Relevant bibliographies by topics / Functions of bounded variation

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

Academic literature on the topic 'Functions of bounded variation'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Functions of bounded variation"

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., Jyoti. "Functions of Bounded Variation." Journal of Advances and Scholarly Researches in Allied Education 15, no. 4 (June 1, 2018): 250–52. http://dx.doi.org/10.29070/15/57855.

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Castillo, Mariela, Sergio Rivas, María Sanoja, and Iván Zea. "Functions of Boundedκφ-Variation in the Sense of Riesz-Korenblum." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/718507.

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We present the space of functions of boundedκφ-variation in the sense of Riesz-Korenblum, denoted byκBVφ[a,b], which is a combination of the notions of boundedφ-variation in the sense of Riesz and boundedκ-variation in the sense of Korenblum. Moreover, we prove that the space generated by this class of functions is a Banach space with a given norm and we prove that the uniformly bounded composition operator satisfies Matkowski's weak condition.
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Lipcsey, Z., I. M. Esuabana, J. A. Ugboh, and I. O. Isaac. "Integral Representation of Functions of Bounded Variation." Journal of Mathematics 2019 (July 8, 2019): 1–11. http://dx.doi.org/10.1155/2019/1065946.

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Functions of bounded variations form important transition between absolute continuous and singular functions. With Bainov’s introduction of impulsive differential equations having solutions of bounded variation, this class of functions had eventually entered into the theory of differential equations. However, the determination of existence of solutions is still problematic because the solutions of differential equations is usually at least absolute continuous which is disrupted by the solutions of bounded variations. As it is known, if f:[a,bλ]→Rn is of bounded variation then f is the sum of an absolute continuous function fa and a singular function fs where the total variation of fs generates a singular measure τ and fs is absolute continuous with respect to τ. In this paper we prove that a function of bounded variation f has two representations: one is f which was described with an absolute continuous part with respect to the Lebesgue measure λ, while in the other an integral with respect to τ forms the absolute continuous part and t(τ) defines the singular measure. Both representations are obtained as parameter transformation images of an absolute continuous function on total variation domain [a,bν].
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Jerrard, R. L., and H. M. Soner. "Functions of bounded higher variation." Indiana University Mathematics Journal 51, no. 3 (2002): 0. http://dx.doi.org/10.1512/iumj.2002.51.2229.

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AISTLEITNER, CHRISTOPH, FLORIAN PAUSINGER, ANNE MARIE SVANE, and ROBERT F. TICHY. "On functions of bounded variation." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 3 (July 26, 2016): 405–18. http://dx.doi.org/10.1017/s0305004116000633.

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AbstractThe recently introduced concept of ${\mathcal D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from [20] whether every function of bounded Hardy–Krause variation is Borel measurable and has bounded ${\mathcal D}$-variation. Moreover, we show that the space of functions of bounded ${\mathcal D}$-variation can be turned into a commutative Banach algebra.
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Aye, Khaing Khaing, and Peng Yee Lee. "The dual of the space of functions of bounded variation." Mathematica Bohemica 131, no. 1 (2006): 1–9. http://dx.doi.org/10.21136/mb.2006.134078.

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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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Ciemnoczolowski, J., and W. Orlicz. "Composing Functions of Bounded ϕ-Variation." Proceedings of the American Mathematical Society 96, no. 3 (March 1986): 431. http://dx.doi.org/10.2307/2046589.

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Cianchi, Andrea, and Nicola Fusco. "Functions of Bounded Variation�and Rearrangements." Archive for Rational Mechanics and Analysis 165, no. 1 (October 1, 2002): 1–40. http://dx.doi.org/10.1007/s00205-002-0214-9.

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Kolyada, V. I., and M. Lind. "On functions of bounded p-variation." Journal of Mathematical Analysis and Applications 356, no. 2 (August 2009): 582–604. http://dx.doi.org/10.1016/j.jmaa.2009.03.042.

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

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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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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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Rivetti, Sabrina. "Bounded variation solutions of capillarity-type equations." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10161.

