Academic literature on the topic 'Quasi-linear operator'
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Journal articles on the topic "Quasi-linear operator"
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Gjonbalaj, Qefsere Doko, and Valdete Rexhëbeqaj Hamiti. "On M−quasi Paranormal Operators." European Journal of Pure and Applied Mathematics 15, no. 3 (July 31, 2022): 830–40. http://dx.doi.org/10.29020/nybg.ejpam.v15i3.4392.
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In this paper we introduce a new class of operators called M−quasi paranormal operators. A bounded linear operator T in a complex Hilbert space H is said to be a M−quasi paranormal operator if it satisfies ∥T 2x∥ 2 ≤ M∥T 3x∥ · ∥T x∥, ∀x ∈ H, where M is a real positive number. We prove basic properties, the structural and spectral properties of this class of operators.
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Wang, Han, and Jianrong Wu. "The norm of continuous linear operator between two fuzzy quasi-normed spaces." AIMS Mathematics 7, no. 7 (2022): 11759–71. http://dx.doi.org/10.3934/math.2022655.
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<abstract> <p>In this paper, firstly, we introduce the concepts of continuity and boundedness of linear operators between two fuzzy quasi-normed spaces with general continuous <italic>t</italic>-norms, prove the equivalence of them, and point out that the set of all continuous linear operators forms a convex cone. Secondly, we establish the family of star quasi-seminorms on the cone of continuous linear operators, and construct a fuzzy quasi-norm of a continuous linear operator.</p> </abstract>
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Abanin, Alexander V., and Julia V. Korablina. "Compactness of Linear Operators on Quasi-Banach Spaces of Holomorphic Functions." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 4-1 (216-1) (December 28, 2022): 83–89. http://dx.doi.org/10.18522/1026-2237-2022-4-1-83-89.
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We state conditions under which some classical operators acting from abstract quasi-Banach spaces of functions holomorphic in a plain domain into a weighted space of the same functions with sup-norm are compact. It is obtained abstract criteria for the compactness of a linear operator on an arbitrary quasi-Banach space which are stated in terms of delta-functions and formulate their realizations for both classical and generalized Fock spaces. The above results are applied to the weighted composition operator. It is established some conditions for the compactness of this operator which are given in terms of norms of delta-functions in the corresponding dual spaces. These results are essential generalizations of the known Zorboska’s ones. Namely, we significantly extended the class of weighted spaces of holomorphic functions with uniform norms for which one can state some conditions for the compactness of an arbitrary linear operator or the weighted composition operator.
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Bakery, Awad A., and Mustafa M. Mohammed. "Some properties of pre-quasi operator ideal of type generalized Cesáro sequence space defined by weighted means." Open Mathematics 17, no. 1 (December 31, 2019): 1703–15. http://dx.doi.org/10.1515/math-2019-0135.
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Abstract Let E be a generalized Cesáro sequence space defined by weighted means and by using s-numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components $$\begin{array}{} \displaystyle S_{E}(X, Y):=\Big\{T\in L(X, Y):((s_{n}(T))_{n=0}^{\infty}\in E\Big\}, \end{array}$$ of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small and the pre-quasi Banach operator ideal constructed by s-numbers is simple Banach space. Finally the pre-quasi operator ideal formed by the sequence of s-numbers and this sequence space is strictly contained in the class of all bounded linear operators, whose sequence of eigenvalues belongs to this sequence space.
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Mohsen, Salim Dawood, and Hanan Khalid Mousa. "Another Results Related of Fuzzy Soft Quasi Normal Operator in Fuzzy Soft Hilbert Space." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012050. http://dx.doi.org/10.1088/1742-6596/2322/1/012050.
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Abstract The goal of this paper, is to introduce another classes of the fuzzy soft bounded linear operator in the fuzzy soft Hilbert space which is a fuzzy soft quasi normal operator, as well as, give some properties about this concept with investigating the relationship among this types of the fuzzy soft bounded linear operator on fuzzy soft Hilbert space with other kinds of fuzzy soft bounded linear operators.
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Lohaj, Shqipe. "Structural and Spectral Properties of k-Quasi Class Q(N) and k-Quasi Class Q*(N) Operators." European Journal of Pure and Applied Mathematics 15, no. 4 (October 31, 2022): 1836–53. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4580.
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Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce two new classes of operators: k−quasi class Q(N ) and k−quasi class Q*(N ). An operator T ∈ L(H) is of k−quasi class Q(N ) for a fixed real number N ≥ 1 and k a natural number, if T satisfies N ∥T^k+1(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ H. An operator T ∈ L(H) is of k−quasi class Q*(N ) for a fixed real number N ≥ 1 and k a natural number, if T satisfiesN ∥T*T^k(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, for all x ∈ H. We study structural and spectral properties of these classes of operators. Also we compare this new classes of operators with other known classes of operators
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Çavuş, Abdullah, Djavvat Khadjiev, and Seda Öztürk. "On periodic solutions to nonlinear differential equations in Banach spaces." Filomat 30, no. 4 (2016): 1069–76. http://dx.doi.org/10.2298/fil1604069c.
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Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by R? is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolvent operators R? are given. Then using these, some theorems on existence of periodic solutions to the non-linear equations ?(A)x = f (x) are given, where ?(A) is a polynomial of A with complex coefficients and f is a continuous mapping of H into itself.
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Malik, Saroj, and Néstor Thome. "On a revisited Moore-Penrose inverse of a linear operator on Hilbert spaces." Filomat 31, no. 7 (2017): 1927–31. http://dx.doi.org/10.2298/fil1707927m.
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For two given Hilbert spaces H and K and a given bounded linear operator A ? L(H,K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive g-inverse G ? L(K,H) of A which is both minimum norm and least squares. In this paper, weaker equivalent conditions for an operator G to be the Moore-Penrose inverse of A are investigated in terms of normal, EP, bi-normal, bi-EP, l-quasi-normal and r-quasi-normal and l-quasi-EP and r-quasi-EP operators.
