Relevant bibliographies by topics / Riesz Functional

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Riesz Functional'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Riesz Functional"

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Buskes, G., B. de Pagter, and A. van Rooij. "Functional calculus on Riesz spaces." Indagationes Mathematicae 2, no. 4 (1991): 423–36. http://dx.doi.org/10.1016/0019-3577(91)90028-6.

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Batko, Bogdan. "On Approximate Solutions of Functional Equations in Vector Lattices." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/547673.

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We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra). The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equationF(x+y)+F(x)+F(y)≠0⇒F(x+y)=F(x)+F(y)in Riesz spaces, the Cauchy equation with squaresF(x+y)2=(F(x)+F(y))2inf-algebras, and the quadratic functional equationF(x+y)+F(x-y)=2F(x)+2F(y)in Riesz spaces.
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Talakua, Mozart W., and Stenly J. Nanuru. "TEOREMA REPRESENTASI RIESZ–FRECHET PADA RUANG HILBERT." BAREKENG: Jurnal Ilmu Matematika dan Terapan 5, no. 2 (December 1, 2011): 1–8. http://dx.doi.org/10.30598/barekengvol5iss2pp1-8.

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Hilbert space is a very important idea of the Davids Hilbert invention. In 1907, Riesz and Fréchet developed one of the theorem in Hilbert space called the Riesz-Fréchet representationtheorem. This research contains some supporting definitions Banach space, pre-Hilbert spaces, Hilbert spaces, the duality of Banach and Riesz-Fréchet representation theorem. On Riesz-Fréchet representation theorem will be shown that a continuous linear functional that exist in the Hilbert space is an inner product, in other words, there is no continuous linear functional on a Hilbert space except the inner product.
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Conway, John B., Domingo A. Herrero, and Bernard B. Morrel. "Completing the Riesz-Dunford functional calculus." Memoirs of the American Mathematical Society 82, no. 417 (1989): 0. http://dx.doi.org/10.1090/memo/0417.

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Yang, Zhuyuan, and Luoqing Li. "Approximation by Riesz means on the rotation group SO(3)." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 04 (April 19, 2017): 1750035. http://dx.doi.org/10.1142/s0219691317500357.

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This paper deals with the approximation properties of Riesz means in [Formula: see text]. The convergence rate of the Riesz means is obtained. The equivalence of Riesz means and the Peetre [Formula: see text]-functional on the rotation group [Formula: see text] is established.
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Kalauch, Anke, Bas Lemmens, and Onno van Gaans. "Riesz completions, functional representations, and anti-lattices." Positivity 18, no. 1 (May 16, 2013): 201–18. http://dx.doi.org/10.1007/s11117-013-0240-x.

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XIAO, XIANG-CHUN, YU-CAN ZHU, and XIAO-MING ZENG. "GENERALIZED p-FRAME IN SEPARABLE COMPLEX BANACH SPACES." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 01 (January 2010): 133–48. http://dx.doi.org/10.1142/s0219691310003419.

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The concept of g-frame and g-Riesz basis in a complex Hilbert space was introduced by Sun.18 In this paper, we generalize the g-frame and g-Riesz basis in a complex Hilbert space to a complex Banach space. Using operators theory and methods of functional analysis, we give some characterizations of a g-frame or a g-Riesz basis in a complex Banach space. We also give a result about the stability of g-frame in a complex Banach space.
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Xiao, Xue Mei. "Perturbation Theorems for Frames and Riesz Bases." Applied Mechanics and Materials 433-435 (October 2013): 44–47. http://dx.doi.org/10.4028/www.scientific.net/amm.433-435.44.

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This paper gives a perturbation theorem for frames in a Hilbert space which is a generalization of a result by Ping Zhao. It is proved that the condition a linear operator is invertible can be weakened to be surjective, and a similar result also be obtained for a Riesz basis. The perturbation theorems for frames and Riesz bases in a Hilbert space were studied by operator theory in functional analysis.
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Batko, Bogdan. "Stability of the Exponential Functional Equation in Riesz Algebras." Abstract and Applied Analysis 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/848540.

