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Journal articles on the topic 'Smooth extension'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Fabrèges, Benoit, Loïc Gouarin, and Bertrand Maury. "A smooth extension method." Comptes Rendus Mathematique 351, no. 9-10 (2013): 361–66. http://dx.doi.org/10.1016/j.crma.2013.05.011.

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2

Pigola, Stefano, and Giona Veronelli. "The smooth Riemannian extension problem." ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE 20, no. 4 (2020): 1507–51. http://dx.doi.org/10.2422/2036-2145.201802_013.

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3

Langenbruch, Michael. "Analytic Extension of Smooth Functions." Results in Mathematics 36, no. 3-4 (1999): 281–96. http://dx.doi.org/10.1007/bf03322117.

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4

Agress, Daniel J., and Patrick Q. Guidotti. "The Smooth Extension Embedding Method." SIAM Journal on Scientific Computing 43, no. 1 (2021): A446—A471. http://dx.doi.org/10.1137/19m1300844.

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5

Zhang, Zhihua. "Approximation of Bivariate Functions via Smooth Extensions." Scientific World Journal 2014 (2014): 1–16. http://dx.doi.org/10.1155/2014/102062.

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For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fouri

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6

Kim, Hoisub, Seungtaik Oh, and Jin-whan Yim. "Smooth surface extension with curvature bound." Computer Aided Geometric Design 22, no. 1 (2005): 27–43. http://dx.doi.org/10.1016/j.cagd.2004.08.003.

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7

Ide, Manabu. "Every Curve of Genus not Greater Than Eight Lies on a K3 Surface." Nagoya Mathematical Journal 190 (2008): 183–97. http://dx.doi.org/10.1017/s0027763000009600.

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Let C be a smooth irreducible complete curve of genus g ≥ 2 over an algebraically closed field of characteristic 0. An ample K3 extension of C is a K3 surface with at worst rational double points which contains C in the smooth locus as an ample divisor.In this paper, we prove that all smooth curve of genera. 2 ≤ g ≤ 8 have ample K3 extensions. We use Bertini type lemmas and double coverings to construct ample K3 extensions.

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8

Bunk, Severin, Lukas Müller, and Richard J. Szabo. "Smooth 2-Group Extensions and Symmetries of Bundle Gerbes." Communications in Mathematical Physics 384, no. 3 (2021): 1829–911. http://dx.doi.org/10.1007/s00220-021-04099-7.

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AbstractWe study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of

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9

Fonf, V. P., and P. Wojtaszczyk. "Extension of smooth subspaces in Lindenstrauss spaces." Studia Mathematica 222, no. 2 (2014): 157–63. http://dx.doi.org/10.4064/sm222-2-3.

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10

Ciesielski, Krzysztof Chris. "Smooth extension theorems for one variable maps." Journal of Mathematical Analysis and Applications 479, no. 2 (2019): 1893–905. http://dx.doi.org/10.1016/j.jmaa.2019.07.030.

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11

Li, Meng Jian, and Wei Dong Geng. "The Extension of Geodesics." Applied Mechanics and Materials 333-335 (July 2013): 95–104. http://dx.doi.org/10.4028/www.scientific.net/amm.333-335.95.

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We introduced an extension of traditional geodesic. Local neighbourhood of smooth curve on manifold shows good propositions which make it possible to construct a geodesic mapping from the neighbourhood to a rectangular district of UV-plane. Length of subsurface extended from smooth curve is defined according to the parameterization induced by geodesic mapping. And extended geodesic is the curve with minimal length of subsurface it extends. We also proposed a constrained mass-spring based approach to solve extended geodesic on discrete mesh. Experimental result shows that it is a high precision

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12

Kunde, Philipp. "Smooth zero-entropy diffeomorphisms with ergodic derivative extension." Commentarii Mathematici Helvetici 95, no. 1 (2020): 1–25. http://dx.doi.org/10.4171/cmh/478.

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13

Blanc, Jérémy, Jean-Philippe Furter, and Pierre-Marie Poloni. "Extension of automorphisms of rational smooth affine curves." Mathematical Research Letters 23, no. 1 (2016): 43–66. http://dx.doi.org/10.4310/mrl.2016.v23.n1.a3.

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14

Zizler, Vaclav E. "Smooth extension of norms and complementability of subspaces." Archiv der Mathematik 53, no. 6 (1989): 585–89. http://dx.doi.org/10.1007/bf01199818.