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2012/2013
We investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
XXV Ciclo
1985
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Quinn, Eugene P. "On the boundedness character of third-order rational difference equations /." View online ; access limited to URI, 2006. http://0-digitalcommons.uri.edu.helin.uri.edu/dissertations/AAI3225327.

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MENEGATTI, GIORGIO. "Sobolev classes and bounded variation functions on domains of Wiener spaces, and applications." Doctoral thesis, Università degli studi di Ferrara, 2018. http://hdl.handle.net/11392/2488305.

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The main thread of this work is the bounded variation (BV) functions in abstract Wiener spaces (a topic in infinite-dimensional analysis). In the first Part of this work, we present some known results, and we introduce the concepts of Wiener space, of Sobolev space in Wiener spaces, of BV functions (and finite perimeter sets) in Wiener spaces, and of BV functions in convex sets of Wiener spaces (by following the definition in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); moreover, we introduce the trace theory on subsets of a Wiener space (by following P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), and the concept of Mosco convergence. In the second Part we present some new results. In Chapter 6, we consider a subset O of a Wiener space which satisfies a regularity condition, and we prove that a function in W^{1,2}(O) has null trace if and only if it is the limit of a sequence of functions with support contained in O. The main chapter is Chapter 7, which is devoted to the extension in the Wiener spaces setting of a result given in the section 8 of (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): if O is a convex bounded set with regular boundary in R^{d} and L is the Laplace operator in O with null Dirichlet boundary condition, then the normalized resolvent of L is contractive in sense L^1 respect to the gradient. We extend this result to the case of L Ornstein-Uhlenbeck operator in O with null Dirichlet boundary condition, with Gaussian measure (by using the results of Chapter 6): in this case O must satisfy a condition (which we call Gaussian convexity) which takes the place of the convexity in the Gaussian setting. Moreover, we extend the result also to the case of: L Laplace operator in an open convex O with null Neumann boundary condition, with Lebesgue measure; L Ornstein-Uhlenbeck operator in an open convex O with null Neumann boundary condition, with Gaussian measure. In the last part of Chapter 7, we use the preceding results to give an alternative definition of BV function (in the case L^2(O)). In Chapter 8, let X the set of continuous functions on [0,1] with starting point 0, provided with the measure induced by the Brownian motion with starting point 0; it is a Wiener space. For every A subset of X, we define Ξ_A, set of functions in X with image in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) it is proved that, if d ≥ 2 and A is an open subset of R^d which satisfies an uniform outer ball condition then Ξ_A has finite perimeter in the sense of Gaussian measure. We present a weaker condition on A (in dimension sufficiently great) such that Ξ_A has finite perimeter: in particular, A can be the complement of a convex unbounded symmetric cone.
L’argomento principale di questo lavoro sono le funzioni a variazione limitata (BV) in spazi di Wiener astratti (un argomento di analisi infinito-dimensionale). Nella prima parte di questo lavoro, presentiamo alcuni risultati noti, e introduciamo i concetti di spazi di Wiener, di classi di Sobolev su spazi di Wiener, di funzioni BV (e insiemi di perimetro finito) in spazi di Wiener, e di funzioni BV in sottoinsiemi convessi di Spazi di Wiener (seguendo la definizione in V. I. Bogachev, A. Y. Pilipenko, A. V. Shaposhnikov, “Sobolev Functions on Infinite-dimensional domains”, J. Math. Anal. Appl., 2014); inoltre, introduciamo la teoria delle tracce su sottoinsiemi di uno spazio di Wiener( seguendo P. Celada, A. Lunardi, “Traces of Sobolev functions on regular surfaces in infinite dimensions”, J. Funct. Anal., 2014), e il concetto di convergenza di Mosco. Nella seconda parte presentiamo alcuni risultati originali. Nel capitolo 6, consideriamo un sottoinsieme O di uno spazio di Wiener che soddisfa a una condizione di regolarità, e proviamo che una funzione in W^{1,2} (O) ha traccia nulla se e solo se è il limite di una sequenza di funzioni con supporto contenuto in O. Il capitolo principale è il 7, che è dedicato all'estensione all'ambito degli spazi di Wiener di un risultato dato nella sezione 8 di (V. Barbu, M. Röckner, “Stochastic variational inequalities and applications to the total variation flow perturbed by linear multiplicative noise”, Arch. Ration. Mech. Anal., 2013): se O è un insieme convesso limitato con frontiera regolare in R^{d} e L è l'operatore di Laplace in O con condizione al bordo di Dirichlet nulla, allora il risolvente normalizzato di L è contrattivo nel senso L^1 rispetto al gradiente. Estendiamo questo risultato al caso di L operatore di Ornstein-Uhlenbeck in O con condizione al bordo di Dirichlet nulla, con misura gaussiana (usando i risultati del Capitolo 6): in questo caso O deve soddisfare una condizione (che chiamiamo convessità Gaussiana) che nel caso gaussiano prende il posto della convessità. Inoltre, estendiamo il risultato anche al caso di: L operatore di Laplace in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura di Lebesgue; L operatore in un insieme aperto e convesso O con condizione al bordo di Neumann nulla, con misura gaussiana. Nell'ultima parte del Capitolo 7, usiamo i precedenti risultati per dare una definizione alternativa di funzione BV in O (nel caso L^2(O) ). Nel Capitolo 8, sia X l'insieme delle funzioni continue in R^d su [ 0,1 ] con punti di partenza nell’origine fornito della misura indotta dal moto browniano con punto di partenza nell’origine; è uno spazio di Wiener. Per ogni A sottoinsieme di X, definiamo Ξ_A, insieme delle funzioni in X con immagine in A. In (M. Hino, H. Uchida, “Reflecting Ornstein–Uhlenbeck processes on pinned path spaces”, Res. Inst. Math. Sci. (RIMS), 2008) viene dimostrato che, se d ≥ 2 e A è un insieme aperto in R^d che soddisfa una condizione di uniforme palla esterna, allora Ξ_A ha perimetro finito nel senso della misura gaussiana. Presentiamo una condizione più debole su A (in dimensione sufficientemente grande) tale che Ξ_A ha perimetro finito: in particolare, A può essere il complementare di un cono convesso illimitato simmetrico.
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Bellavia, Mark R. "Long term behavior or the positive solutions of the non-autonomous difference equation : x [subscript] n+1 = A [subscript] n [superscript] x [subscript] n-1 [divided by] 1+x [subscript] n, n=0,1,2... /." Link to online version, 2005. https://ritdml.rit.edu/dspace/handle/1850/1117.