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We deal with the stability of the exponential Cauchy functional equationF(x+y)=F(x)F(y)in the class of functionsF:G→Lmapping a group (G, +) into a Riesz algebraL. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.
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Miana, Pedro J. "Algebra Structure of Operator-Valued Riesz Means." Journal of Operators 2014 (May 18, 2014): 1–7. http://dx.doi.org/10.1155/2014/923616.

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We characterize operator-valued Riesz means via an algebraic law of composition and establish their functional calculus accordingly. With this aim, we give a new integral expression of the Leibniz derivation rule for smooth functions.
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Dissertations / Theses on the topic "Riesz Functional"

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Caglar, Mert. "Invariant Subspaces Of Positive Operators On Riesz Spaces And Observations On Cd0(k)-spaces." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606391/index.pdf.

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The present work consists of two main parts. In the first part, invariant subspaces of positive operators or operator families on locally convex solid Riesz spaces are examined. The concept of a weakly-quasinilpotent operator on a locally convex solid Riesz space has been introduced and several results that are known for a single operator on Banach lattices have been generalized to families of positive or close-to-them operators on these spaces. In the second part, the so-called generalized Alexandroff duplicates are studied and CDsigma, gamma(K, E)-type spaces are investigated. It has then been shown that the space CDsigma, gamma(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff duplicate of K.
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Yoo, Seonguk. "Extremal sextic truncated moment problems." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1113.

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Inverse problems naturally occur in many branches of science and mathematics. An inverse problem entails finding the values of one or more parameters using the values obtained from observed data. A typical example of an inverse problem is the inversion of the Radon transform. Here a function (for example of two variables) is deduced from its integrals along all possible lines. This problem is intimately connected with image reconstruction for X-ray computerized tomography. Moment problems are a special class of inverse problems. While the classical theory of moments dates back to the beginning of the 20th century, the systematic study of truncated moment problems began only a few years ago. In this dissertation we will first survey the elementary theory of truncated moment problems, and then focus on those problems with cubic column relations. For a degree 2n real d-dimensional multisequence β ≡ β (2n) ={β i}i∈Zd+,|i|≤2n to have a representing measure μ, it is necessary for the associated moment matrix Μ(n) to be positive semidefinite, and for the algebraic variety associated to β, Vβ, to satisfy rank Μ(n)≤ card Vβ as well as the following consistency condition: if a polynomial p(x)≡ ∑|i|≤2naixi vanishes on Vβ, then Λ(p):=∑|i|≤2naiβi=0. In 2005, Professor Raúl Curto collaborated with L. Fialkow and M. Möller to prove that for the extremal case (Μ(n)= Vβ), positivity and consistency are sufficient for the existence of a (unique, rank Μ(n)-atomic) representing measure. In joint work with Professor Raúl Curto we have considered cubic column relations in M(3) of the form (in complex notation) Z3=itZ+ubar Z, where u and t are real numbers. For (u,t) in the interior of a real cone, we prove that the algebraic variety Vβ consists of exactly 7 points, and we then apply the above mentioned solution of the extremal moment problem to obtain a necessary and sufficient condition for the existence of a representing measure. This requires a new representation theorem for sextic polynomials in Z and bar Z which vanish in the 7-point set Vβ. Our proof of this representation theorem relies on two successive applications of the Fundamental Theorem of Linear Algebra. Finally, we use the Division Algorithm from algebraic geometry to extend this result to other situations involving cubic column relations.
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Ercan, Zafer. "Riesz spaces of Riesz space valued functions." Thesis, Queen's University Belfast, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359063.

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Polat, Faruk. "On The Generalizations And Properties Of Abramovich-wickstead Spaces." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/12610166/index.pdf.

