delivered in 2010 in Melbourne, Australia with the aim of promoting Reflexive Antiracism (RA), a novel diversity training approach. To assess the impact of the program on its participants, the Reflexive Antiracism Scale- Indigenous (RAS-I) was devised and administered before and after the program both to participants and a matched control group. The progr...
Trigeminocardiac Reflex during Maxillary Reconstruction Surgery: A Case Report
Mayank Kulshrestha; Sahil Kapur; Col. M Kapadia
2014-01-01
Systemic hypotension, cardiac dysrhythmia especially bradycardia, apnoea, and gastric hypermotility occurring presumably after stimulation of any of the sensory branches of trigeminal nerve is coined as trigeminocardiac reflex (TCR). It has been described to occur in various surgeries like cerebello-pontine angle and pituitary fossa surgeries. Such bradycardic reflex responses have also been observed during maxillofacial surgeries. The TCR presents as a challenge to both the Anaesthesiologis...
Emetic stimulation inhibits the swallowing reflex in decerebrate rats.
Kurozumi, Chiharu; Yamagata, Ryuzo; Himi, Naoyuki; Koga, Tomoshige
2008-01-01
The effects of emetic stimulation on the swallowing reflex were investigated in decerebrated rats. Hypoxia, gastric distension and LiCl administration were used as emetic stimulations. The swallowing reflex was elicited by electrical stimulation of the superior laryngeal nerve (SLN, 20 Hz, 3-5 V, 0.3 ms duration) for 20 s. To examine the effect of hypoxia, nitrogen gas was inhaled under artificial ventilation. There were significantly fewer swallows during a decrease in PO(2) than under air v...
Variable Patterned Pudendal Nerve Stimuli Improves Reflex Bladder Activation
Bruns, Tim M.; Bhadra, Narendra; Gustafson, Kenneth J.
2008-01-01
We evaluated variable patterns of pudendal nerve (PN) stimuli for reflex bladder excitation. Reflex activation of the bladder has been demonstrated previously with 20–33 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 (0.5–100 Hz) was performed under isovolumetric conditio...
Neurophysiology and Clinical Implications of the Laryngeal Adductor Reflex
Domer, Amanda S.; Kuhn, Maggie A.; Belafsky, Peter C.
2013-01-01
The laryngeal adductor reflex (LAR) is an involuntary protective response to stimuli in the larynx. The superior laryngeal nerve (SLN) acts as the afferent limb and the recurrent laryngeal nerve (RLN) as the efferent limb of this reflex, which is modulated by the central nervous system. Perhaps the most clinically significant application of the LAR is its use in laryngopharyngeal (LP) sensory discrimination testing. Importantly, aberrations in the LAR may predict dysphagia or portend clinical...
Pain-related somatosensory evoked potentials in cortical reflex myoclonus.
Kakigi, R; Shibasaki, H; Neshige, R; Ikeda, A.; Mamiya, K.; Kuroda, Y
1990-01-01
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 ...
A tapetal-like fundus reflex in a healthy male
Schatz, Patrik; Bregnhøj, Jesper; Arvidsson, Henrik; Sharon, Dror; Mizrahi-Meissonnier, Liliana; Sander, Birgit; Grønskov, Karen; Larsen, Michael
2012-01-01
To report on the retinal function and structure in a 37-year-old male who presented with a tapetal-like reflex (TLR) indistinguishable from that seen in female carriers of X-linked retinitis pigmentosa (XLRP).......To report on the retinal function and structure in a 37-year-old male who presented with a tapetal-like reflex (TLR) indistinguishable from that seen in female carriers of X-linked retinitis pigmentosa (XLRP)....
The Reflexive Nature of Reading as Ethnographic Practice: Editorial Note
Roth, Wolff-Michael
2004-01-01
In diesem Editorial schlage ich vor, das Lesen publizierter Texte nicht nur als Betreiben von Ethnographie zu verstehen, sondern darüber hinausgehend konkretisiert sich das Lesen auch in der Produktion von neuen Texten, und in diesem Prozess werden die kulturellen Praktiken reproduziert, die in den gelesenen Texten analysiert wurden. Als ethnographische Methode ist das Lesen ein reflexives Projekt. Ich skizziere einen dialektischen Ansatz, der diese reflexive Natur des Lesens theoretisiert.