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15

Frerick, Leonhard, Enrique Jordá, and Jochen Wengenroth. "Tame linear extension operators for smooth Whitney functions." Journal of Functional Analysis 261, no. 3 (2011): 591–603. http://dx.doi.org/10.1016/j.jfa.2011.04.008.

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16

Xu, Jin. "Smooth B-Spline Curves Extension with Ordered Points Constraint." Advanced Materials Research 311-313 (August 2011): 1439–45. http://dx.doi.org/10.4028/www.scientific.net/amr.311-313.1439.

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An algorithm for extending B-spline curves with a sequence of ordered points constraint is presented based on the curve unclamping algorithm. The ordered points are divided into two categories: interpolation points and approximation points. The number of interpolation points increases gradually during the curve extension process. The most important feature of this algorithm is the ability to optimize the knots of the extended curve segment according to the ordered points. Thus, with minimum number of interpolation points, the maximum deviation of the extended curve segment from the ordered poi

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17

Atkin, C. J. "Extension of smooth functions in infinite dimensions II: manifolds." Studia Mathematica 150, no. 3 (2002): 215–41. http://dx.doi.org/10.4064/sm150-3-2.

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18

Chui, Charles K., and H. N. Mhaskar. "Smooth function extension based on high dimensional unstructured data." Mathematics of Computation 83, no. 290 (2014): 2865–91. http://dx.doi.org/10.1090/s0025-5718-2014-02819-6.

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19

Aĭrapetyan, R. A. "EXTENSION OF CR-FUNCTIONS FROM PIECEWISE SMOOTH CR-MANIFOLDS." Mathematics of the USSR-Sbornik 62, no. 1 (1989): 111–20. http://dx.doi.org/10.1070/sm1989v062n01abeh003229.

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20

Chui, Charles K., and H. N. Mhaskar. "MRA contextual-recovery extension of smooth functions on manifolds." Applied and Computational Harmonic Analysis 28, no. 1 (2010): 104–13. http://dx.doi.org/10.1016/j.acha.2009.04.004.

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21

Morton, Jeremy, and Larry Silverberg. "Fourier series of half-range functions by smooth extension." Applied Mathematical Modelling 33, no. 2 (2009): 812–21. http://dx.doi.org/10.1016/j.apm.2007.12.009.

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22

Zobin, Nahum. "Extension of smooth functions from finitely connected planar domains." Journal of Geometric Analysis 9, no. 3 (1999): 491–511. http://dx.doi.org/10.1007/bf02921985.

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23

DAUMAIL, LAURENT, and PATRICK FLORCHINGER. "A CONSTRUCTIVE EXTENSION OF ARTSTEIN'S THEOREM TO THE STOCHASTIC CONTEXT." Stochastics and Dynamics 02, no. 02 (2002): 251–63. http://dx.doi.org/10.1142/s0219493702000418.

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The aim of this paper is to extend Artstein's theorem on the stabilization of affine in the control nonlinear deterministic systems to nonlinear stochastic differential systems when both the drift and the diffusion terms are affine in the control. We prove that the existence of a smooth control Lyapunov function implies smooth stabilizability.

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24

SMOLYANOV, O. G., and H. v. WEIZSÄCKER. "SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 02, no. 01 (1999): 51–78. http://dx.doi.org/10.1142/s0219025799000047.

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We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differentiable measure the analog of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein–Uhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite straight forward and does not u

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25

Kori, Tosiaki, and Yuto Imai. "Lie algebra extensions of current algebras on S3." International Journal of Geometric Methods in Modern Physics 12, no. 09 (2015): 1550087. http://dx.doi.org/10.1142/s0219887815500875.

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An affine Kac–Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac–Moody algebras give it for two-dimensional conformal field theory.

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26

Fry, R. "Extensions of uniformly smooth norms on Banach spaces." Bulletin of the Australian Mathematical Society 65, no. 3 (2002): 423–30. http://dx.doi.org/10.1017/s0004972700020463.

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We give a characterisation for the extension of uniformly smooth norms from subspaces Y of superreflexive spaces X to uniformly smooth norms on all of X. This characterisation is applied to obtain results in various contexts.

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27

DELLA SALA, GIUSEPPE, and ALBERTO SARACCO. "SEMIGLOBAL EXTENSION OF MAXIMALLY COMPLEX SUBMANIFOLDS." Bulletin of the Australian Mathematical Society 84, no. 3 (2011): 458–74. http://dx.doi.org/10.1017/s0004972711002498.