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Reinwand, Simon [Verfasser], Jürgen [Gutachter] Appell, Daria [Gutachter] Bugajewska, and Gianluca [Gutachter] Vinti. "Functions of Bounded Variation: Theory, Methods, Applications / Simon Reinwand ; Gutachter: Jürgen Appell, Daria Bugajewska, Gianluca Vinti." Würzburg : Universität Würzburg, 2021. http://d-nb.info/1232647632/34.

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CAMFIELD, CHRISTOPHER SCOTT. "Comparison of BV Norms in Weighted Euclidean Spaces and Metric Measure Spaces." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1211551579.

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Soneji, Parth. "Lower semicontinuity and relaxation in BV of integrals with superlinear growth." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:c7174516-588e-46ae-93dc-56d4a95f1e6f.

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Books on the topic "Functions of bounded variation"

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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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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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Braides, Andrea. Approximation of free-discontinuity problems. Berlin: Springer-Verlag, 1998.

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Dudley, R. M. Differentiability of six operators on nonsmooth functions and p-variation. Berlin: Springer, 1999.

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Cheverry, Christophe. Systèmes de lois de conservation et stabilité BV. [Paris, France]: Société mathématique de France, 1998.

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

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Jerbashian, Armen M., and Joel E. Restrepo. Functions of Omega-Bounded Type. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-49885-5.

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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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Book chapters on the topic "Functions of bounded variation"

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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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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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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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Coclite, Giuseppe Maria. "Functions with Bounded Variation." In Scalar Conservation Laws, 59–72. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-3984-4_5.

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Gordon, Russell. "Functions of generalized bounded variation." In Graduate Studies in Mathematics, 89–105. Providence, Rhode Island: American Mathematical Society, 1994. http://dx.doi.org/10.1090/gsm/004/06.

