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Journal articles on the topic 'Smooth deformations'

Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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1

Williamson, M., and A. Majumdar. "Effect of Surface Deformations on Contact Conductance." Journal of Heat Transfer 114, no. 4 (November 1, 1992): 802–10. http://dx.doi.org/10.1115/1.2911886.

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This study experimentally investigates the influence of surface deformations on contact conductance when two dissimilar metals are brought into contact. Most relations between the contact conductance and the load use the surface hardness to characterize surface deformations. This inherently assumes that deformations are predominantly plastic. To check the validity of this assumption, five tests were conducted in the contact pressure range of 30 kPa to 4 MPa, with sample combinations of (I) smooth aluminum-rough stainless steel, (II) rough aluminum-smooth stainless steel, (III) rough copper-smooth stainless steel, (IV) smooth copper-rough stainless steel, and (V) smooth aluminum-smooth stainless steel. The experimental results of tests I, II, and IV indicate that the conductance of the first load-unload cycle showed hysteresis, suggesting that the plastic deformation was significant. However, for subsequent load cycles, no conductance hysteresis was observed, implying that elastic deformation was predominant. In contrast, no conductance hysteresis was observed for all load-unload cycles of tests III and V. Therefore, the surface deformation for this combination was always predominantly elastic. In practical applications where plastic deformation is significant for the first loading, mechanical vibrations can produce oscillating loads, which can finally lead to predominance of elastic deformation. Comparison of the results of tests II and V show that even though plastic deformation was significant for the first loading of a rough aluminum surface, elastic deformation was always predominant for the smoother aluminum surface

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2

Gaussier, Hervé, and Xianghong Gong. "Smooth Equivalence of Deformations of Domains in Complex Euclidean Spaces." International Mathematics Research Notices 2020, no. 18 (July 31, 2018): 5578–610. http://dx.doi.org/10.1093/imrn/rny168.

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Abstract We prove that two smooth families of 2-connected domains in $\mathbf{C}$ are smoothly equivalent if they are equivalent under a possibly discontinuous family of biholomorphisms. We construct, for $\infty > m \geq 3$, two smooth families of smoothly bounded $m$-connected domains in $\mathbf{C}$, and for $n\geq 2$, two families of strictly pseudoconvex domains in $\mathbf{C}^n$, which are equivalent under discontinuous families of biholomorphisms but not under any continuous family of biholomorphisms. Finally, we give sufficient conditions for the smooth equivalence of two smooth families of domains.

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3

Ilten, Nathan Owen. "Deformations of smooth toric surfaces." Manuscripta Mathematica 134, no. 1-2 (July 29, 2010): 123–37. http://dx.doi.org/10.1007/s00229-010-0386-9.

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4

Sako, Akifumi. "Recent Developments in Instantons in Noncommutative." Advances in Mathematical Physics 2010 (2010): 1–28. http://dx.doi.org/10.1155/2010/270694.

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We review recent developments in noncommutative deformations of instantons in . In the operator formalism, we study how to make noncommutative instantons by using the ADHM method, and we review the relation between topological charges and noncommutativity. In the ADHM methods, there exist instantons whose commutative limits are singular. We review smooth noncommutative deformations of instantons, spinor zero-modes, the Green's functions, and the ADHM constructions from commutative ones that have no singularities. It is found that the instanton charges of these noncommutative instanton solutions coincide with the instanton charges of commutative instantons before noncommutative deformation. These smooth deformations are the latest developments in noncommutative gauge theories, and we can extend the procedure to other types of solitons. As an example, vortex deformations are studied.

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5

DE BARTOLOMEIS, PAOLO, and ANDREI IORDAN. "DEFORMATIONS OF LEVI FLAT STRUCTURES IN SMOOTH MANIFOLDS." Communications in Contemporary Mathematics 16, no. 02 (April 2014): 1350015. http://dx.doi.org/10.1142/s0219199713500156.