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AbstractLet A be a domain of the boundary of a (weakly) pseudoconvex domain Ω of ℂn and M a smooth, closed, maximally complex submanifold of A. We find a subdomain E of ℂn, depending only on Ω and A, and a complex variety W⊂E such that bW=M in E. Moreover, a generalization to analytic sets of depth at least 4 is given.

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28

Karabegov, Alexander. "Star Products with Separation of Variables Admitting a Smooth Extension." Letters in Mathematical Physics 101, no. 2 (2012): 125–42. http://dx.doi.org/10.1007/s11005-012-0561-x.

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29

Berraho, Mourad. "Extension of Bochnak–Siciak theorem for smooth Denjoy–Carleman functions." ANNALI DELL'UNIVERSITA' DI FERRARA 67, no. 1 (2021): 33–42. http://dx.doi.org/10.1007/s11565-021-00359-5.

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30

Jiménez-Sevilla, M., and L. Sánchez-González. "On some problems on smooth approximation and smooth extension of Lipschitz functions on Banach–Finsler manifolds." Nonlinear Analysis: Theory, Methods & Applications 74, no. 11 (2011): 3487–500. http://dx.doi.org/10.1016/j.na.2011.03.004.

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31

Baracco, Luca, and Giuseppe Zampieri. "CR Extension from Manifolds of Higher Type." Canadian Journal of Mathematics 60, no. 6 (2008): 1219–39. http://dx.doi.org/10.4153/cjm-2008-052-x.

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AbstractThis paper deals with the extension of CR functions fromamanifold M ⊂ ℂn into directions produced by higher order commutators of holomorphic and antiholomorphic vector fields. It uses the theory of complex “sectors” attached to real submanifolds introduced in recent joint work of the authors with D. Zaitsev. In addition, it develops a new technique of approximation of sectors by smooth discs.

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32

Gardner, Carl L., and Christian Ringhofer. "The Quantum Hydrodynamic Smooth Effective Potential." VLSI Design 6, no. 1-4 (1998): 17–20. http://dx.doi.org/10.1155/1998/89074.

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An extension of the quantum hydrodynamic (QHD) model is discussed which is valid for classical potentials with discontinuities. The effective stress tensor for the QHD equations cancels the leading singularity in the classical potential at a barrier and leaves a residual smooth effective potential with a lower potential height in the barrier region. The smoothing makes the barrier partially transparent to the particle flow and provides the mechanism for particle tunneling in the QHD model.

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33

Schulze, Felix, and Brian White. "A local regularity theorem for mean curvature flow with triple edges." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 758 (2020): 281–305. http://dx.doi.org/10.1515/crelle-2017-0044.

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AbstractMean curvature flow of clusters of n-dimensional surfaces in {\mathbb{R}^{n+k}} that meet in triples at equal angles along smooth edges and higher order junctions on lower-dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-tim

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34

Stein, David B., Robert D. Guy, and Becca Thomases. "Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains." Journal of Computational Physics 335 (April 2017): 155–78. http://dx.doi.org/10.1016/j.jcp.2017.01.010.

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35

Wang*, Ruidong. "On the extension problem between separable smooth Banach spaces with RNP." Quaestiones Mathematicae 34, no. 1 (2011): 67–73. http://dx.doi.org/10.2989/16073606.2011.570295.

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36

Canavati, José A. "On the extension of smooth functions by means of orthogonal polynomials." Numerical Functional Analysis and Optimization 10, no. 3-4 (1989): 265–74. http://dx.doi.org/10.1080/01630568908816303.

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37

Schmolck, Alexander, and Richard Everson. "Smooth relevance vector machine: a smoothness prior extension of the RVM." Machine Learning 68, no. 2 (2007): 107–35. http://dx.doi.org/10.1007/s10994-007-5012-z.

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38

Frerick, Leonhard, Enrique Jordá, and Jochen Wengenroth. "Extension operators for smooth functions on compact subsets of the reals." Mathematische Zeitschrift 295, no. 3-4 (2019): 1537–52. http://dx.doi.org/10.1007/s00209-019-02388-5.

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39

Vähäkangas, Antti V. "On Regularity and Extension of Green’s Operator on Bounded Smooth Domains." Potential Analysis 37, no. 1 (2011): 57–77. http://dx.doi.org/10.1007/s11118-011-9245-x.