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Leoni, Giovanni. "Functions of bounded pointwise variation." In Graduate Studies in Mathematics, 39–72. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/105/02.

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Braides, Andrea. "Special functions of bounded variation." In Approximation of Free-Discontinuity Problems, 27–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0097347.

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Conference papers on the topic "Functions of bounded variation"

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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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Surender, Mehak Malhotra, and Monika Arora. "A short note on functions of bounded variation." In PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: (PTLICISIWS-2022). AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0144575.

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Long, Philip M. "On the sample complexity of learning functions with bounded variation." In the eleventh annual conference. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/279943.279970.

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Posner, S. E., and S. R. Kulkarni. "On-line learning of functions of bounded variation under various sampling schemes." In the sixth annual conference. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/168304.168392.

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Murdianingsih, Indah Dwi, Susilo Hariyanto, Titi Udjiani, Yusephus D. Sumanto, and Idha Sihwaningrum. "Properties of bounded variation function of two variables." In THE 8TH INTERNATIONAL CONFERENCE AND WORKSHOP ON BASIC AND APPLIED SCIENCE (ICOWOBAS) 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0104246.

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Dodonov, Nikolay Yu, and Vladimir V. Zhuk. "Uniform approximation of continuous functions of bounded variation by aggregates of summatory type." In 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP). IEEE, 2015. http://dx.doi.org/10.1109/scp.2015.7342146.

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Dimitriu, G., and B. Satco. "Urysohn measure driven integral equations in the space of bounded variation functions and applications." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 8th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’16. Author(s), 2016. http://dx.doi.org/10.1063/1.4964972.

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Zheng, Qian, and Fen Wu. "State Feedback and Output Feedback Control of Polynomial Nonlinear Systems Using Fractional Lyapunov Functions." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42147.

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In this paper, we will study the state feedback control problem of polynomial nonlinear systems using fractional Lyapunov functions. By adding constraints to bound the variation rate of each state, the general difficulty of calculating derivative of nonquadratic Lyapunov function is effectively overcome. As a result, the state feedback conditions are simplified as a set of Linear Matrix Inequalities (LMIs) with polynomial entries. Computationally tractable solution is obtained by Sum-of-Squares (SOS) decomposition. And it turns out that both of the Lyapunov matrix and the state feedback gain are state dependent fractional matrix functions, where the numerator as well as the denominator can be polynomials with flexible forms and higher nonlinearities involved in. Same idea is extended to a class of output dependent nonlinear systems and the stabilizing output feedback controller is specified as polynomial of output. Synthesis conditions are similarly derived as using constant Lyapunov function except that all entries in LMIs are polynomials of output with derivative of output involved in. By bounding the variation rate of output and gridding on the bounded interval, the LMIs are solvable by SOS decomposition. Finally, two examples are used to materialize the design scheme and clarify the various choices on state boundaries.
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Lee, Dong Hwan. "Local stability and stabilization of discrete-time Takagi-Sugeno fuzzy systems using bounded variation rates of the membership functions." In 2013 IEEE Symposium on Computational Intelligence in Control and Automation (CICA). IEEE, 2013. http://dx.doi.org/10.1109/cica.2013.6611665.

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Wibowo, Supriyadi, V. Y. Kurniawan, and Siswanto. "The relation between Fα – absolutely continuous of order α ∈ (0, 1) and function of bounded variation." In THE 4TH INDOMS INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATION (IICMA 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0019249.

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Reports on the topic "Functions of bounded variation"

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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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Manski, Charles, and John Pepper. How Do Right-To-Carry Laws Affect Crime Rates? Coping With Ambiguity Using Bounded-Variation Assumptions. Cambridge, MA: National Bureau of Economic Research, November 2015. http://dx.doi.org/10.3386/w21701.

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Hanslow, Kevin. A General Welfare Decomposition for CGE Models. GTAP Technical Paper, March 2001. http://dx.doi.org/10.21642/gtap.tp19.