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In this thesis, we study two problems. The first problem is to introduce the general version of Abramovich-Wickstead type spaces and investigate its order properties. In particular, we study the ideals, order bounded sets, disjointness properties, Dedekind completion and the norm properties of this Riesz space. We also define a new concrete example of Riesz space-valued uniformly continuous functions, denoted by CDr0 which generalizes the original Abramovich-Wickstead space. It is also shown that similar spaces CD0 and CDw introduced earlier by Alpay and Ercan are decomposable lattice-normed spaces. The second problem is related to analytic representations of different classes of dominated operators on these spaces. Our main representation theorems say that regular linear operators on CDr0 or linear dominated operators on CD0 may be represented as the sum of integration with respect to operator-valued measure and summation operation. In the case when the operator is order continuous or bo-continuous, then these representations reduce to discrete parts.
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Koné, Mamadou Ibrahima. "Contrôle optimal et calcul des variations en présence de retard sur l'état." Thesis, Paris 1, 2016. http://www.theses.fr/2016PA01E063/document.

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L'objectif de cette thèse est de contribuer à l'optimisation de problèmes dynamiques en présence de retard. Le point de vue qui nous intéressera est celui de Pontryagin qui dans son ouvrage publié en 1962 a donné les conditions nécessaires d'existence de solutions pour ce type de problème. Warga dans son ouvrage publié en 1972 a fait un catalogue des solutions possible, Li et al. ont étudié le cas de contrôle périodique. Notre méthode de démonstration est directement inspirée de la démonstration de P. Michel du cas des systèmes gouvernés par des équations différentielles ordinaires. La principale difficulté pour cette approche est l'utilisation de la résolvante de l'équation différentielle fonctionnelle linéarisée de l'équation différentielle fonctionnelle d'évolution qui gouverne le système. Nous traitons aussi de condition d'Euler-Lagrange dans le cadre d'un problème de calcul variationnel avec retard
In this thesis, we have attempted to contribute to the optimization of dynamical problems with delay in state space. We are specifically interested in the viewpoint of Pontryagin who outlined in his book published in 1962 the necessary conditions required for solving such problems. In his work published in 1972, Warga catalogued the possible solutions. Li and al. analyzed the case of periodic control. We will treat an optimal control problem governed by a Delay Functional Differential Equation. Our method is close to the one of P. Michel on dynamical system governed by Ordinary Differential Equations. The main problem ariving out in this approach is the use of the resolvent of the Delay Functional Differential Equation. We also consider with Euler-Lagrange condition in the framework of variational problems with delay
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Norqvist, Jimmy. "The Riesz representation theorem for positive linear functionals." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-124649.

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Strandell, Gustaf. "Linear and Non-linear Deformations of Stochastic Processes." Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributr], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3689.

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Bhandari, Mukta Bahadur. "Inequalities associated to Riesz potentials and non-doubling measures with applications." Diss., Kansas State University, 2010. http://hdl.handle.net/2097/4375.

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Doctor of Philosophy
Department of Mathematics
Charles N. Moore
The main focus of this work is to study the classical Calder\'n-Zygmund theory and its recent developments. An attempt has been made to study some of its theory in more generality in the context of a nonhomogeneous space equipped with a measure which is not necessarily doubling. We establish a Hedberg type inequality associated to a non-doubling measure which connects two famous theorems of Harmonic Analysis-the Hardy-Littlewood-Weiner maximal theorem and the Hardy-Sobolev integral theorem. Hedberg inequalities give pointwise estimates of the Riesz potentials in terms of an appropriate maximal function. We also establish a good lambda inequality relating the distribution function of the Riesz potential and the fractional maximal function in $(\rn, d\mu)$, where $\mu$ is a positive Radon measure which is not necessarily doubling. Finally, we also derive potential inequalities as an application.
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Abbott, Catherine Ann. "Operators on Continuous Function Spaces and Weak Precompactness." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331171/.

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If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property.
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Dahmani, Kamilia. "Weighted LP estimates on Riemannian manifolds." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30188/document.