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Bakery, Awad A., and Mustafa M. Mohammed. "Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces." Journal of Function Spaces 2019 (May 2, 2019): 1–9. http://dx.doi.org/10.1155/2019/7265010.
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In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. The completeness and denseness of its ideal components are specified and Scesφ constructs a pre-quasi Banach operator ideal. Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained. Moreover, we have presented the sufficient conditions on cesφ such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known for cesp (1<p<∞).
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Micic, Jadranka, and Kemal Hot. "Inequalities among quasi-arithmetic means for continuous field of operators." Filomat 26, no. 5 (2012): 977–91. http://dx.doi.org/10.2298/fil1205977m.
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In this paper we study inequalities among quasi-arithmetic means for a continuous field of self-adjoint operators, a field of positive linear mappings and continuous strictly monotone functions which induce means. We present inequalities with operator convexity and without operator convexity of appropriate functions. Also, we present a general formulation of converse inequalities in each of these cases. Furthermore, we obtain refined inequalities without operator convexity. As applications, we obtain inequalities among power means.
Dissertations / Theses on the topic "Quasi-linear operator"
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Kultima, J. (Jaakko). "Direct and inverse scattering problems for quasi-linear biharmonic operator in 3D." Master's thesis, University of Oulu, 2019. http://jultika.oulu.fi/Record/nbnfioulu-201908272824.
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Abstract. We consider direct and inverse scattering problems for three-dimensional biharmonic operator
\(Hu = ∆^2u + Vu\),
where \(∆\) is the Laplacian and \(V\) is a scalar valued perturbation. The scattering problem for this operator is given as a partial differential equation \(Hu = k^4u\), with a parameter \(k\).
In the direct scattering problem, our goal is to find the solution \(u\) while the perturbation (V\) is known. We also assume that the solution \(u\) can be written as a sum of two functions \(u_{0}\) and \(u_{sc}\), where \(u_{0}\) is a plane wave and \(u_{sc}\) is an outgoing wave in the sense that it satisfies to the Sommerfeld radiation conditions at the infinity. Our approach in this text is to first modify the partial differential equation into an integral equation by using the fundamental solution. Next, we show that this integral equation is solvable, and it has a unique solution. Finally, we prove two main results of this text; an asymptotic formula for the solution with large values of \(x ∈ \mathbb{R}^3\) and Saito’s formula. The asymptotic behaviour of the solution leads us to defining the scattering amplitude.
In the inverse scattering problem, the goal is to gather some information about the unknown perturbation V while the behaviour of the function u is known. With Saito’s formula we obtain two corollaries regarding the inverse scattering problem, namely uniqueness and a representation formula for the function \(V(x, 1)\), when the scattering amplitude is known. We end the text by first defining the inverse Born approximation for both full scattering data and backscattering data. We also discuss some results that have been obtained previously with this approach.
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ZONGO, WEND BENEDO EMMANUEL. "BOUNDARY VALUE PROBLEMS FOR QUASI-LINEAR AND HIGHER-ORDER ELLIPTIC OPERATORS AND APPLICATION TO BIFURCATION AND STABILIZATION." Doctoral thesis, Università degli Studi di Milano, 2022. http://hdl.handle.net/2434/892091.
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In this thesis, we are interested in the study of nonlinear eigenvalue problem and the controllability of partial differential equations in a smooth bounded domain with boundary.
The first part is devoted to the analysis of an eigenvalue problem for quasilinear elliptic operators involving homogeneous Dirichlet boundary conditions.
We investigate the asymptotic behaviour of the spectrum of the related problem by showing on the one hand the bifurcation results from trivial solutions using the Krasnoselski bifurcation theorem and bifurcation from infinity using the Leray-Schauder degree on the other hand. We also prove the existence of multiple critical points using variational methods and the Krasnoselski genus.
At last, we show a stabilization result for the damped plate equation with logarithmic decay of the associated energy. The proof of this result is achieved by means of a proper Carleman estimate for the fourth-order elliptic operators involving the so-called Lopatinskii-Šapiro boundary conditions and a resolvent
estimate for the generator of the damped plate semigroup associated with these
boundary conditions.
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Drogoul, Audric. "Méthode du gradient topologique pour la détection de contours et de structures fines en imagerie." Thesis, Nice, 2014. http://www.theses.fr/2014NICE4063/document.
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Cette thèse porte sur la méthode du gradient topologique appliquée au traitement d'images. Principalement, on s'intéresse à la détection d'objets assimilés, soit à des contours si l'intensité de l'image à travers la structure comporte un saut, soit à une structure fine (filaments et points en 2D) s'il n'y a pas de saut à travers la structure. On commence par généraliser la méthode du gradient topologique déjà utilisée en détection de contours pour des images dégradées par du bruit gaussien, à des modèles non linéaires adaptés à des images contaminées par un processus poissonnien ou du bruit de speckle et par différents types de flous. On présente également un modèle de restauration par diffusion anisotrope utilisant le gradient topologique pour un domaine fissuré. Un autre modèle basé sur une EDP elliptique linéaire utilisant un opérateur anisotrope préservant les contours est proposé. Ensuite, on présente et étudie un modèle de détection de structures fines utilisant la méthode du gradient topologique. Ce modèle repose sur l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées secondes d'une régularisation de l'image solution d'une EDP d'ordre 4 de type Kirchhoff. En particulier on explicite les gradients topologiques pour des domaines 2D fissurés ou perforés, et des domaines 3D fissurés. Plusieurs applications pour des images 2D et 3D, floutées et contaminées par du bruit gaussien, montrent la robustesse et la rapidité de la méthode. Enfin on généralise notre approche pour la détection de contours et de structures fines par l'étude de la sensibilité topologique d'une fonction coût utilisant les dérivées m−ième d'une régularisation de l'image dégradée, solution d'une EDP d'ordre 2mThis thesis deals with the topological gradient method applied in imaging. Particularly, we are interested in object detection. Objects can be assimilated either to edges if the intensity across the structure has a jump, or to fine structures (filaments and points in 2D) if there is no jump of intensity across the structure. We generalize the topological gradient method already used in edge detection for images contaminated by Gaussian noise, to quasi-linear models adapted to Poissonian or speckled images possibly blurred. As a by-product, a restoration model based on an anisotropic diffusion using the topological gradient is presented. We also present a model based on an elliptical linear PDE using an anisotropic differential operator preserving edges. After that, we study a variational model based on the topological gradient to detect fine structures. It consists in the study of the topological sensitivity of a cost function involving second order derivatives of a regularized version of the image solution of a PDE of Kirchhoff type. We compute the topological gradients associated to perforated and cracked 2D domains and to cracked 3D domains. Many applications performed on 2D and 3D blurred and Gaussian noisy images, show the robustness and the fastness of the method. An anisotropic restoration model preserving filaments in 2D is also given. Finally, we generalize our approach by the study of the topological sensitivity of a cost function involving the m − th derivatives of a regularization of the image solution of a 2m order PDE
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Ernst, Oliver G. "Minimal and orthogonal residual methods and their generalizations for solving linear operator equations." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2009. http://nbn-resolving.de/urn:nbn:de:swb:105-3293998.