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We study intrinsic deformations of Levi flat structures on a smooth manifold. A Levi flat structure on a smooth manifold L is a couple (ξ, J) where ξ ⊂ T(L) is an integrable distribution of codimension 1 and J : ξ → ξ is a bundle automorphism which defines a complex integrable structure on each leaf. A deformation of a Levi flat structure (ξ, J) is a smooth family {(ξt, Jt)}t∈]-ε,ε[ of Levi flat structures on L such that (ξ0, J0) = (ξ, J). We define a complex whose cohomology group of order 1 contains the infinitesimal deformations of a Levi flat structure. In the case of real analytic Levi flat structures, this cohomology group is [Formula: see text] where (𝒵*(L), δ, {⋅,⋅}) is the differential graded Lie algebra associated to ξ.

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6

Capistrano, Abraão J. S. "Constraints on cosmokinetics of smooth deformations." Monthly Notices of the Royal Astronomical Society 448, no. 2 (February 10, 2015): 1232–39. http://dx.doi.org/10.1093/mnras/stv052.

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7

Neshveyev, Sergey. "Smooth Crossed Products of Rieffel’s Deformations." Letters in Mathematical Physics 104, no. 3 (November 29, 2013): 361–71. http://dx.doi.org/10.1007/s11005-013-0675-9.

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8

SALUR, SEMA. "DEFORMATIONS OF SPECIAL LAGRANGIAN SUBMANIFOLDS." Communications in Contemporary Mathematics 02, no. 03 (August 2000): 365–72. http://dx.doi.org/10.1142/s0219199700000177.

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In [7], R. C. McLean showed that the moduli space of nearby submanifolds of a smooth, compact, orientable special Lagrangian submanifold L in a Calabi-Yau manifold X is a smooth manifold and its dimension is equal to the dimension of ℋ1(L), the space of harmonic 1-forms on L. In this paper, we will show that the moduli space of all infinitesimal special Lagrangian deformations of L in a symplectic manifold with non-integrable almost complex structure is also a smooth manifold of dimension b1(L), the first Betti number of L.

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9

Iacono, Donatella, and Marco Manetti. "On Deformations of Pairs (Manifold, Coherent Sheaf)." Canadian Journal of Mathematics 71, no. 5 (January 9, 2019): 1209–41. http://dx.doi.org/10.4153/cjm-2018-027-8.

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AbstractWe analyse infinitesimal deformations of pairs $(X,{\mathcal{F}})$ with ${\mathcal{F}}$ a coherent sheaf on a smooth projective variety $X$ over an algebraically closed field of characteristic 0. We describe a differential graded Lie algebra controlling the deformation problem, and we prove an analog of a Mukai–Artamkin theorem about the trace map.

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10

Baladi, Viviane, and Daniel Smania. "Smooth deformations of piecewise expanding unimodal maps." Discrete & Continuous Dynamical Systems - A 23, no. 3 (2009): 685–703. http://dx.doi.org/10.3934/dcds.2009.23.685.

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11

Schmidt, Tobias. "On unitary deformations of smooth modular representations." Israel Journal of Mathematics 193, no. 1 (October 11, 2012): 15–46. http://dx.doi.org/10.1007/s11856-012-0131-z.

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12

Feshchenko, Bohdan. "Deformations of smooth functions on 2-torus." Proceedings of the International Geometry Center 12, no. 3 (December 1, 2019): 30–50. http://dx.doi.org/10.15673/tmgc.v12i3.1528.

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Let $f$ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be the group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the Kronrod-Reeb graph of $f$ induced by elements from $\mathcal{S}'(f)$, and $\Delta'$ be the subgroup of $\mathcal{S}'(f)$ consisting of diffeomorphisms which trivially act on the graph of $f$ and are isotopic to the identity map. The group $\pi_0\mathcal{S}'(f)$ can be viewed as an analogue of a mapping class group for $f$-preserved diffeomorphisms of $M$. The groups $\pi_0\Delta'(f)$ and $G(f)$ encode ``combinatorially trivial'' and ``combinatorially nontrivial'' counterparts of $\pi_0\mathcal{S}'(f)$ respectively. In the paper we compute groups $\pi_0\mathcal{S}'(f)$, $G(f)$, and $\pi_0\Delta'(f)$ for Morse functions on $2$-torus $T^2$.

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13

Colbois, Bruno, Florence Newberger, and Patrick Verovic. "Some smooth Finsler deformations of hyperbolic surfaces." Annals of Global Analysis and Geometry 35, no. 2 (October 14, 2008): 191–226. http://dx.doi.org/10.1007/s10455-008-9130-z.