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Huff and Hertel (2001) derive a welfare decomposition for the equivalent variation in the GTAP model. The derivation appears to be very specific to GTAP. Nevertheless, it contains nearly all the ingredients required for performing welfare decomposition for any CGE model. In this paper, the approach of Huff and Hertel (2001) is generalised to derive a welfare decomposition that can be applied to most, if not all, CGE models. General production and utility functions are accommodated, as are foreign income flows. A brief guide to coding the proposed welfare decomposition in GEMPACK is also provided. The decomposition is applied to decomposing the equivalent variation in GTAP.
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Cameron, Arthur, Shimshon Ben-Yehoshua, and Rebecca Hernandez. Design and Function of Modified Atmosphere Packaging Systems for Fresh Produce: a Unified Approach for Optimizing Oxygen, Carbon Dioxide and Relative Humidity. United States Department of Agriculture, January 1996. http://dx.doi.org/10.32747/1996.7613019.bard.

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Oxygen uptake, CO2 production and respiratory quotient (RQ) of strawberry, raspberry and cherry were measured as functions of temperature and oxygen level. The effect of cultivar was studied in strawberry ('Honey' and 'Allstar'). The effect of harvest date was studied for raspberry. The lower O2 limit increased markedly with incraqsing temperature for all fruits studied. Red bell pepper O2 uptake was measured as a function of O2 at 20o C. Lowering the inpackage humidity using NaCl reduced decay of bell pepper sealed in low-density polyethylene packages when stored at 8o C. Analyses of a model developed for MA-packaged red bell pepper fruit demonstrated that when RQ was near one and when CO2 exceeded O2 permeability, transient CO2 levels increased to a maximum before dropping to steady-state levels. An isothermal model of O2, CO2 and water vapor exchange in MA packages was developed for red bell pepper and tested empirically. A comprehensive model was developed for small fruits that also incorporated water vapor and the effects of changing temperature. Variation in package O2 levels was measured and modeled as a function of variation in respiration and film permeability.
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Jander, Georg, and Daniel Chamovitz. Investigation of growth regulation by maize benzoxazinoid breakdown products. United States Department of Agriculture, January 2015. http://dx.doi.org/10.32747/2015.7600031.bard.

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Introduction Previous research had suggested that benzoxazinoids, a class of defensive metabolites found in maize, wheat, rye, and wild barley, are not only direct insect deterrents, but also influence other areas of plant metabolism. In particular, the benzoxazinoid 2,4-dihydroxy-7-methoxy-2H-1,4-benzoxa- zin-3(4H)- one (DIMBOA) was implicated in: (i) altering plant growth by interfering with auxin signaling, and (ii) leading to the induction of gene expression changes and secondary plant defense responses. The overall goal of this proposal was to identify mechanisms by which benzoxazinoids influence other aspects of plant growth and defense. Specifically, the following hypotheses were proposed to be tested as part of an approved BARD proposal: Benzoxazinoid breakdown products directly interfere with auxin perception Global changes in maize and barley gene expression are induced by benzoxazinoid activation. There is natural variation in the maize photomorphogenic response to benzoxazinoids. Although the initial proposal included experiments with both maize and barley, there were some technical difficulties with the proposed transgenic barley experiments and most of the experimental results were generated with maize. Summary of major findings Previous research by other labs, involving both maize and other plant species, had suggested that DIMBOA alters plant growth by interfering with auxin signaling. However, experiments conducted in both the Chamovitz and the Jander labs using Arabidopsis and maize, respectively, were unable to confirm previously published reports of exogenously added DIMBOA effects on auxin signaling. Nevertheless, analysis of bx1 and bx2 maize mutant lines, which have almost no detectable benzoxazinoids, showed altered responses to blue light signaling. Transcriptomic analysis of maize mutant lines, variation in inbred lines, and responses to exogenously added DIMBOA showed alteration in the transcription of a blue light receptor, which is required for plant growth responses. This finding provides a novel mechanistic explanation of the trade-off between growth and defense that is often observed in plants. Experiments by the Jander lab and others had demonstrated that DIMBOA not only has direct toxicity against insect pests and microbial pathogens, but also induces the formation of callose in both maize and wheat. In the current project, non-targeted metabolomic assays of wildtype maize and mutants with defects in benzoxazinoid biosynthesis were used to identify unrelated metabolites that are regulated in a benzoxazinoid-dependent manner. Further investigation identified a subset of these DIMBOA-responsive compounds as catechol, as well as its glycosylated and acetylated derivatives. Analysis of co-expression data identified indole-3-glycerol phosphate synthase (IGPS) as a possible regulator of benzoxazinoid biosynthesis in maize. In the current project, enzymatic activity of three predicted maize IGPS genes was confirmed by heterologous expression. Transposon knockout mutations confirmed the function of the maize genes in benzoxazinoid biosynthesis. Sub-cellular localization studies showed that the three maize IGPS proteins are co-localized in the plastids, together with BX1 and BX2, two previously known enzymes of the benzoxazinoid biosynthesis pathway. Implications Benzoxazinoids are among the most abundant and effective defensive metabolites in maize, wheat, and rye. Although there is considerable with-in species variation in benzoxazinoid content, very little is known about the regulation of this variation and the specific effects on plant growth and defense. The results of this research provide further insight into the complex functions of maize benzoxazinoids, which are not only toxic to pests and pathogens, but also regulate plant growth and other defense responses. Knowledge gained through the current project will make it possible to engineer benzoxazinoid biosynthesis in a more targeted manner to produce pest-tolerant crops without negative effects on growth and yield.
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Hertel, Thomas, David Hummels, Maros Ivanic, and Roman Keeney. How Confident Can We Be in CGE-Based Assessments of Free Trade Agreements? GTAP Working Paper, June 2003. http://dx.doi.org/10.21642/gtap.wp26.