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This thesis is concerned with the solution of linear operator equations by projection methods known as minimal residual (MR) and orthogonal residual (OR) methods. We begin with a rather abstract framework of approximation by orthogonal and oblique projection in Hilbert space. When these approximation schemes are applied to sequences of nested spaces, with a simple requirement relating trial and test spaces in case of the OR method, one can derive at this rather general level the basic relations which have been proved for many specific Krylov subspace methods for solving linear systems of equations in the literature. The crucial quantities with which we describe the behavior of these methods are angles between subspaces. By replacing the given inner product with one that is basis-dependent, one can also incorporate methods based on non-orthogonal bases such as those based on the non-Hermitian Lanczos process for solving linear systems. In fact, one can show that any reasonable approximation method based on a nested sequence of approximation spaces can be interpreted as an MR or OR method in this way. When these abstract approximation techniques are applied to the solution of linear operator equations, there are three generic algorithmic formulations, which we identify with some algorithms in the literature. Specializing further to Krylov trial and test spaces, we recover the well known Krylov subspace methods. Moreover, we show that our general framework also covers in a natural way many recent generalizations of Krylov subspace methods, which employ techniques such as augmentation, deflation, restarts and truncation. We conclude with a chapter on error and residual bounds, deriving some old and new results based on the angles framework. This work provides a natural and consistent framework for the sometimes confusing plethora of methods of Krylov subspace type introduced in the last 50 years.
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Ernst, Oliver G. "Minimal and orthogonal residual methods and their generalizations for solving linear operator equations." Doctoral thesis, [S.l. : s.n.], 2000. https://tubaf.qucosa.de/id/qucosa%3A22355.
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This thesis is concerned with the solution of linear operator equations by projection methods known as minimal residual (MR) and orthogonal residual (OR) methods. We begin with a rather abstract framework of approximation by orthogonal and oblique projection in Hilbert space. When these approximation schemes are applied to sequences of nested spaces, with a simple requirement relating trial and test spaces in case of the OR method, one can derive at this rather general level the basic relations which have been proved for many specific Krylov subspace methods for solving linear systems of equations in the literature. The crucial quantities with which we describe the behavior of these methods are angles between subspaces. By replacing the given inner product with one that is basis-dependent, one can also incorporate methods based on non-orthogonal bases such as those based on the non-Hermitian Lanczos process for solving linear systems. In fact, one can show that any reasonable approximation method based on a nested sequence of approximation spaces can be interpreted as an MR or OR method in this way. When these abstract approximation techniques are applied to the solution of linear operator equations, there are three generic algorithmic formulations, which we identify with some algorithms in the literature. Specializing further to Krylov trial and test spaces, we recover the well known Krylov subspace methods. Moreover, we show that our general framework also covers in a natural way many recent generalizations of Krylov subspace methods, which employ techniques such as augmentation, deflation, restarts and truncation. We conclude with a chapter on error and residual bounds, deriving some old and new results based on the angles framework. This work provides a natural and consistent framework for the sometimes confusing plethora of methods of Krylov subspace type introduced in the last 50 years.
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Gosselin, Frédéric. "Modèles stochastiques d'extinction de population : propriétés mathématiques et leurs applications." Paris 6, 1997. http://www.theses.fr/1997PA066358.
