Relevant bibliographies by topics / Functions of bounded deformation

Academic literature on the topic 'Functions of bounded deformation'

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Published: 14 March 2023

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Journal articles on the topic "Functions of bounded deformation"

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Dal Maso, Gianni. "Generalised functions of bounded deformation." Journal of the European Mathematical Society 15, no. 5 (2013): 1943–97. http://dx.doi.org/10.4171/jems/410.

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Conti, Sergio, Matteo Focardi, and Flaviana Iurlano. "Which special functions of bounded deformation have bounded variation?" Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 1 (October 17, 2017): 33–50. http://dx.doi.org/10.1017/s030821051700004x.

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Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions that are piecewise affine on a Caccioppoli partition are in GSBV, and we prove that SBDp functions are approximately continuous -almost everywhere away from the jump set. On the negative side, we construct a function that is BD but not in BV and has distributional strain consisting only of a jump part, and one that has a distributional strain consisting of only a Cantor part.
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Babadjian, Jean-Francois. "Traces of functions of bounded deformation." Indiana University Mathematics Journal 64, no. 4 (2015): 1271–90. http://dx.doi.org/10.1512/iumj.2015.64.5601.

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Ambrosio, Luigi, Alessandra Coscia, and Gianni Dal Maso. "Fine Properties of Functions with Bounded Deformation." Archive for Rational Mechanics and Analysis 139, no. 3 (October 27, 1997): 201–38. http://dx.doi.org/10.1007/s002050050051.

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Nie, Ziwei, and Xiaoping Yang. "Deformable Image Registration Using Functions of Bounded Deformation." IEEE Transactions on Medical Imaging 38, no. 6 (June 2019): 1488–500. http://dx.doi.org/10.1109/tmi.2019.2896170.

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Hajłasz, Piotr. "On approximate differentiability of functions with bounded deformation." Manuscripta Mathematica 91, no. 1 (December 1996): 61–72. http://dx.doi.org/10.1007/bf02567939.

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Chambolle, Antonin. "An approximation result for special functions with bounded deformation." Journal de Mathématiques Pures et Appliquées 83, no. 7 (July 2004): 929–54. http://dx.doi.org/10.1016/j.matpur.2004.02.004.

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Nie, Ziwei, Chen Li, Hairong Liu, and Xiaoping Yang. "Deformable Image Registration Based on Functions of Bounded Generalized Deformation." International Journal of Computer Vision 129, no. 5 (February 4, 2021): 1341–58. http://dx.doi.org/10.1007/s11263-021-01439-x.

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Ebobisse, François B. "Lusin-type approximation of BD functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 4 (1999): 697–705. http://dx.doi.org/10.1017/s0308210500013081.

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The purpose of this paper is to establish a Lusin-type approximation of functions with bounded deformation by Lipschitz or C1 functions. The main ingredients inthe proof of our result are the maximal function of the measure Eu, the ‘Poincaré-type’ result by Kohn and the approximate symmetric differentiability of BD functions by Ambrosio and others.
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Fuchs, M., and M. Bildhauer. "Compact embeddings of the space of functions with bounded logarithmic deformation." Journal of Mathematical Sciences 172, no. 1 (December 17, 2010): 165–83. http://dx.doi.org/10.1007/s10958-010-0190-9.

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Dissertations / Theses on the topic "Functions of bounded deformation"

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Johan, Filip Rindler Johan Filip. "Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c4736fa2-ab51-4cb7-b1d9-cbab0ede274b.

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Lind, Martin. "Functions of bounded variation." Thesis, Karlstad University, Division for Engineering Sciences, Physics and Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-209.

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The paper begins with a short survey of monotone functions. The functions of bounded variation are introduced and some basic properties of these functions are given. Finally the jump function of a function of bounded variation is defined.

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Lind, Martin. "Functions of Generalized Bounded Variation." Doctoral thesis, Karlstads universitet, Institutionen för matematik och datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-26342.