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With the proliferation of Free Trade Agreements (FTAs) over the past decade, demand for quantitative analysis of their likely impacts has surged. The main quantitative tool for performing such analysis is Computable General Equilibrium (CGE) modeling. Yet these models have been widely criticized for performing poorly (Kehoe, 2002) and having weak econometric foundations (McKitrick, 1998; Jorgenson, 1984). FTA results have been shown to be particularly sensitive to the trade elasticities, with small trade elasticities generating large terms of trade effects and relatively modest efficiency gains, whereas large trade elasticities lead to the opposite result. Critics are understandably wary of results being determined largely by the authors’ choice of trade elasticities. Where do these trade elasticities come from? CGE modelers typically draw these elasticities from econometric work that uses time series price variation to identify an elasticity of substitution between domestic goods and composite imports (Alaouze, 1977; Alaouze, et al., 1977; Stern et al., 1976; Gallaway, McDaniel and Rivera, 2003). This approach has three problems: the use of point estimates as “truth”, the magnitude of the point estimates, and estimating the relevant elasticity. First, modelers take point estimates drawn from the econometric literature, while ignoring the precision of these estimates. As we will make clear below, the confidence one has in various CGE conclusions depends critically on the size of the confidence interval around parameter estimates. Standard “robustness checks” such as systematically raising or lowering the substitution parameters does not properly address this problem because it ignores information about which parameters we know with some precision and which we do not. A second problem with most existing studies derives from the use of import price series to identify home vs. foreign substitution, for example, tends to systematically understate the true elasticity. This is because these estimates take price variation as exogenous when estimating the import demand functions, and ignore quality variation. When quality is high, import demand and prices will be jointly high. This biases estimated elasticities toward zero. A related point is that the fixed-weight import price series used by most authors are theoretically inappropriate for estimating the elasticities of interest. CGE modelers generally examine a nested utility structure, with domestic production substitution for a CES composite import bundle. The appropriate price series is then the corresponding CES price index among foreign varieties. Constructing such an index requires knowledge of the elasticity of substitution among foreign varieties (see below). By using a fixed-weight import price series, previous estimates place too much weight on high foreign prices, and too small a weight on low foreign prices. In other words, they overstate the degree of price variation that exists, relative to a CES price index. Reconciling small trade volume movements with large import price series movements requires a small elasticity of substitution. This problem, and that of unmeasured quality variation, helps explain why typical estimated elasticities are very small. The third problem with the existing literature is that estimates taken from other researchers’ studies typically employ different levels of aggregation, and exploit different sources of price variation, from what policy modelers have in mind. Employment of elasticities in experiments ill-matched to their original estimation can be problematic. For example, estimates may be calculated at a higher or lower level of aggregation than the level of analysis than the modeler wants to examine. Estimating substitutability across sources for paddy rice gives one a quite different answer than estimates that look at agriculture as a whole. When analyzing Free Trade Agreements, the principle policy experiment is a change in relative prices among foreign suppliers caused by lowering tariffs within the FTA. Understanding the substitution this will induce across those suppliers is critical to gauging the FTA’s real effects. Using home v. foreign elasticities rather than elasticities of substitution among imports supplied from different countries may be quite misleading. Moreover, these “sourcing” elasticities are critical for constructing composite import price series to appropriate estimate home v. foreign substitutability. In summary, the history of estimating the substitution elasticities governing trade flows in CGE models has been checkered at best. Clearly there is a need for improved econometric estimation of these trade elasticities that is well-integrated into the CGE modeling framework. This paper provides such estimation and integration, and has several significant merits. First, we choose our experiment carefully. Our CGE analysis focuses on the prospective Free Trade Agreement of the Americas (FTAA) currently under negotiation. This is one of the most important FTAs currently “in play” in international negotiations. It also fits nicely with the source data used to estimate the trade elasticities, which is largely based on imports into North and South America. Our assessment is done in a perfectly competitive, comparative static setting in order to emphasize the role of the trade elasticities in determining the conventional gains/losses from such an FTA. This type of model is still widely used by government agencies for the evaluation of such agreements. Extensions to incorporate imperfect competition are straightforward, but involve the introduction of additional parameters (markups, extent of unexploited scale economies) as well as structural assumptions (entry/no-entry, nature of inter-firm rivalry) that introduce further uncertainty. Since our focus is on the effects of a PTA we estimate elasticities of substitution across multiple foreign supply sources. We do not use cross-exporter variation in prices or tariffs alone. Exporter price series exhibit a high degree of multicolinearity, and in any case, would be subject to unmeasured quality variation as described previously. Similarly, tariff variation by itself is typically unhelpful because by their very nature, Most Favored Nation (MFN) tariffs are non-discriminatory in nature, affecting all suppliers in the same way. Tariff preferences, where they exist, are often difficult to measure – sometimes being confounded by quantitative barriers, restrictive rules of origin, and other restrictions. Instead we employ a unique methodology and data set drawing on not only tariffs, but also bilateral transportation costs for goods traded internationally (Hummels, 1999). Transportation costs vary much more widely than do tariffs, allowing much more precise estimation of the trade elasticities that are central to CGE analysis of FTAs. We have highly disaggregated commodity trade flow data, and are therefore able to provide estimates that precisely match the commodity aggregation scheme employed in the subsequent CGE model. We follow the GTAP Version 5.0 aggregation scheme which includes 42 merchandise trade commodities covering food products, natural resources and manufactured goods. With the exception of two primary commodities that are not traded, we are able to estimate trade elasticities for all merchandise commodities that are significantly different form zero at the 95% confidence level. Rather than producing point estimates of the resulting welfare, export and employment effects, we report confidence intervals instead. These are based on repeated solution of the model, drawing from a distribution of trade elasticity estimates constructed based on the econometrically estimated standard errors. There is now a long history of CGE studies based on SSA: Systematic Sensitivity Analysis (Harrison and Vinod, 1992; Wigle, 1991; Pagon and Shannon, 1987) Ho
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Collins, Clarence O., and Tyler J. Hesser. altWIZ : A System for Satellite Radar Altimeter Evaluation of Modeled Wave Heights. Engineer Research and Development Center (U.S.), February 2021. http://dx.doi.org/10.21079/11681/39699.