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Des modeles d'extinction de population sont frequemment employes comme outils d'aide a la decision pour la gestion de populations animales ou vegetales menacees. Le but de cette these est de prouver des resultats mathematiques decrivant la maniere dont se passe l'extinction dans la plupart de ces modeles, et de les appliquer a quelques cas particuliers. Apres une revue bibliographique sur l'extinction de populations et les modeles utilises pour l'apprehender, je propose une serie de resultats mathematiques, pour la plupart asymptotiques, generalisant au cadre plus etendu des chaines de markov a espace d'etats denombrable des resultats connus pour les chaines de markov finies ou les processus de ramification. Je prouve l'extinction certaine de ces modeles et deux types de stabilisation stochastique et asymptotique conditionnellement a la non-extinction. C'est l'utilisation de resultats d'analyse lineaire qui aura permis une telle extension. Je presente ensuite deux manieres de simuler numeriquement ces modeles, dont l'une est en partie nouvelle, puis j'etudie a la lumiere des resultats de cette these un modele d'extinction correspondant a une population reelle. Je clos ce travail par une discussion sur l'applicabilite, l'utilisation et l'utilite de mes resultats pour la modelisation de l'extinction, mais aussi dans d'autres domaines biologiques. Les principales conclusions sont que mes resultats s'appliquent a un grand nombre de modeles d'extinction existants et possedent des applications conceptuelles interessantes en ecologie theorique, concernant les notions d'equilibre et de stabilite, mais qu'ils ne sont pas systematiquement utiles dans l'interpretation des simulations et qu'ils doivent etre utilises avec une certaine rigueur mathematique
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Millán, Reinier Díaz. "Vários algoritmos para os problemas de desigualdade variacional e inclusão." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4562.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Nesta tese apresentamos v arios algoritmos para resolver os problemas de Desigualdade Variacional e Inclus~ao. Para o problema de desigualdade variacional propomos, no Cap tulo 2 uma generaliza c~ao do algoritmo cl assico extragradiente, utilizando vetores normais n~ao nulos do conjunto vi avel. Em particular, dois algoritmos conceituais s~ao propostos e cada um deles cont^em tr^es variantes diferentes de proje c~ao que est~ao relacionadas com algoritmos extragradientes modi cados. Duas buscas diferentes s~ao propostas, uma sobre a borda do conjunto vi avel e a outra ao longo das dire c~oes vi aveis. Cada algoritmo conceitual tem uma estrat egia diferente de busca e tr^es formas de proje c~ao especiais, gerando tr^es sequ^encias com diferente e interessantes propriedades. E feito a an alise da converg^encia de ambos os algoritmos conceituais, pressupondo a exist^encia de solu c~oes, continuidade do operador e uma condi c~ao mais fraca do que pseudomonotonia. No Cap tulo 4, n os introduzimos um algoritmo direto de divis~ao para o problema variacional em espa cos de Hilbert. J a no Cap tulo 5, propomos um algoritmo de proje c~ao relaxada em Espa cos de Hilbert para a soma de m operadores mon otonos maximais ponto-conjunto, onde o conjunto vi avel do problema de desigualdade variacional e dado por uma fun c~ao n~ao suave e convexa. Neste caso, as proje c~oes ortogonais ao conjunto vi avel s~ao substitu das por proje c~oes em hiperplanos que separam a solu c~ao da itera c~ao atual. Cada itera c~ao do m etodo proposto consiste em proje c~oes simples de tipo subgradientes, que n~ao exige a solu c~ao de subproblemas n~ao triviais, utilizando apenas os operadores individuais, explorando assim a estrutura do problema. Para o problema de Inclus~ao, propomos variantes do m etodo de divis~ao de forward-backward para achar um zero da soma de dois operadores, a qual e a modi ca c~ao cl assica do forwardbackward proposta por Tseng. Um algoritmo conceitual e proposto para melhorar o apresentado por Tseng em alguns pontos. Nossa abordagem cont em, primeramente, uma busca linear tipo Armijo expl cita no esp rito dos m etodos tipo extragradientes para desigualdades variacionais. Durante o processo iterativo, a busca linear realiza apenas um c alculo do operador forward-backward em cada tentativa de achar o tamanho do passo. Isto proporciona uma consider avel vantagem computacional pois o operador forward-backward e computacionalmente caro. A segunda parte do esquema consiste em diferentes tipos de proje c~oes, gerando sequ^encias com caracter sticas diferentes.
In this thesis we present various algorithms to solve the Variational Inequality and Inclusion Problems. For the variational inequality problem we propose, in Chapter 2, a generalization of the classical extragradient algorithm by utilizing non-null normal vectors of the feasible set. In particular, two conceptual algorithms are proposed and each of them has three di erent projection variants which are related to modi ed extragradient algorithms. Two di erent linesearches, one on the boundary of the feasible set and the other one along the feasible direction, are proposed. Each conceptual algorithm has a di erent linesearch strategy and three special projection steps, generating sequences with di erent and interesting features. Convergence analysis of both conceptual algorithms are established, assuming existence of solutions, continuity and a weaker condition than pseudomonotonicity on the operator. In Chapter 4 we introduce a direct splitting method for solving the variational inequality problem for the sum of two maximal monotone operators in Hilbert space. In Chapter 5, for the same problem, a relaxed-projection splitting algorithm in Hilbert spaces for the sum of m nonsmooth maximal monotone operators is proposed, where the feasible set of the variational inequality problem is de ned by a nonlinear and nonsmooth continuous convex function inequality. In this case, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore, each iteration of the proposed method consists of simple subgradient-like steps, which does not demand the solution of a nontrivial subproblem, using only individual operators, which explores the structure of the problem. For the Inclusion Problem, in Chapter 3, we propose variants of forward-backward splitting method for nding a zero of the sum of two operators, which is a modi cation of the classical forward-backward method proposed by Tseng. The conceptual algorithm proposed here improves Tseng's method in many instances. Our approach contains rstly an explicit Armijo-type line search in the spirit of the extragradient-like methods for variational inequalities. During the iterative process, the line search performs only one calculation of the forward-backward operator in each tentative for nding the step size. This achieves a considerable computational saving when the forward-backward operator is computationally expensive. The second part of the scheme consists of special projection steps bringing several variants.
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Křehlík, Štěpán. "Strukturované multisystémy a multiautomaty indukované časovými procesy." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2015. http://www.nusl.cz/ntk/nusl-234457.
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In the thesis we discuss binary hyperstructures of linear differential operators of the second order both in general and (inspired by models of specific time processes) in a special case of the Jacobi form. We also study binary hyperstructures constructed from distributive lattices and suggest transfer of this construction to n-ary hyperstructures. We use these hyperstructures to construct multiautomata and quasi-multiautomata. The input sets of all these automata structures are constructed so that the transfer of information for certain specific modeling time functions is facilitated. For this reason we use smooth positive functions or vectors components of which are real numbers or smooth positive functions. The above hyperstructures are state-sets of these automata structures. Finally, we investigate various types of compositions of the above multiautomata and quasi-multiautomata. In order to this we have to generalize the classical definitions of Dörfler. While some of the concepts can be transferred to the hyperstructure context rather easily, in the case of Cartesian composition the attempt to generalize it leads to some interesting results.