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This thesis is devoted to the study of different generalizations of the classical conception of a function of bounded variation. First, we study the functions of bounded p-variation introduced by Wiener in 1924. We obtain estimates of the total p-variation (1<p<∞) and other related functionals for a periodic function f in Lp([0,1]) in terms of its Lp-modulus of continuity ω(f;δ)p. These estimates are sharp for any rate of decay of ω(f;δ)p. Moreover, the constant coefficients in them depend on parameters in an optimal way. Inspired by these results, we consider the relationship between the Riesz type generalized variation vp,α(f) (1<p<∞, 0≤α≤1-1/p) and the modulus of p-continuity  ω1-1/p(f;δ). These functionals generate scales of spaces that connect the space of functions of bounded p-variation and the Sobolev space Wp1. We prove sharp estimates of vp,α(f) in terms of ω1-1/p(f;δ). In the same direction, we study relations between moduli of p-continuity and q-continuity for 1<p<q<∞. We prove an inequality that estimates ω1-1/p(f;δ) in terms of ω1-1/q(f;δ). The inequality is sharp for any order of decay of ω1-1/q(f;δ). Next, we study another generalization of bounded variation: the so-called bounded Λ-variation, introduced by Waterman in 1972. We investigate relations between the space ΛBV of functions of bounded Λ-variation, and classes of functions defined via integral smoothness properties. In particular, we obtain the necessary and sufficient condition for the embedding of the class Lip(α;p) into ΛBV. This solves a problem of Wang (2009). We consider also functions of two variables. Applying our one-dimensional result, we obtain sharp estimates of the Hardy-Vitali type p-variation of a bivariate function in terms of its mixed modulus of continuity in Lp([0,1]2). Further, we investigate Fubini-type properties of the space Hp(2) of functions of bounded Hardy-Vitali p-variation. This leads us to consider the symmetric mixed norm space Vp[Vp]sym of functions of bounded iterated p-variation. For p>1, we prove that Hp(2) is not embedded into Vp[Vp]sym, and that Vp[Vp]sym is not embedded into Hp(2). In other words, Fubini-type properties completely fail in the class of functions of bounded Hardy-Vitali type p-variation for p>1.
Baksidestext The classical concept of the total variation of a function has been extended in several directions. Such extensions find many applications in different areas of mathematics. Consequently, the study of notions of generalized bounded variation forms an important direction in the field of mathematical analysis. This thesis is devoted to the investigation of various properties of functions of generalized bounded variation.  In particular, we obtain the following results: sharp relations between spaces of generalized bounded variation and spaces of functions  defined by integral smoothness conditions  (e.g., Sobolev and Besov spaces); optimal properties of certain scales of function spaces of frac- tional smoothness generated by functionals of variational type; sharp embeddings within  the scale of spaces of functions of bounded p-variation; results concerning bivariate functions of bounded p-variation, in particular sharp estimates of total variation in terms of the mixed Lp-modulus of continuity, and Fubini-type properties.
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Fällström, Anders. "Algebras of bounded holomorphic functions." Doctoral thesis, Umeå universitet, Institutionen för matematik, teknik och naturvetenskap, 1994. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-114744.

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Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved. If A(f2) is the Banach algebra of functions holomorphic in the bounded domain Q in Cn and continuous on the boundary and if p is a point in Q, then the following problem is known as Gleason’s Problem for A(Q) : Is the maximal ideal in A(Q) consisting of functions vanishing at p generated by (Zl ~Pl) , ■■■ , (Zn - Pn) ? A sufficient condition for solving Gleason’s Problem for A(Q) for all points in Q is given. In particular, this condition is fulfilled by a convex domain Q with Lipi+£-boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenzon. One of the ideas in the methods of proof is integration along specific polygonal lines. If Gleason’s Problem can be solved in a point it can be solved also in a neighbourhood of the point. It is shown, that the coefficients in this case depends holomorphically on the points. Defining a projection from the spectrum of a uniform algebra of holomorphic functions to Cn, one defines the fiber in the spectrum over a point as the elements in the spectrum that projects on that point. Defining a kind of maximum modulus property for domains in Cn, some problems concerning the fibers and the number of elements in the fibers in certain algebras of bounded holomorphic functions are solved. It is, for example, shown that the set of points, over which the fibers contain more than one element is closed. A consequence is also that a starshaped domain with the maximum modulus property has schlicht /y°°-envelope of holomorphy. These kind of problems are also connected with Gleason’s problem. A survey paper on general properties of algebras of bounded holomorphic functions of several variables is included. The paper, in particular, treats aspects connecting iy°°-envelopes of holomorphy and some areas in the theory of uniform algebras.