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This Coastal and Hydraulics Engineering Technical Note (CHETN) describes the design and implementation of a wave model evaluation system, altWIZ, which uses wave height observations from operational satellite radar altimeters. The altWIZ system utilizes two recently released altimeter databases: Ribal and Young (2019) and European Space Agency Sea State Climate Change Initiative v.1.1 level 2 (Dodet et al. 2020). The system facilitates model evaluation against 1 Hz1 altimeter data or a product created by averaging altimeter data in space and time around model grid points. The system allows, for the first time, quantitative analysis of spatial model errors within the U.S. Army Corps of Engineers (USACE) Wave Information Study (WIS) 30+ year hindcast for coastal United States. The system is demonstrated on the WIS 2017 Atlantic hindcast, using a 1/2° basin scale grid and a 1/4° regional grid of the East Coast. Consistent spatial patterns of increased bias and root-mean-square-error are exposed. Seasonal strengthening and weakening of these spatial patterns are found, related to the seasonal variation of wave energy. Some model errors correspond to areas known for high currents, and thus wave-current interaction. In conjunction with the model comparison, additional functions for pairing altimeter measurements with buoy data and storm tracks have been built. Appendices give information on the code access (Appendix I), organization and files (Appendix II), example usage (Appendix III), and demonstrating options (Appendix IV).
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Echevarria-Doyle, Waleska, S. McKay, and Susan Bailey. Sensitivity of sediment transport analyses in dam removal applications. Engineer Research and Development Center (U.S.), September 2023. http://dx.doi.org/10.21079/11681/47595.