Die reflexive Natur des Lesens als ethnografische Praxis (Editorial)
Roth, Wolff-Michael
2004-01-01
In diesem Editorial schlage ich vor, das Lesen publizierter Texte nicht nur als Betreiben von Ethnographie zu verstehen, sondern darüber hinausgehend konkretisiert sich das Lesen auch in der Produktion von neuen Texten, und in diesem Prozess werden die kulturellen Praktiken reproduziert, die in den gelesenen Texten analysiert wurden. Als ethnographische Methode ist das Lesen ein reflexives Projekt. Ich skizziere einen dialektischen Ansatz, der diese reflexive Natur des Lesens theoretisiert. ...
Control of attention before reflexive and intentional saccades
Casana-Perez, Susana Maria
2004-01-01
The relation between covert and overt spatial attention and saccadic eye movements was investigated in control subjects, Parkinson’s Disease (PD) patients, and cerebellar patients in a dual-task paradigm. The main question was how different types of cues (reflexive/intentional) guide the spatial attention during fixation or during the preparation phase of a saccade. The subjects were asked to follow a reflexive or intentional cue, to discriminate a character that appeared either at the cued s...
Reflex anuria: a rare cause of acute kidney injury
Dhakarwal, Pradeep; Adediran, Samuel
2014-01-01
Background: Acute Kidney Injury results from pre renal, post renal or intrinsic renal causes. Reflex anuria is a very rare cause of renal impairment which happens due to irritation or trauma to one kidney or ureter, or severely painful stimuli to other nearby organs.Case Presentation: Here we present a case of acute kidney injury secondary to reflex anuria in a patient who underwent extensive gynecological surgery along with ureteral manipulation which recovered spontaneously.Conclusion: Refl...
Innovation society today: the reflexive creation of novelty
Hutter, Michael; Knoblauch, Hubert; Rammert, Werner; Windeler, Arnold
2015-01-01
"While innovation has shaped modern society from its very inception, it is currently gaining new dimensions: Innovation is becoming increasingly reflexive, heterogeneously distributed, and ubiquitous. Reflexivity implies more than the intentional transformation of routine actions; it also refers to the transformation of social practices based on continuously (re-) produced knowledge about innovation. Thus, innovation itself becomes the aim and purpose of social activities: as the meaning and ...
Razani A
2010-01-01
Full Text Available Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper, we consider the following viscosity approximation sequence , where (0, 1, is a uniformly asymptotically regular sequence, and f is a weakly contractive mapping. Strong convergence of the sequence is proved.
On a minimax problem of ricceri
Cordaro Giuseppe
2001-01-01
Let be a real separable and reflexive Banach space, weakly closed and unbounded, and two non-constant weakly sequentially lower sernicontinuous functionals defined on , such that is coercive for each . In this setting, if for every , then, one has for every concave function .
On the calculation of the polar cone of the solution set of a differential inclusion
Polovinkin, E. S.
2012-01-01
A general form of the polar cone is obtained for the solution set of an arbitrary differential inclusion such that the graph of its right-hand side is a convex closed cone and the solutions take values in a reflexive Banach space.
ÜLGER, Ali; Lau, Anthony To-Ming
2014-01-01
Let A be a commutative Banach algebra with a BAI (=bounded approximate identity). We equip A** with the (first) Arens multiplication. To each idempotent element u of A** we associate the closed ideal I-u = {a is an element of A : au = 0} in A. In this paper we present a characterization of the closed ideals of A with BAI's in terms of idempotent elements of A**. The main results are: a) A closed ideal I of A has a BAT if there is an idempotent u is an element of A** such that I = I-u and the ...
Fuzzy Closure Spaces vs. Fuzzy Rough Sets
S. P. Tiwari; Shambhu Sharan; Yadav, Vijay K.
2014-01-01
This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a cer...
HPLC analysis of closed, open, and reflex eye tear proteins
Sitaramamma T
1998-01-01
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.
Anticausatives are weak scalar expressions, not reflexive expressions
Florian Schäfer
2016-07-01
Full Text Available We discuss conceptual and empirical arguments from Germanic, Romance and Slavic languages against an analysis treating anticausative verbs as derived from their lexical causative counterparts under reflexivization. Instead, we defend the standard account to the semantics of the causative alternation according to which anticausatives in general, and anticausatives marked with reflexive morphology in particular, denote simple one-place inchoative events that are logically entailed by their lexical causative counterparts. Under such an account, anticausative verbs are weak scalar expressions that stand in a semantico-pragmatic opposition to their strong lexical causative counterparts. Due to this scalar relation, the use of an anticausative can trigger the implicature that the use of its lexical causative counterpart is too strong. As usual with implicatures, they can be ‘metalinguistically’ denied, cancelled, or reinforced and we argue that these mechanisms explain all central empirical facts brought up in the literature in favor of a treatment of anticausatives as semantically reflexive predicates. Our results reinforce the view that the reflexive morphemes used in many (Indo-European languages to mark anticausatives do not necessarily trigger reflexive semantics. However, we also show that a string involving a reflexively marked (anti-causative verb can be forced into a semantically reflexive construal under particular conceptual or grammatical circumstances.