Diss. (sammanfattning) Umeå : Umeå universitet, 1994, härtill 6 uppsatser


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Backlund, Ulf. "Envelopes of holomorphy for bounded holomorphic functions." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 1992. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-141155.

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Some problems concerning holomorphic continuation of the class of bounded holo­morphic functions from bounded domains in Cn that are domains of holomorphy are solved. A bounded domain of holomorphy Ω in C2 with nonschlicht H°°-envelope of holomorphy is constructed and it is shown that there is a point in D for which Glea­son’s Problem for H°°(Ω) cannot be solved. Furthermore a proof of the existence of a bounded domain of holomorphy in C2 for which the volume of the H°°-envelope of holomorphy is infinite is given. The idea of the proof is to put a family of so-called ”Sibony domains” into the unit bidisk by a packing procedure and patch them together by thin neighbourhoods of suitably chosen curves. If H°°(Ω) is the Banach algebra of bounded holomorphic functions on a bounded domain Ω in Cn and if p is a point in Ω, then the following problem is known as Gleason’s Problem for Hoo(Ω) : Is the maximal ideal in H°°(Ω) consisting of functions vanishing at p generated by (z1 -p1) , ... ,   (zn - pn) ? A sufficient condition for solving Gleason’s Problem for 77°° (Ω) for all points in Ω is given. In particular, this condition is fulfilled by a convex domain Ω with Lip1+e boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenson. It is also proved that Gleason’s Problem can be solved for all points in certain unions of two polydisks in C2. One of the ideas in the methods of proof is integration along specific polygonal lines. Certain properties of some open sets defined by global plurisubharmonic func­tions in Cn are studied. More precisely, the sets Du = {z e Cn : u(z) < 0} and Eh = {{z,w) e Cn X C : h(z,w) < 1} are considered where ti is a plurisubharmonic function of minimal growth and h≠0 is a non-negative homogeneous plurisubharmonic function. (That is, the functions u and h belong to the classes L(Cn) and H+(Cn x C) respectively.) It is examined how the fact that Eh and the connected components of Du are H°°-domains of holomorphy is related to the structure of the set of disconti­nuity points of the global defining functions and to polynomial convexity. Moreover it is studied whether these notions are preserved under a certain bijective mapping from L(Cn) to H+(Cn x C). Two counterexamples are given which show that polynomial convexity is not preserved under this bijection. It is also proved, for example, that if Du is bounded and if the set of discontinuity points of u is pluripolar then Du is of type H°°. A survey paper on general properties of envelopes of holomorphy is included. In particular, the paper treats aspects of the theory for the bounded holomorphic functions. The results for the bounded holomorphic functions are compared with the corresponding ones for the holomorphic functions.
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Chirikhin, Andrey. "Polynomial distribution functions on bounded closed intervals." Thesis, University of Warwick, 2007. http://wrap.warwick.ac.uk/3678/.