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Langer, Stefan. "Preconditioned Newton methods for ill-posed problems." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B396-D.
Full textBook chapters on the topic "Quasi-linear operator"
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Riva, Matteo Dalla, Massimo Lanza de Cristoforis, and Paolo Musolino. "A Local Uniqueness Result for a Quasi-linear Heat Transmission Problem in a Periodic Two-phase Dilute Composite." In Recent Trends in Operator Theory and Partial Differential Equations, 193–227. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47079-5_10.
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Fiorini, Camilla, Pierre-Marie Boulvard, Long Li, and Etienne Mémin. "A Two-Step Numerical Scheme in Time for Surface Quasi Geostrophic Equations Under Location Uncertainty." In Mathematics of Planet Earth, 57–67. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_5.
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AbstractIn this work we consider the surface quasi-geostrophic (SQG) system under location uncertainty (LU) and propose a Milstein-type scheme for these equations, which is then used in a multi-step method. The SQG system considered here consists of one stochastic partial differential equation, which models the stochastic transport of the buoyancy, and a linear operator linking the velocity and the buoyancy. In the LU setting, the Euler-Maruyama scheme converges with weak order 1 and strong order 0.5. Our aim is to develop higher order schemes in time, based on a Milstein-type scheme in a multi-step framework. First we compared different kinds of Milstein schemes. The scheme with the best performance is then included in the two-step scheme. Finally, we show how our two-step scheme decreases the error in comparison to other multi-step schemes.
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Curto, Raúl E., and Lawrence A. Fialkow. "Operator Factorizations and Quasi-Similarity Orbits." In Linear Operators in Function Spaces, 151–64. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7250-8_10.
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Zeidler, Eberhard. "Monotone Operators and Quasi-Linear Elliptic Differential Equations." In Nonlinear Functional Analysis and its Applications, 553–79. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0981-2_2.
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Zeidler, Eberhard. "Pseudomonotone Operators and Quasi-Linear Elliptic Differential Equations." In Nonlinear Functional Analysis and its Applications, 580–614. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4612-0981-2_3.
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Davis, Burgess, and Renming Song. "Extrapolation and Interpolation of Quasi-Linear Operators on Martingales." In Selected Works of Donald L. Burkholder, 108–63. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-7245-3_11.
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Röckner, Michael, and Boguslaw Zegarlinski. "The Dirichlet Problem for Quasi-Linear Partial Differential Operators with Boundary Data Given by a Distribution." In Stochastic Processes and their Applications, 301–26. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-2117-7_17.
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Chen, Zhen-Qing, and Masatoshi Fukushima. "Symmetric Markovian Semigroups and Dirichlet Forms." In Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691136059.003.0001.
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This chapter studies the concepts of Dirichlet form and Dirichlet space by first working with a σ-finite measure space (E,B(E),m) without any topological assumption on E and establish the correspondence of the above-mentioned notions to the semigroups of symmetric Markovian linear operators. Later on the chapter assumes that E is a Hausdorff topological space and considers the semigroups and Dirichlet forms generated by symmetric Markovian transition kernels on E. The chapter also considers quasi-regular Dirichlet forms and the quasi-homeomorphism of Dirichlet spaces. From here, the chapter shows that there is a nice Markov process called an m-tight special Borel standard process associated with every quasi-regular Dirichlet form.
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Ventre, Salvatore, Bruno Carpentieri, Gaspare Giovinco, Antonello Tamburrino, Fabio Villone, and Guglielmo Rubinacci. "An Effective H2-LU Preconditioner for Iterative Solution of MQS Integral-Based Formulation P." In Advances in Fusion Energy Research. From Theory to Models, Algorithms, and Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.108106.
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We present iterative solution strategies for solving efficiently Magneto-Quasi-Static (MQS) problems expressed in terms of an integral formulation based on the electric vector potential. Integral formulations give rise to discrete models characterized by linear systems with dense coefficient matrices. Iterative Krylov subspace methods combined with fast compression techniques for the matrix-vector product operation are the only viable approach for treating large scale problems, such as those considered in this study. We propose a fully algebraic preconditioning technique built upon the theory of H2-matrix representation that can be applied to different integral operators and to changes in the geometry, only by tuning a few parameters. Numerical experiments show that the proposed methodology performs much better than the existing one in terms of ability to reduce the number of iterations of a Krylov subspace method, especially for fast transient analysis.
Conference papers on the topic "Quasi-linear operator"
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Berry, L. A. "Positive Quasi Linear Operator Formulation." In RADIO FREQUENCY POWER IN PLASMAS: 16th Topical Conference on Radio Frequency Power in Plasmas. AIP, 2005. http://dx.doi.org/10.1063/1.2098192.
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Huang, Jiacai, YangQuan Chen, and Zhuo Li. "Mathematical Model of Human Operator Using Fractional Calculus for Human-in-the-Loop Control." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47464.
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Mathematical models of human operator play a very important role in the Human-in-the-Loop manual control system. For several decades, modeling human operator’s dynamic has been an active research area. The traditional classical human operator models are usually developed using the Quasi-linear transfer function method, the optimal control theory method, and so on. The human operator models established by the above methods have deficiencies such as complicated and over parameterized, even for basic control elements. In this paper, based on the characteristics of human brain and behaviour, two kinds of fractional order mathematical models for describing human operator behavior are proposed. Through validation and comparison by the actual data, the best_fit model with smallest root mean squared error (RMSE) is obtained, which has simple structure with only few parameters, and each parameter has definite physical meaning.
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Rengarajan, Sankar B., Michael D. Bryant, and Jaewon Choi. "An Exploratory Optimization Plus Kalman Filtering Based Method for Parameter Estimation in Model Based Diagnostics." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6017.