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40

ZAYED, E. M. E. "AN INVERSE PROBLEM FOR A GENERAL DOUBLY-CONNECTED BOUNDED DOMAIN: AN EXTENSION TO HIGHER DIMENSIONS." Tamkang Journal of Mathematics 28, no. 4 (1997): 277–95. http://dx.doi.org/10.5556/j.tkjm.28.1997.4305.

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The spectral function $\Theta(t)=\sum_{\nu=1}^\infty \exp(-t\lambda_\nu)$, where $\{\lambda_\nu\}_{\nu=1}^\infty$ are the eigenvalues of the negative Laplacian $-\nabla^2=-\sum_{i=1}^3(\frac{\partial}{\partial x_i})^2$ in the $(x^1, x^2, x^3)$-space, is studied for an arbitrary doubly connected bounded domain $\Omega$ in $R^3$ together with its smooth inner bounding surface $\tilde S_1$ and its smooth outer bounding surface $\tilde S_2$, where piecewise smooth impedance boundary conditions on the parts $S_1^*$, $S_2^*$ of $\tilde S_1$ and $S_3^*$, $S_4^*$ of $\tilde S_2$ are considered, such t

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41

Reeger, J. A., B. Fornberg, and M. L. Watts. "Numerical quadrature over smooth, closed surfaces." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2194 (2016): 20160401. http://dx.doi.org/10.1098/rspa.2016.0401.

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The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable. An efficient method for computing surface integrals on the sphere is detailed in the literature (Reeger & Fornberg 2016 Stud. Appl. Math. 137 , 174–188. ( doi:10.1111/sapm.12106 )). The method uses local radial basis function interpolation to reduce computational complexit

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42

Lu, Yiyu, Peng Yue, and Sibei Wei. "Extension of Calculus Operations in Cartesian Tensor Analysis." Mathematics 8, no. 4 (2020): 561. http://dx.doi.org/10.3390/math8040561.

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In this paper, we derive and propose basic differential operations and generalized Green’s integral theorems applicable to multidimensional spaces based on Cartesian tensor analysis to solve some nonlinear problems in smooth spaces in the necessary dimensions. In practical applications, the theorem can be applied to numerical analysis in the conservation law, effectively reducing the dimensions of high-dimensional problems and reducing the computational difficulty, which can be effectively used in the solution of complex dimensional mechanical problems.

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43

Atkin, C. J. "Extension of smooth functions in infinite dimensions, I: unions of convex sets." Studia Mathematica 146, no. 3 (2001): 201–26. http://dx.doi.org/10.4064/sm146-3-1.

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44

FU, Yunteng, Shukei SUGITA, Eijiro MAEDA, and Takeo MATSUMOTO. "Effects of forcible extension of contracted arteries on their smooth muscle contractility." Proceedings of the Bioengineering Conference Annual Meeting of BED/JSME 2017.29 (2017): 1C21. http://dx.doi.org/10.1299/jsmebio.2017.29.1c21.

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45

Saito, Takeshi. "Log smooth extension of a family of curves and semi-stable reduction." Journal of Algebraic Geometry 13, no. 2 (2004): 287–321. http://dx.doi.org/10.1090/s1056-3911-03-00338-2.

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46

Vityaev, Andrei E. "On extension of CR functions from piecewise smooth manifolds into a wedge." Illinois Journal of Mathematics 41, no. 2 (1997): 193–213. http://dx.doi.org/10.1215/ijm/1256060831.

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47

Drozdov, Alexander N., and Shigeo Hayashi. "An Extension of the Kramers Rate Theory to Cusped and Smooth Potentials." Journal of the Physical Society of Japan 68, no. 7 (1999): 2252–58. http://dx.doi.org/10.1143/jpsj.68.2252.

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48

Fiori, Simone. "Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID)." SIAM Journal on Control and Optimization 59, no. 1 (2021): 78–102. http://dx.doi.org/10.1137/19m1307743.

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49

Maire, Henri-Michel, and Francine Meylan. "Extension of smooth CR mappings between non-essentially finite hypersurfaces in C3." Arkiv för Matematik 35, no. 1 (1997): 185–99. http://dx.doi.org/10.1007/bf02559598.

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50

Chen, Yanping, and Zihua Guo. "An extension of Calderón-Zygmund type singular integral with non-smooth kernel." Journal of Functional Analysis 281, no. 9 (2021): 109196. http://dx.doi.org/10.1016/j.jfa.2021.109196.

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