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The thesis explores several topics, related to polynomial distribution functions and their densities on [0,1]M, including polynomial copula functions and their densities. The contribution of this work can be subdivided into two areas. - Studying the characterization of the extreme sets of polynomial densities and copulas, which is possible due to the Choquet theorem. - Development of statistical methods that utilize the fact that the density is polynomial (which may or may not be an extreme density). With regard to the characterization of the extreme sets, we first establish that in all dimensions the density of an extreme distribution function is an extreme density. As a consequence, characterizing extreme distribution functions is equivalent to characterizing extreme densities, which is easier analytically. We provide the full constructive characterization of the Choquet-extreme polynomial densities in the univariate case, prove several necessary and sufficient conditions for the extremality of densities in arbitrary dimension, provide necessary conditions for extreme polynomial copulas, and prove characterizing duality relationships for polynomial copulas. We also introduce a special case of reflexive polynomial copulas. Most of the statistical methods we consider are restricted to the univariate case. We explore ways to construct univariate densities by mixing the extreme ones, propose non-parametric and ML estimators of polynomial densities. We introduce a new procedure to calibrate the mixing distribution and propose an extension of the standard method of moments to pinned density moment matching. As an application of the multivariate polynomial copulas, we introduce polynomial coupling and explore its application to convolution of coupled random variables. The introduction is followed by a summary of the contributions of this thesis and the sections, dedicated first to the univariate case, then to the general multivariate case, and then to polynomial copula densities. Each section first presents the main results, followed by the literature review.
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Don, Sebastiano. "Functions of bounded variation in Carnot-Carathéodory spaces." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3426813.

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We study properties of functions with bounded variation in Carnot-Carathéodory spaces. In Chapter 2 we prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative. In Chapter 3 we prove a rank-one theorem à la G. Alberti for the derivatives of vector-valued maps with bounded variation in a class of Carnot groups that includes all Heisenberg groups H^n with n ≥ 2. Some important tools for the proof are properties linking the horizontal derivatives of a real-valued function with bounded variation to its subgraph. In Chapter 4 we prove a compactness result for bounded sequences (u_j) of functions with bounded variation in metric spaces (X, d_j) where the space X is fixed, but the metric may vary with j. We also provide an application to Carnot-Carathéodory spaces. The results of Chapter 4 are fundamental for the proofs of some facts of Chapter 2.
Analizziamo alcune proprietà di funzioni a variazione limitata in spazi di Carnot-Carathéodory. Nel Capitolo 2 dimostriamo che esse sono approssimativamente differenziabili quasi ovunque, esaminiamo il loro insieme di discontinuità approssimata e la decomposizione della loro derivata distribuzionale. Assumendo un'ipotesi addizionale sullo spazio, che chiamiamo proprietà R, mostriamo che quasi tutti i punti di discontinuità approssimata sono di salto e studiamo una formula per la parte di salto della derivata. Nel Capitolo 3 dimostriamo un teorema di rango uno à la G. Alberti per la derivata distribuzionale di funzioni vettoriali a variazione limitata in una classe di gruppi di Carnot che contiene tutti i gruppi di Heisenberg H^n con n ≥ 2. Uno strumento chiave nella dimostrazione è costituito da alcune proprietà che legano le derivate orizzontali di una funzione a variazione limitata con il suo sottografico. Nel Capitolo 4 dimostriamo un risultato di compattezza per succesioni (u_j) equi-limitate in spazi metrici (X, d_j) quando lo spazio X è fissato ma la metrica può variare con j. Mostriamo inoltre un'applicazione agli spazi di Carnot-Carathéodory. I risultati del Capitolo 4 sono fondamentali per la dimostrazione di alcuni fatti contenuti nel Capitolo 2.
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Dawson, Dan Paul. "Concerning Integral Approximations of Bounded Finitely Additive Set Functions." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc332650/.

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The purpose of this paper is to generalize a theorem that characterizes absolute continuity of bounded finitely additive set functions in the form of an integral approximation. We show that his integral exists if the condition of absolute continuity is removed.
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Gurney, David R. (David Robert). "Bounded, Finitely Additive, but Not Absolutely Continuous Set Functions." Thesis, University of North Texas, 1989. https://digital.library.unt.edu/ark:/67531/metadc332375/.