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Dam removal has become a widespread river management practice in the US for a variety of goals including ecosystem restoration, removing aging infrastructure, flood risk management, and recreation. The ability to forecast the sediment impacts of dam removal is critical to evaluating different management alternatives that can minimize adverse consequences for ecosystems and human communities. Tullos et al. (2016) identified seven Common Management Concerns (CMCs) associated with dam removal. Four of these CMCs; degree and rate of reservoir sediment erosion, excessive channel incision upstream of reservoirs, downstream sediment aggradation, and elevated downstream turbidity are associated with stored sediment release and changing fluvial hydraulics. There are a range of existing qualitative and quantitative tools developed to infer or quantify geomorphic implications of disturbances like these in river environments (McKay et al. 2019). This study investigated how a one-dimensional (1D) sediment transport model can inform these four CMCs, develop an approach for assessing sediment transport model sensitivity in the context of the Simkins Dam removal, and use sensitivity analyses to identify key uncertainties, which can inform data collection and model building for other dam removal projects. For the selected case study, model outputs including the mean effective invert change (MEIC) and eroded sediment volume from reservoir were highly sensitive to the variation of the reservoir sediment gradation and sorting method selection. These model outputs also showed some sensitivity to the selected transport functions. Erosion method sensitivity using the channel evolution method will vary depending on side slope and channel parameter selection.
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Neipert, Elizabeth, Todd Steissberg, and Charles Theiling. Spatial screening for environmental pool management opportunities. Engineer Research and Development Center (U.S.), October 2023. http://dx.doi.org/10.21079/11681/47719.

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US Army Corps of Engineers (USACE) reservoir projects significantly alter river ecosystem structure and function. Each project adheres to a defined set of operating rules to achieve primary objectives, which typically include flood risk management, hydropower, or navigation along with ancillary objectives for drinking water/irrigation, recreation, and natural resources management. Environmental flows (E-Flows) planning under the Sustainable Rivers Program has demonstrated new opportunities for environmental pool management (EPM; Theiling et al. 2021a, 2021b) that have no negative impact on other reservoir functions. In some locations, water level drivers can be managed to improve ecological outcomes, like wetlands, waterbirds, reptiles, and water quality, by altering the magnitude, timing, frequency, and duration of pool level changes that affect riparian and shoreline plant communities. Reservoirs with large delta areas may provide particularly important wetland or riparian habitat management along avian migratory pathways or in wildlife conservation regions (Johnson 2002). These large deltas can be identified and characterized using available satellite imagery, which along with water level habitat drivers available in hydrology databases, can be used to identify USACE reservoirs with good potential for EPM. A spatial analysis of USACE reservoirs capable to support EPM can be developed utilizing estimates of water occurrence, transition, and seasonality as well as surface elevation data derived from satellite imagery to assess geomorphology drivers. USACE water management records can be used to assess wetland drivers. Nationwide screening will be broken down into ecoregions to establish the anticipated geographic range of variation for wetland and riparian habitat drivers. Southwestern US reservoirs, for example, will have much different hydrology and fauna than Midwest and Eastern US reservoirs.
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