H-reflex changes following spinal cord injury.
Little, J W; Halar, E M
1985-01-01
Changes in both central synaptic excitability (CSE) and peripheral sensitivity of muscle spindle stretch receptors have been hypothesized to contribute to hyperactive stretch reflexes of spasticity. To assess CSE, the monosynaptic H-reflex to the triceps surae muscles was tested serially over the first six months after traumatic spinal cord injury (SCI). Six clinically complete SCI patients were compared to age-matched control subjects. As a measure of H-reflex excitability, H/M ratios were calculated by dividing maximum H-reflex by maximum M-response amplitude. Analysis of variance over the testing trials showed significant change in H/M ratios for SCI patients (p less than 0.01). T-tests comparing mean H/M ratios at different time periods after SCI revealed a significant increment after three months (p less than 0.01). H-reflex amplitude also increased significantly over this time period (p less than 0.04), but M-response amplitude did not change significantly. These increases in H/M ratio and H-reflex amplitude suggest that an increase in CSE may contribute to the appearance of hyperreflexia after SCI. PMID:3966862
Cortical control of hering-breuer reflexes in anesthetized rats
Aleksandrov VG
2009-12-01
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.
Vestibuloocular reflex of rhesus monkeys after spaceflight
Cohen, Bernard; Kozlovskaia, Inessa; Raphan, Theodore; Solomon, David; Helwig, Denice; Cohen, Nathaniel; Sirota, Mikhail; Iakushin, Sergei
1992-01-01
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.
Shuo ZHOU; Shi Tong YANG; Wen WANG
2011-01-01
In this paper,the Hermitian reflexive (Anti-Hermitian reflexive) least-squares solutions of matrix equations (AX =B,XC =D) are considered.With special properties of partitioned matrices and Hermitian reflexive (Anti-Hermitian reflexive) matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.
Additive subgroups of topological vector spaces
Banaszczyk, Wojciech
1991-01-01
The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY%弱代数性自反与强代数性自反
陶常利; 鲁世杰; 陈培鑫
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
A method of reflexive balancing in a pragmatic, interdisciplinary and reflexive bioethics.
Ives, Jonathan
2014-07-01
In recent years there has been a wealth of literature arguing the need for empirical and interdisciplinary approaches to bioethics, based on the premise that an empirically informed ethical analysis is more grounded, contextually sensitive and therefore more relevant to clinical practice than an 'abstract' philosophical analysis. Bioethics has (arguably) always been an interdisciplinary field, and the rise of 'empirical' (bio)ethics need not be seen as an attempt to give a new name to the longstanding practice of interdisciplinary collaboration, but can perhaps best be understood as a substantive attempt to engage with the nature of that interdisciplinarity and to articulate the relationship between the many different disciplines (some of them empirical) that contribute to the field. It can also be described as an endeavour to explain how different disciplinary approaches can be integrated to effectively answer normative questions in bioethics, and fundamental to that endeavour is the need to think about how a robust methodology can be articulated that successfully marries apparently divergent epistemological and metaethical perspectives with method. This paper proposes 'Reflexive Bioethics' (RB) as a methodology for interdisciplinary and empirical bioethics, which utilizes a method of 'Reflexive Balancing' (RBL). RBL has been developed in response to criticisms of various forms of reflective equilibrium, and is built upon a pragmatic characterization of Bioethics and a 'quasi-moral foundationalism', which allows RBL to avoid some of the difficulties associated with RE and yet retain the flexible egalitarianism that makes it intuitively appealing to many. PMID:23444909
A *-mixing convergence theorem for convex set valued processes
R. Kleyle
1987-03-01
Full Text Available In this paper the concept of a *-mixing process is extended to multivalued maps from a probability space into closed, bounded convex sets of a Banach space. The main result, which requires that the Banach space be separable and reflexive, is a convergence theorem for *-mixing sequences which is analogous to the strong law of large numbers. The impetus for studying this problem is provided by a model from information science involving the utilization of feedback data by a decision maker who is uncertain of his goals. The main result is somewhat similar to a theorem for real valued processes and is of interest in its own right.