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In leading up to the proof, methods for constructing fields and finitely additive set functions are introduced with an application involving the Tagaki function given as an example. Also, non-absolutely continuous set functions are constructed using Banach limits and maximal filters.
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Sababheh, Mohammad Suboh. "Constructions of bounded functions related to two-sided Hardy inequalities." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102160.

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We investigate inequalities that can be viewed as generalizations of Hardy's inequality about the Fourier coefficients of a function analytic on the circle. The proof of the Littlewood conjecture opened a wide door in front of questions regarding possible generalizations of Hardy's inequality. The proof of the Littlewood conjecture was based on some constructions of bounded functions having particular properties.
In 1993, I. Klemes investigated one of the constructions (we shall call it the algebraic construction) and proved what is called a mixed norm generalization of Hardy's inequality. It turns out that we can work with the same construction and examine more properties of it in order to get more results.
The objectives of the thesis are to give more detailed properties of the algebraic construction and to use these properties in order to prove various versions of two-sided Hardy inequalities.
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Books on the topic "Functions of bounded deformation"

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Sheremeta, M. Analytic functions of bounded index. Kiev, Ukraine: VNTL Publishers, 1999.

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Blaschke products: Bounded analytic functions. Ann Arbor: University of Michigan Press, 1985.

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author, Banas Jozef 1950, and Merentes Díaz, Nelson José, author, eds. Bounded variation and around. Berlin: Walter de Gruyter GmbH & Co. KG, 2013.

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Ziemer, William P. Weakly differentiable functions: Sobolev spaces and functions of bounded variation. New York: Springer-Verlag, 1989.

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Temli͡akov, V. N. Approximation of functions with bounded mixed derivative. Providence, R.I: American Mathematical Society, 1989.

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Liflyand, Elijah. Functions of Bounded Variation and Their Fourier Transforms. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04429-9.

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Nicola, Fusco, and Pallara Diego, eds. Functions of bounded variation and free discontinuity problems. Oxford: Clarendon Press, 2000.

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On the algebraic foundation of bounded cohomology. Providence, R.I: American Mathematical Society, 2011.

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Pytlik, T. Spherical functions and uniformly bounded representations of free group. Wroclaw: Mathem. inst. univ. Wroclaw, 1986.

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Quantum bounded symmetric domains. Providence, R.I: American Mathematical Society, 2010.

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Book chapters on the topic "Functions of bounded deformation"

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Bounded Harmonic Functions." In Harmonic Function Theory, 31–44. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-8137-3_2.

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Axler, Sheldon, Paul Bourdon, and Wade Ramey. "Bounded Harmonic Functions." In Harmonic Function Theory, 31–44. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/0-387-21527-1_2.

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Ziemer, William P. "Functions of Bounded Variation." In Weakly Differentiable Functions, 220–82. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-1015-3_5.

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van der Vaart, Aad W., and Jon A. Wellner. "Spaces of Bounded Functions." In Weak Convergence and Empirical Processes, 34–42. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-2545-2_5.

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Laczkovich, Miklós, and Vera T. Sós. "Functions of Bounded Variation." In Real Analysis, 399–406. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2766-1_17.

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Wyner, A. D. "Spectra of Bounded Functions." In Open Problems in Communication and Computation, 46–48. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4808-8_9.

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Rana, Inder. "Functions of bounded variation." In Graduate Studies in Mathematics, 397–99. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/gsm/045/17.

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Leoni, Giovanni. "Functions of bounded variation." In Graduate Studies in Mathematics, 377–414. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/105/13.

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Braides, Andrea. "Functions of bounded variation." In Approximation of Free-Discontinuity Problems, 7–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0097346.

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Convertito, Gregory, and David Cruz-Uribe. "Functions of Bounded Variation." In The Stieltjes Integral, 89–136. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781351242813-3.

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Conference papers on the topic "Functions of bounded deformation"

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Papetti, Daniele M., Vasco Coelho, Daniel A. Ashlock, Paolo Cazzaniga, Simone Spolaor, Daniela Besozzi, and Marco S. Nobile. "Local Bubble Dilation Functions: Hypersphere-bounded Landscape Deformations Simplify Global Optimization." In 2022 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB). IEEE, 2022. http://dx.doi.org/10.1109/cibcb55180.2022.9863041.