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Cette thèse s'inscrit dans le domaine de l'analyse harmonique et plus exactement, des estimations à poids. Un intérêt particulier est porté aux estimations Lp à poids des transformées de Riesz sur des variétés Riemanniennes complètes ainsi qu'à l'optimalité des résultats en terme de la puissance de la caractéristique des poids. On obtient un premier résultat (en terme de la linéarité et de la non dépendance de la dimension) sur des espaces pas nécessairement de type homogène, lorsque p = 2 et la courbure de Bakry-Emery est positive. On utilise pour cela une approche analytique en exhibant une fonction de Bellman concrète. Puis, en utilisant des techniques stochastiques et une domination éparse, on démontre que les transformées de Riesz sont bornées sur Lp, pour p ∈ (1, +∞) et on déduit également le résultat précèdent. Enfin, on utilise un changement élégant dans la preuve précèdente pour affaiblir l'hypothèse sur la courbure et la supposer minorée
The topics addressed in this thesis lie in the field of harmonic analysis and more pre- cisely, weighted inequalities. Our main interests are the weighted Lp-bounds of the Riesz transforms on complete Riemannian manifolds and the sharpness of the bounds in terms of the power of the characteristic of the weights. We first obtain a linear and dimensionless result on non necessarily homogeneous spaces, when p = 2 and the Bakry-Emery curvature is non-negative. We use here an analytical approach by exhibiting a concrete Bellman function. Next, using stochastic techniques and sparse domination, we prove that the Riesz transforms are Lp-bounded for p ∈ (1, +∞) and obtain the previous result for free. Finally, we use an elegant change in the precedent proof to weaken the condition on the curvature and assume it is bounded from below
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Books on the topic "Riesz Functional"

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Conway, John B. Completing the Riesz-Dunford functional calculus. Providence, R.I., USA: American Mathematical Society, 1989.

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1941-, Portenier Claude, ed. Radon integrals: An abstract approach to integration and Riesz representation through function cones. Boston: Birkäuser, 1992.

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Beata, Randrianantoanina, and Walter de Gruyter & Co, eds. Narrow operators on function spaces and vector lattices. 2013.

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Smithies, Laura. Basisity of eigenvectors of Kreĭn space operators. 1991.

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Book chapters on the topic "Riesz Functional"

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Colombo, Fabrizio, Irene Sabadini, and Daniele C. Struppa. "Appendix: The Riesz–Dunford functional calculus." In Noncommutative Functional Calculus, 201–10. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0110-2_5.

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Gohberg, Israel, Seymour Goldberg, and Marinus A. Kaashoek. "Riesz Projections and Functional Calculus." In Classes of Linear Operators Vol. I, 4–24. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7509-7_2.

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Yosida, Kôsaku. "The Orthogonal Projection and F. Riesz’ Representation Theorem." In Functional Analysis, 81–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-61859-8_4.

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Wong, Yau-chuen. "Embedding Properties of Locally Convex Riesz Spaces." In Functional Analysis in China, 171–86. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0185-8_15.

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Zaanen, Adriaan C. "Functional Calculas and Multiplication." In Introduction to Operator Theory in Riesz Spaces, 221–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60637-3_18.

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Border, Kim C. "Functional Analytic Tools for Expected Utility Theory." In Positive Operators, Riesz Spaces, and Economics, 69–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58199-1_4.

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Matsuoka, Katsuo. "d-Modified Riesz Potentials on Central Campanato Spaces." In Operator Theory, Functional Analysis and Applications, 423–39. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-51945-2_21.

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Tschinke, Francesco. "Riesz-Fischer Maps, Semi-frames and Frames in Rigged Hilbert Spaces." In Operator Theory, Functional Analysis and Applications, 625–45. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-51945-2_29.

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Batko, Bogdan, and Janusz Brzdȩk. "A Remark on Some Simultaneous Functional Inequalities in Riesz Spaces." In Topics in Mathematical Analysis and Applications, 111–17. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06554-0_5.

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Groenewegen, G. L. M., and A. C. M. van Rooij. "Riesz Spaces." In Spaces of Continuous Functions, 41–57. Paris: Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-201-4_5.

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Conference papers on the topic "Riesz Functional"

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Karshygina, Gulden Zh. "Optimal embeddings of Bessel and Riesz type potentials on the basis of weighted Lorentz spaces." In INTERNATIONAL CONFERENCE “FUNCTIONAL ANALYSIS IN INTERDISCIPLINARY APPLICATIONS” (FAIA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5000613.