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14

CATANESE, FABRIZIO. "CANONICAL SYMPLECTIC STRUCTURES AND DEFORMATIONS OF ALGEBRAIC SURFACES." Communications in Contemporary Mathematics 11, no. 03 (June 2009): 481–93. http://dx.doi.org/10.1142/s0219199709003478.

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We show that a minimal surface of general type has a canonical symplectic structure (unique up to symplectomorphism) which is invariant for smooth deformation. We show that the symplectomorphism type is also invariant for deformations which allow certain normal singularities, provided one remains in the same smoothing component. We use this technique to show that the Manetti surfaces yield examples of surfaces of general type which are not deformation equivalent but are canonically symplectomorphic.

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15

Wang, Zhenjian. "On Deformations of Nodal Hypersurfaces." Canadian Mathematical Bulletin 61, no. 3 (September 1, 2018): 659–72. http://dx.doi.org/10.4153/cmb-2017-069-x.

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16

Rubinsztein, Ryszard L. "On Some Deformations of Riemann Surfaces. I." MATHEMATICA SCANDINAVICA 86, no. 2 (June 1, 2000): 179. http://dx.doi.org/10.7146/math.scand.a-14288.

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We define a family of infinitesimal deformations of compact Riemann surfaces of genus $g > 2$ which generalizes the Fenchel-Nielsen deformations. Those new deformations are associated to smooth vector fields on the circle. We compute a representation of the deformations in terms of Poincaré series and determine the corresponding Eichler cohomology classes.

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17

Nasu, Hirokazu. "Obstructions to deforming curves on a 3-fold, III: Deformations of curves lying on a K3 surface." International Journal of Mathematics 28, no. 13 (December 2017): 1750099. http://dx.doi.org/10.1142/s0129167x17500999.

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We study the deformations of a smooth curve [Formula: see text] on a smooth projective [Formula: see text]-fold [Formula: see text], assuming the presence of a smooth surface [Formula: see text] satisfying [Formula: see text]. Generalizing a result of Mukai and Nasu, we give a new sufficient condition for a first order infinitesimal deformation of [Formula: see text] in [Formula: see text] to be primarily obstructed. In particular, when [Formula: see text] is Fano and [Formula: see text] is [Formula: see text], we give a sufficient condition for [Formula: see text] to be (un)obstructed in [Formula: see text], in terms of [Formula: see text]-curves and elliptic curves on [Formula: see text]. Applying this result, we prove that the Hilbert scheme [Formula: see text] of smooth connected curves on a smooth quartic [Formula: see text]-fold [Formula: see text] contains infinitely many generically non-reduced irreducible components, which are variations of Mumford’s example for [Formula: see text].

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18

Goodbrake, Christian, Alain Goriely, and Arash Yavari. "The mathematical foundations of anelasticity: existence of smooth global intermediate configurations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20200462. http://dx.doi.org/10.1098/rspa.2020.0462.

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A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption is on unsatisfactory ground. Here, we derive a sufficient condition for the existence of global intermediate configurations, starting from a multiplicative decomposition of the deformation gradient. We show that these global configurations are unique up to isometry. We examine the result of isometrically embedding these configurations in higher-dimensional Euclidean space, and construct multiplicative decompositions of the deformation gradient reflecting these embeddings. As an example, for a family of radially symmetric deformations, we construct isometric embeddings of the resulting intermediate configurations, and compute the residual stress fields explicitly.

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19

CRESSON, JACKY. "NON-DIFFERENTIABLE DEFORMATIONS OF ℝn." International Journal of Geometric Methods in Modern Physics 03, no. 07 (November 2006): 1395–415. http://dx.doi.org/10.1142/s0219887806001752.