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Laura, Patricio A. A. "Solution of Dynamic Problems of Structural Elements Using Simple Polynomial Approximations." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0314.

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Abstract A survey of studies dealing with vibrating structural elements using simple polynomial approximations in connection with Rayleigh-Ritz or Galerkin-type methods is presented. The classical use of polynomials when solving dynamic problems of deformable bodies consists of constructing a set of coordinate functions in such a way that they satisfy at least the essential boundary conditions and that they represent “reasonably well” the deformation field of the structural element under study. An alternative and more rational procedure has been developed and used in recent years whereby orthogonal polynomials are used. A “base function” is constructed and then one generates a set of orthogonal polynomials using the Gram-Schmidt or equivalent procedure. The present paper presents comparisons of numerical results in the case of different types of vibrating structural elements Special emphasis is placed on Rayleigh’s optimization procedure which consists of taking one of the exponents of the polynomial coordinate functions as an optimization parameter “γ”. Since the calculated eigenvalues constitute upper bounds, by minimizing them with respect to “γ” one is able to optimize the eigenvalues.
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Jacobson, Alec, Ilya Baran, Jovan Popović, and Olga Sorkine. "Bounded biharmonic weights for real-time deformation." In ACM SIGGRAPH 2011 papers. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1964921.1964973.

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Varol, Durdane, Melike Aydoğan, and Yaşar Polatoğlu. "Bounded harmonic mappings related to starlike functions." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882553.

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Singh, Akhilesh Kumar. "Functions of bounded variation on effect algebras." In ADVANCEMENT IN MATHEMATICAL SCIENCES: Proceedings of the 2nd International Conference on Recent Advances in Mathematical Sciences and its Applications (RAMSA-2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5008701.

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Yaghoubi, Shakiba, Keyvan Majd, Georgios Fainekos, Tomoya Yamaguchi, Danil Prokhorov, and Bardh Hoxha. "Risk-bounded Control using Stochastic Barrier Functions." In 2021 American Control Conference (ACC). IEEE, 2021. http://dx.doi.org/10.23919/acc50511.2021.9483118.

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Sinha, Shriprakash, and Gert J. Ter Horst. "Bounded multivariate surfaces on monovariate internal functions." In 2011 18th IEEE International Conference on Image Processing (ICIP 2011). IEEE, 2011. http://dx.doi.org/10.1109/icip.2011.6115595.

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Mohamed, Norlyda, Aminah Abdul Malek, Nik Haziqah Wan Hamzah, Nur Suziana Suhaini, and Nurul Syahirah Madzuki. "Third Hankel determinant of bounded analytic functions." In THE 4TH INNOVATION AND ANALYTICS CONFERENCE & EXHIBITION (IACE 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5121062.

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Diakonikolas, Ilias, Daniel M. Kane, and Jelani Nelson. "Bounded Independence Fools Degree-2 Threshold Functions." In 2010 IEEE 51st Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2010. http://dx.doi.org/10.1109/focs.2010.8.

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Le Merdy, Christian. "Square functions, bounded analytic semigroups, and applications." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-12.

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Reports on the topic "Functions of bounded deformation"

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Martinsson, Per-Gunnar, Vladimir Rokhlin, and Mark Tygert. On Interpolation and Integration in Finite-Dimensional Spaces of Bounded Functions. Fort Belvoir, VA: Defense Technical Information Center, March 2005. http://dx.doi.org/10.21236/ada458904.

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Stefanski, L. A., R. J. Carroll, and D. Ruppert. Optimally Bounded Score Functions for Generalized Linear Models with Applications to Logistic Regression. Fort Belvoir, VA: Defense Technical Information Center, April 1985. http://dx.doi.org/10.21236/ada160348.

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Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

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Abstract:
Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.
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