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Pandey, Rajesh K., and Om P. Agrawal. "Numerical Scheme for Generalized Isoparametric Constraint Variational Problems With A-Operator." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12388.

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This paper presents a numerical scheme for a class of Isoperimetric Constraint Variational Problems (ICVPs) defined in terms of an A-operator introduced recently. In this scheme, Bernstein’s polynomials are used to approximate the desired function and to reduce the problem from a functional space to an eigenvalue problem in a finite dimensional space. Properties of the eigenvalues and eigenvectors of this problem are used to obtain approximate solutions to the problem. Results for two examples are presented to demonstrate the effectiveness of the proposed scheme. In special cases the A-operator reduce to Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo, and several other fractional derivatives defined in the literature. Thus, the approach presented here provides a general scheme for ICVPs defined using different types of fractional derivatives. Although, only Bernstein’s polynomials are used here to approximate the solutions, many other approximation schemes are possible. Effectiveness of these approximation schemes will be presented in the future.
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Di Nola, Antonio, Giacomo Lenzi, and Gaetano Vitale. "Riesz-McNaughton functions and Riesz MV-algebras of nonlinear functions." In 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2015. http://dx.doi.org/10.1109/fuzz-ieee.2015.7337916.

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Magin, Richard L., and Dumitru Baleanu. "NMR Measurements of Anomalous Diffusion Reflect Fractional Order Dynamics." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34224.

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Diffusion weighted MRI is often used to detect and stage neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion measurements relies on the design of selective phase encoding pulses that alter the intensity of the acquired signal according to biophysical models of spin diffusion in tissue. The most common approach utilizes a bipolar or Stejskal-Tanner gradient pulse sequence to encode the apparent diffusion coefficient as an exponential, multi-exponential or stretched exponential function of experimentally-controlled parameters. Several studies have investigated the ability of the stretched exponential to provide an improved fit to diffusion-weighted imaging data. These results were recently analyzed by establishing a direct link between water diffusion, as measured using NMR, and fractal structural models of tissues. In this paper we suggest an alternative description for stretched exponential behavior that reflects fractional order dynamics of a generalized Bloch-Torrey equation in either space or time. Such generalizations are the basis for similar anomalous diffusion phenomena observed in optical spectroscopy, polymer dynamics and electrochemistry. Here we demonstrate a correspondence between the detected NMR signal and anomalous diffusional dynamics of water through the Riesz fractional order space derivative and the Caputo form of the fractional order Riemann-Liouville time derivative.
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Yu, Q., F. Liu, I. Turner, and K. Burrage. "Analytical and Numerical Solutions of the Space and Time Fractional Bloch-Torrey Equation." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47613.

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Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et at, J. Magnetic Resonance, 190 (2008) 255–270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.
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Pozniak, Natalija, and Leonidas Sakalauskas. "The method for the optimal experiment design." In Contemporary Issues in Business, Management and Economics Engineering. Vilnius Gediminas Technical University, 2019. http://dx.doi.org/10.3846/cibmee.2019.012.

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Purpose – is to develop the Bayesian method of optimal engineering design by a series of experiments, aiming to manage experimental resources in a rational economic way. Research methodology – is based on modelling of experimental data by Gaussian random fields (GRF) and using matri-ces of fractional Euclidean distances. Next, the P-algorithm for the planning of the experiment series is created in order to optimize the values of the response surface. Findings – the application of the developed method in engineering design enable us to create plans for the experiment se-ries in order to create new functional products and processes managing experimental resources in a rational economic way. Research limitations – the creation of the plans of the experiment series can require a large amount of computer time re-lated to the application of the Monte Carlo procedure in order to ensure the optimality of created plans. However, this limitation can be avoided using distributed computing tools. Practical implications – the created method helps engineers to seek solutions to experimental problems, considering the economic viability of each potential solution along with the technical aspects. Originality/Value – in creating functional products and processes engineers are using the experimental design process, which usually is highly iterative. The developed approach enables us to design the experimental series inflexible way, de-creasing the number of required experiments and avoiding of rather expensive methods such as factorial experiments, steepest descent, etc., usually applied for experimental design in engineering practice
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