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Many problems of physics or biology involve very irregular objects like the rugged surface of a malignant cell nucleus or the structure of space-time at the atomic scale. We define and study non-differentiable deformations of the classical Cartesian space ℝn which can be viewed as the basic bricks to construct irregular objects. They are obtained by taking the topological product of n-graphs of nowhere differentiable real valued functions. Our point of view is to replace the study of a non-differentiable function by the dynamical study of a one-parameter family of smooth regularization of this function. In particular, this allows us to construct a one-parameter family of smooth coordinates systems on non-differentiable deformations of ℝn, which depend on the smoothing parameter via an explicit differential equation called a scale law. Deformations of ℝn are examples of a new class of geometrical objects called scale manifolds which are defined in this paper. As an application, we derive rigorously the main results of the scale-relativity theory developed by Nottale in the framework of a scale space-time manifold.

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20

Liu, Chuanbo, Chengqing Yuan, and Shutian Liu. "The Effect of Intrinsic Mechanical Properties on Reducing the Friction-Induced Ripples of Hard-Filler-Modified HDPE." Polymers 15, no. 2 (January 4, 2023): 268. http://dx.doi.org/10.3390/polym15020268.

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Ripple deformations induced by friction on polymeric materials have negative effects on the entire stability of operating machineries. These deformations are formed as a response to contacting mechanics, caused by the intrinsic mechanical properties. High-density polyethylene (HDPE) with varying silicon nitride (Si3N4) contents is used to investigate different ripple deformation responses by conducting single-asperity scratch tests. The relationship between the intrinsic mechanical properties and the ripple deformations caused by filler modifications is analyzed in this paper. The results show the coupling of the inherent mechanical properties, and the stick-slip motion of HDPE creates ripple deformations during scratching. The addition of the Si3N4 filler changes the frictional response; the filler weakens the ripples and almost smoothens the scratch, particularly at 4 wt.%, but the continued increase in the Si3N4 content produces noticeable ripples and fluctuations. These notable differences can be attributed to the yield and post-yield responses; the high yield stress and strain-hardening at 4 wt.% provide good friction resistance and stress distribution, thus a smooth scratch is observed. In contrast, increasing the filler content weakens both the yield and post-yield responses, leading to deformation. The results herein reveal the mechanism behind the initial ripple deformation, thus providing fundamental insights into universally derived friction-induced ripples.

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21

Tsuji, Hajime. "Deformation invariance of plurigenera." Nagoya Mathematical Journal 166 (June 2002): 117–34. http://dx.doi.org/10.1017/s002776300000828x.

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22

Gallego, Francisco Javier, Miguel González, and Bangere P. Purnaprajna. "Deformation of finite morphisms and smoothing of ropes." Compositio Mathematica 144, no. 3 (May 2008): 673–88. http://dx.doi.org/10.1112/s0010437x07003326.

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AbstractIn this paper we prove that most ropes of arbitrary multiplicity supported on smooth curves can be smoothed. By a rope being smoothable we mean that the rope is the flat limit of a family of smooth, irreducible curves. To construct a smoothing, we connect, on the one hand, deformations of a finite morphism to projective space and, on the other hand, morphisms from a rope to projective space. We also prove a general result of independent interest, namely that finite covers onto smooth irreducible curves embedded in projective space can be deformed to a family of 1:1 maps. We apply our general theory to prove the smoothing of ropes of multiplicity 3 on P1. Even though this paper focuses on ropes of dimension 1, our method yields a general approach to deal with the smoothing of ropes of higher dimension.

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23

Ito, Kazuhiro, Tetsushi Ito, and Christian Liedtke. "Deformations of rational curves in positive characteristic." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 769 (December 1, 2020): 55–86. http://dx.doi.org/10.1515/crelle-2020-0003.

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AbstractWe study deformations of rational curves and their singularities in positive characteristic. We use this to prove that if a smooth and proper surface in positive characteristic p is dominated by a family of rational curves such that one member has all δ-invariants (resp. Jacobian numbers) strictly less than {\frac{1}{2}(p-1)} (resp. p), then the surface has negative Kodaira dimension. We also prove similar, but weaker results hold for higher-dimensional varieties. Moreover, we show by example that our result is in some sense optimal. On our way, we obtain a sufficient criterion in terms of Jacobian numbers for the normalization of a curve over an imperfect field to be smooth.

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24

Lecomte, P. B. A., and C. Roger. "Formal deformations of the associative algebra of smooth matrices." Letters in Mathematical Physics 15, no. 1 (January 1988): 55–63. http://dx.doi.org/10.1007/bf00416572.