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Physics based models can be used to detect and isolate system faults. As a machine degrades, system outputs deviate from desired outputs, generating residuals defined by the error between sensor measurements and corresponding model simulated signals. Residuals contain valuable information to interpret system states and parameters. A framework for parameter estimation and system identification of non-linear dynamical systems is presented with focus on DC motors and 3-phase induction motors. Tuning combines artificial intelligence techniques like Quasi-Monte Carlo sampling (Hammersley sequencing) and Genetic Algorithm (NSGA II) with an Extended Kalman filter (EKF) that utilizes the system dynamics information via physical models. A tentative Graphical User Interface (GUI) simplified interactions between machine operator and module. Implementation details and results comparing healthy and faulty systems are included.
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Coelho, Leandro dos Santos, and Viviana Cocco Mariani. "Discrete Variable Structure Control Based on Optimization by Cultural Differential Evolution Approach." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15554.
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Advanced conceptions to design industrial control systems are, in general, dependent of mathematical models of the controlled process. Also, the task of the controllers is to achieve an optimum performance when facing with various types of disturbances that are, sometimes, unknown in practical applications. An advanced methodology for control design is the variable structure control (VSC) with sliding mode. This paper considers the non-linear control of industrial processes based on self-tuning discrete VSC technique. A novel and systematic VSC design methodology is proposed, which integrates an estimator based on recursive least square algorithm, a discrete quasi-sliding surface and a optimization method. Contrary to the trial and error selection of the variable structure feedback gains reported in the literature, the selection in present work is done using differential evolution (DE) optimization, an evolutionary computation technique, with a new operator based on normative knowledge of cultural algorithms. The proposed design has been applied to a control valve described by a non-linear Wiener model. Numerical simulation results reveal that the new DE approach is applicable and promising for the VSC design.
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Benoit, Alexandre, Alin Bostan, and Joris van der Hoeven. "Quasi-optimal Multiplication of Linear Differential Operators." In 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2012. http://dx.doi.org/10.1109/focs.2012.57.
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Zhang, Yandong, and S. C. Sinha. "Control of Nonlinear Time-Periodic Systems Via Feedback Linearization." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85621.
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The problem of designing controllers for nonlinear time periodic systems is addressed. The idea is to find proper coordinate transformations and state feedback under which the original system can be (approximately) transformed into a linear control system. Then a controller can be designed using the well-known linear method to guarantee the stability of the system. We propose two approaches for the feedback linearization of the nonlinear time periodic system. The first approach is designed to achieve local control of nonlinear systems with periodic coefficients desired to be driven either to a periodic orbit or to a fixed point. In this case the system equations can be represented by a quasi-linear system containing nonlinear monomials with periodic coefficients. Using near identity transformations and normal form theory, the original close loop problem is approximately transformed into a linear time periodic system with unknown gains. Then by using a symbolic computation method, the Floquet multipliers are placed in the desired locations in order to determine the control gains. We also give the sufficient conditions under which the system is feedback linearizable up to the rth order. The second approach is a generalization of the classical exact feedback linearization method for autonomous systems but applicable to general time-periodic affine systems. By defining a time-dependent Lie operator, the input-output nonlinear time periodic problem is transformed into a linear autonomous problem for which control system can be designed easily. A sufficient condition under which the system is feedback linearizable is also given.
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MADENCI, ERDOGAN, ATILA BARUT, and NAM PHAN. "BOND-BASED PERIDYNAMICS WITH STRETCH AND ROTATION KINEMATICS FOR MODELING COMPOSITE LAMINATES." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36502.
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This study presents the bond-based (BB) peridynamics (PD) with stretch and rotation kinematics for modeling the linear elastic deformation of a composite laminate. The laminate experiences only in-plane and transverse shear deformations and disregards the transverse normal deformation. The PD equilibrium equation for a laminate is derived under the assumption of small deformation and is solved by employing implicit techniques. The in-plane PD forces are expressed by considering the PD bond interactions among the points. The forces arising from the interaction of adjacent layers are expressed by considering a pointwise approach that utilizes PD differential operator (PDDO) in conjunction with the shear-lag theory. The micro-moduli associated with stretch and rotation are directly related to the constitutive relations between stress and strain components in continuum mechanics. It is restricted to only one constraint on the material constants leading to a fixed value of in-plane shear modulus. The capability of this approach is demonstrated by considering progressive failure in a quasi-isotropic laminate with a pre-existing crack. It employs critical stretch, the critical skew (relative rotation) angle and critical delamination angle in the bond breakage criteria.
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Buryachenko, Valeriy A. "Effective Behavior of Peridynamic Random Structure Composites Subjected to Body Force With Compact Support." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-95107.
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Abstract We consider a static problem for statistically homogeneous matrix linear bond-based peridynamic composite materials (CMs). Even for locally elastic composites subjected to inhomogeneous loading, the effective deformations are described by a nonlocal (either the differential or integral) operator relating a statistical average of stresses in the point being considered with a statistical average of strains in the vicinity of this point. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts (see for details [1]). The method is based on estimation of a perturbator introduced by one inclusion that is, in fact, the solutions of the basic problem for one inclusion inside the infinite peristatic matrix subjected to the body force. The statistical averages of both the displacements and stresses are estimated by summation of these perturbators for all possible locations of inclusions (in so doing, renormalizing procedure is not required). It allows us to estimate not only the effective nonlocal constitutive equation but also to evaluate the statistical field averages (inhomogeneous and nonlocal) inside the phases at the fine scale that is critically important for advanced modelling (e.g. for any nonlinear phenomena). In particular, in the generalized effective field method (EFM) proposed, the effective field is evaluated from self-consistent estimations by the use of closing of a corresponding integral equation in the framework of the quasi-crystalline approximation. In so doing, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. Numerical results for the estimation of effective displacements are obtained for 1D statistically homogeneous CM bar with the prescribed self equilibrated body forces.
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Frumkes, T. E., F. Naarendorp, T. Eysteinsson, N. Denny, and S. Goldberg. "Quasi-linear and highly nonlinear rod-cone interactions." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.tuz3.