The Approximation Theorem of Convolution Operator in △p Set-valued Function Space
Pei-xin Ye
2002-01-01
The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space,
Can Treadmill Perturbations Evoke Stretch Reflexes in the Calf Muscles?
Lizeth H Sloot
Full Text Available Disinhibition of reflexes is a problem amongst spastic patients, for it limits a smooth and efficient execution of motor functions during gait. Treadmill belt accelerations may potentially be used to measure reflexes during walking, i.e. by dorsal flexing the ankle and stretching the calf muscles, while decelerations show the modulation of reflexes during a reduction of sensory feedback. The aim of the current study was to examine if belt accelerations and decelerations of different intensities applied during the stance phase of treadmill walking can evoke reflexes in the gastrocnemius, soleus and tibialis anterior in healthy subjects. Muscle electromyography and joint kinematics were measured in 10 subjects. To determine whether stretch reflexes occurred, we assessed modelled musculo-tendon length and stretch velocity, the amount of muscle activity, as well as the incidence of bursts or depressions in muscle activity with their time delays, and co-contraction between agonist and antagonist muscle. Although the effect on the ankle angle was small with 2.8±1.0°, the perturbations caused clear changes in muscle length and stretch velocity relative to unperturbed walking. Stretched muscles showed an increasing incidence of bursts in muscle activity, which occurred after a reasonable electrophysiological time delay (163-191 ms. Their amplitude was related to the muscle stretch velocity and not related to co-contraction of the antagonist muscle. These effects increased with perturbation intensity. Shortened muscles showed opposite effects, with a depression in muscle activity of the calf muscles. The perturbations only slightly affected the spatio-temporal parameters, indicating that normal walking was retained. Thus, our findings showed that treadmill perturbations can evoke reflexes in the calf muscles and tibialis anterior. This comprehensive study could form the basis for clinical implementation of treadmill perturbations to functionally
Gravity and Development of Cardiopulmonary Reflex
Nagaoka, Shunji; Eno, Yuko; Ohira, Yoshinobu
Cardio-pulmonary reflex, which our cardiac activity is synchronized to the respiration by autonomic nervous system regulation, is called as "respiratory sinus arrhythmia" and commonly found in adult. The physiological function of the espiratory sinus arrhythmia is considered to maximize the gas exchange during respiration cycle. This respiration induced heart rate variability (RHRV) is only found in mammals and avian showing a remarkable postnatal development, whereas no RHRV in aquatic species such as fish or amphibian. To elucidate our hypothesis that gravity exposure may plays a key role in the postnatal development of RHRV as well as its evolutional origin in these ground animals, we have studied effects of hypergravity (2G) on the postnatal development of RHRV using rat. Pregnant Wister rats were kept in centrifugal cages system for 38 days from 6th days of pregnant mother to have neonates until 23 days old. Electrocardiograph was recorded from the neonates in 2 to 23 days old in 2G group with simultaneous control (1G) group. The RHRV analysis was performed by calculating a component of Fourier power spectral coincide with the respiration frequency. In both groups, averaged resting heart rate gradually increase from 2 to 23 days old. When comparing the heart rate between the two groups, the 2G group indicated significantly lower (240± 8 bpm) than 1G control (326±21 bpm, p¡0.001) in 2 days old, where as no significance in 23 days old. The RHRV of 2 days old neonates in both groups indicated very small magnitude but significantly lower in 2G group than 1G control (p¡0.01). The RHRV gradually increase during the first 2 weeks and then rapid increased to reached 45 fold of magnitude in 1G control, whereas 69 fold in 2G group. The results strongly suggested that the postnatal innervation from respiration to cardiovascular centers was gravity dependent.
Trembach, Vera
2014-01-01
Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.
Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces
Veli B. SHAKHMUROV
2006-01-01
This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators Dα from this space to Eα -valued Lp,γ spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.
Faroese long-distance reflexives face off against Icelandic long-distance reflexives
Tania E. Strahan
2009-01-01
Full Text Available Long-distance reflexives (LDRs in Faroese are often compared to those in Icelandic, and are even considered to have the same distribution (Thráinsson et al., 2004. In this paper I evaluate the extent to which this is true. The results from recent fieldwork show that there are clear differences between the LDR in the two closely related languages, in particular that Faroese speakers often reject LDR sentences that contain a non-third person, and that Faroese LDR is often completely acceptable out of a non-complement clause. In addition, initial findings suggest that there may be dialectal variation with respect to at least these two aspects of LDR in Faroese.