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Many studies have shown interaction between the long-wavelength rod-cone mechanism and the rod mechanism. Quasi-linear additions of rod- and cone-related photic responses are most clearly implicated in the increment threshold studies of Buck, Frumkes, and MacLeod and the flicker studies of MacLeod and van den Berg, but have been suggested by a wide variety of other electrophysiological and psychophysical techniques. Quasi-linear rod-cone interactions are discerned when light flashes stimulate both rods and cones and the underlying mechanism can be understood in terms of a convergence of like polarity signals at some common neural locus. Highly nonlinear interactions between the same two spectral mechanisms have been recently and independently demonstrated by Alexander, Arden, Coletta, and Goldberg. Nonlinear rod-cone interactions involve a suppressive influence of rods on cone-mediated flicker sensations which is maximal when rods are totally dark-adapted. We now directly compare these two sets of mechanisms both by means of psychophysical procedures in humans and intracellular recording in subhuman species. These types of rod-cone interaction must be considered distinct since they have different magnitudes and different space and time constants. But since both types are observed in the same neurons in the distal most retina, they reflect the operation of the same elements simultaneously interacting with one another in several different manners.
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Ohayon, Roger. "Symmetric Formulations for Modal Analysis of Internal Fluid Structure Systems." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0044.
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Abstract This paper deals with appropriate computational methods for modal analysis of elastic structures containing an inviscid fluid (gas or liquid). These methods, based on Ritz-Galerkin projection using appropriate functional basis, allow us to construct reduced models expressed in terms of physical displacement vector field u in the structure, and generalized coordinates vector r describing the behavior of the fluid. Those reduced models lead to symmetric generalized eigenvalue matrix system involving a reduced number of degrees of freedom for the fluid. More precisely, we construct symmetric matrix models of the fluid considered as a subsystem, by considering the response of the fluid to a prescribed normal displacement of the fluid-structure interface. Two distinct situations are analyzed, namely linear vibrations of an elastic structure completely filled with a compressible gas or liquid and linear vibrations of an elastic structure containing an incompressible liquid with free surface effects due to gravity. The first case is a structural acoustic problem with modal interaction between structural modes with acoustic modes in rigid motionless cavity. Wall impedance can also be easily introduced in order to take into account fluid-structure interface dissipation, for further forced response studies. The second case is a hydroelastic-sloshing problem with modal interaction between incompressible hydroelastic structural modes with incompressible liquid sloshing modes in rigid motionless cavity, involving an elastogravity operator related to the wall normal displacement of the fluid-structure interface. For the construction of reduced models, the static behavior at zero frequency play an important role. This is why we start from “well-posed” variational formulations of the problem, in the sense that zero-frequency behavior must be well retrieved in the equations. It should be noted that the so-called “quasi-static correction” term plays a fundamental role in the Ritz-Galerkin procedure (error truncation). The general methodology corresponds to dynamic substructuring procedures adapted to fluid-structure modal analysis. For general presentations of computational methods using appropriate finite element and dynamic substructuring procedures applied to modal analysis of elastic structures containing inviscid fluids (sloshing, hydroelasticity and structural-acoustics), we refer the reader to Morand and Ohayon (1995).
Reports on the topic "Quasi-linear operator"
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McPhedran, R., K. Patel, B. Toombs, P. Menon, M. Patel, J. Disson, K. Porter, A. John, and A. Rayner. Food allergen communication in businesses feasibility trial. Food Standards Agency, March 2021. http://dx.doi.org/10.46756/sci.fsa.tpf160.
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Background: Clear allergen communication in food business operators (FBOs) has been shown to have a positive impact on customers’ perceptions of businesses (Barnett et al., 2013). However, the precise size and nature of this effect is not known: there is a paucity of quantitative evidence in this area, particularly in the form of randomised controlled trials (RCTs). The Food Standards Agency (FSA), in collaboration with Kantar’s Behavioural Practice, conducted a feasibility trial to investigate whether a randomised cluster trial – involving the proactive communication of allergen information at the point of sale in FBOs – is feasible in the United Kingdom (UK). Objectives: The trial sought to establish: ease of recruitments of businesses into trials; customer response rates for in-store outcome surveys; fidelity of intervention delivery by FBO staff; sensitivity of outcome survey measures to change; and appropriateness of the chosen analytical approach. Method: Following a recruitment phase – in which one of fourteen multinational FBOs was successfully recruited – the execution of the feasibility trial involved a quasi-randomised matched-pairs clustered experiment. Each of the FBO’s ten participating branches underwent pair-wise matching, with similarity of branches judged according to four criteria: Food Hygiene Rating Scheme (FHRS) score, average weekly footfall, number of staff and customer satisfaction rating. The allocation ratio for this trial was 1:1: one branch in each pair was assigned to the treatment group by a representative from the FBO, while the other continued to operate in accordance with their standard operating procedure. As a business-based feasibility trial, customers at participating branches throughout the fieldwork period were automatically enrolled in the trial. The trial was single-blind: customers at treatment branches were not aware that they were receiving an intervention. All customers who visited participating branches throughout the fieldwork period were asked to complete a short in-store survey on a tablet affixed in branches. This survey contained four outcome measures which operationalised customers’: perceptions of food safety in the FBO; trust in the FBO; self-reported confidence to ask for allergen information in future visits; and overall satisfaction with their visit. Results: Fieldwork was conducted from the 3 – 20 March 2020, with cessation occurring prematurely due to the closure of outlets following the proliferation of COVID-19. n=177 participants took part in the trial across the ten branches; however, response rates (which ranged between 0.1 - 0.8%) were likely also adversely affected by COVID-19. Intervention fidelity was an issue in this study: while compliance with delivery of the intervention was relatively high in treatment branches (78.9%), erroneous delivery in control branches was also common (46.2%). Survey data were analysed using random-intercept multilevel linear regression models (due to the nesting of customers within branches). Despite the trial’s modest sample size, there was some evidence to suggest that the intervention had a positive effect for those suffering from allergies/intolerances for the ‘trust’ (β = 1.288, p<0.01) and ‘satisfaction’ (β = 0.945, p<0.01) outcome variables. Due to singularity within the fitted linear models, hierarchical Bayes models were used to corroborate the size of these interactions. Conclusions: The results of this trial suggest that a fully powered clustered RCT would likely be feasible in the UK. In this case, the primary challenge in the execution of the trial was the recruitment of FBOs: despite high levels of initial interest from four chains, only one took part. However, it is likely that the proliferation of COVID-19 adversely impacted chain participation – two other FBOs withdrew during branch eligibility assessment and selection, citing COVID-19 as a barrier. COVID-19 also likely lowered the on-site survey response rate: a significant negative Pearson correlation was observed between daily survey completions and COVID-19 cases in the UK, highlighting a likely relationship between the two. Limitations: The trial was quasi-random: selection of branches, pair matching and allocation to treatment/control groups were not systematically conducted. These processes were undertaken by a representative from the FBO’s Safety and Quality Assurance team (with oversight from Kantar representatives on pair matching), as a result of the chain’s internal operational restrictions.
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Wu, Yingjie, Selim Gunay, and Khalid Mosalam. Hybrid Simulations for the Seismic Evaluation of Resilient Highway Bridge Systems. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2020. http://dx.doi.org/10.55461/ytgv8834.
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Bridges often serve as key links in local and national transportation networks. Bridge closures can result in severe costs, not only in the form of repair or replacement, but also in the form of economic losses related to medium- and long-term interruption of businesses and disruption to surrounding communities. In addition, continuous functionality of bridges is very important after any seismic event for emergency response and recovery purposes. Considering the importance of these structures, the associated structural design philosophy is shifting from collapse prevention to maintaining functionality in the aftermath of moderate to strong earthquakes, referred to as “resiliency” in earthquake engineering research. Moreover, the associated construction philosophy is being modernized with the utilization of accelerated bridge construction (ABC) techniques, which strive to reduce the impact of construction on traffic, society, economy and on-site safety. This report presents two bridge systems that target the aforementioned issues. A study that combined numerical and experimental research was undertaken to characterize the seismic performance of these bridge systems. The first part of the study focuses on the structural system-level response of highway bridges that incorporate a class of innovative connecting devices called the “V-connector,”, which can be used to connect two components in a structural system, e.g., the column and the bridge deck, or the column and its foundation. This device, designed by ACII, Inc., results in an isolation surface at the connection plane via a connector rod placed in a V-shaped tube that is embedded into the concrete. Energy dissipation is provided by friction between a special washer located around the V-shaped tube and a top plate. Because of the period elongation due to the isolation layer and the limited amount of force transferred by the relatively flexible connector rod, bridge columns are protected from experiencing damage, thus leading to improved seismic behavior. The V-connector system also facilitates the ABC by allowing on-site assembly of prefabricated structural parts including those of the V-connector. A single-column, two-span highway bridge located in Northern California was used for the proof-of-concept of the proposed V-connector protective system. The V-connector was designed to result in an elastic bridge response based on nonlinear dynamic analyses of the bridge model with the V-connector. Accordingly, a one-third scale V-connector was fabricated based on a set of selected design parameters. A quasi-static cyclic test was first conducted to characterize the force-displacement relationship of the V-connector, followed by a hybrid simulation (HS) test in the longitudinal direction of the bridge to verify the intended linear elastic response of the bridge system. In the HS test, all bridge components were analytically modeled except for the V-connector, which was simulated as the experimental substructure in a specially designed and constructed test setup. Linear elastic bridge response was confirmed according to the HS results. The response of the bridge with the V-connector was compared against that of the as-built bridge without the V-connector, which experienced significant column damage. These results justified the effectiveness of this innovative device. The second part of the study presents the HS test conducted on a one-third scale two-column bridge bent with self-centering columns (broadly defined as “resilient columns” in this study) to reduce (or ultimately eliminate) any residual drifts. The comparison of the HS test with a previously conducted shaking table test on an identical bridge bent is one of the highlights of this study. The concept of resiliency was incorporated in the design of the bridge bent columns characterized by a well-balanced combination of self-centering, rocking, and energy-dissipating mechanisms. This combination is expected to lead to minimum damage and low levels of residual drifts. The ABC is achieved by utilizing precast columns and end members (cap beam and foundation) through an innovative socket connection. In order to conduct the HS test, a new hybrid simulation system (HSS) was developed, utilizing commonly available software and hardware components in most structural laboratories including: a computational platform using Matlab/Simulink [MathWorks 2015], an interface hardware/software platform dSPACE [2017], and MTS controllers and data acquisition (DAQ) system for the utilized actuators and sensors. Proper operation of the HSS was verified using a trial run without the test specimen before the actual HS test. In the conducted HS test, the two-column bridge bent was simulated as the experimental substructure while modeling the horizontal and vertical inertia masses and corresponding mass proportional damping in the computer. The same ground motions from the shaking table test, consisting of one horizontal component and the vertical component, were applied as input excitations to the equations of motion in the HS. Good matching was obtained between the shaking table and the HS test results, demonstrating the appropriateness of the defined governing equations of motion and the employed damping model, in addition to the reliability of the developed HSS with minimum simulation errors. The small residual drifts and the minimum level of structural damage at large peak drift levels demonstrated the superior seismic response of the innovative design of the bridge bent with self-centering columns. The reliability of the developed HS approach motivated performing a follow-up HS study focusing on the transverse direction of the bridge, where the entire two-span bridge deck and its abutments represented the computational substructure, while the two-column bridge bent was the physical substructure. This investigation was effective in shedding light on the system-level performance of the entire bridge system that incorporated innovative bridge bent design beyond what can be achieved via shaking table tests, which are usually limited by large-scale bridge system testing capacities.