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25

Cynk, Sławomir, and Duco van Straten. "Infinitesimal deformations of double covers of smooth algebraic varieties." Mathematische Nachrichten 279, no. 7 (May 2006): 716–26. http://dx.doi.org/10.1002/mana.200310388.

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26

Dloussky, Georges, and Andrei Teleman. "Smooth deformations of singular contractions of class VII surfaces." Mathematische Zeitschrift 296, no. 3-4 (February 27, 2020): 1521–37. http://dx.doi.org/10.1007/s00209-020-02481-0.

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27

Wilson, P. M. H. "Elliptic ruled surfaces on Calabi–Yau threefolds." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (July 1992): 45–52. http://dx.doi.org/10.1017/s0305004100070742.

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In [5], we studied the behaviour of the Kähler cone of Calabi–Yau threefolds under deformations. We saw that the Kähler cone is locally constant in a smooth family of Calabi–Yau threefolds, unless some of the threefolds Xb contain elliptic ruled surfaces. Moreover, if X is a Calabi–Yau threefold containing an elliptic ruled surface, then the Kähler cone is not invariant under a generic small deformation.

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28

NORDSTRÖM, JOHANNES. "Deformations of asymptotically cylindricalG2-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 2 (September 2008): 311–48. http://dx.doi.org/10.1017/s0305004108001333.

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AbstractWe prove that for a 7-dimensional manifoldMwith cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-freeG2-structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically cylindricalG2-manifold is exactlyG2if and only if the fundamental group π1(M) is finite and neitherMnor any double cover ofMis homeomorphic to a cylinder.

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29

Kawamata, Yujiro. "Non-commutative deformations of perverse coherent sheaves and rational curves." Journal of Algebraic Geometry 32, no. 1 (May 17, 2022): 59–91. http://dx.doi.org/10.1090/jag/805.

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We consider non-commutative deformations of sheaves on algebraic varieties. We develop some tools to determine parameter algebras of versal non-commutative deformations for partial simple collections and the structure sheaves of smooth rational curves. We apply them to universal flopping contractions of length 2 2 and higher. We confirm Donovan-Wemyss conjecture in the case of deformations of Laufer’s flops.

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30

Bjo¨rklund, S. "A Random Model for Micro-Slip Between Nominally Flat Surfaces." Journal of Tribology 119, no. 4 (October 1, 1997): 726–32. http://dx.doi.org/10.1115/1.2833877.

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A random surface model has been developed for the deformations of contacting surfaces subjected to both normal and tangential load. The model is restricted to nominally flat (rough) elastic surfaces in contact with perfectly flat (smooth) elastic surfaces. The deformations of the asperities are assumed to be independent of each other and the heights of the asperities are assumed to be randomly distributed. Depending on the height of an asperity, it will either slip or stick. The relation between tangential deformation and load will consequently be non-linear and this effect is often named micro-slip. Results are presented for two types of deformation laws for the individual asperities, with three different asperity height distributions. The results show typical micro-slip behaviour, independent of both the individual asperity deformation and the type of asperity height distribution. The influence of the standard deviation of asperity heights is strong and is an important factor when determining the micro-slip of nominally flat surfaces in contact.

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31

MACCHI, A., H. RUHL, and F. CORNOLTI. "Laser absorption and fast electron transport in deformed targets." Laser and Particle Beams 18, no. 3 (July 2000): 375–79. http://dx.doi.org/10.1017/s0263034600183041.

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The effect of surface deformations on laser absorption and transport in overdense plasma targets is investigated with 2D Vlasov simulations. Fractional absorption increases strongly with the deformation depth and scales weakly with density or intensity. Fast electrons generated in the skin layer have high tangential velocity directed toward the deformation center. In the case of a single, smooth deformation, they may be collimated by magnetic fields into a single jet which penetrates deeply into the plasma. Small-scale surface corrugations are able to destroy the collimation of a single jet leading to multiple jets or diffuse electron sprays.

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32

BAKLOUTI, ALI, SAMI DHIEB, and KHALED TOUNSI. "WHEN IS THE DEFORMATION SPACE $\mathscr{T}(\Gamma, H_{2n+1}, H)$ A SMOOTH MANIFOLD?" International Journal of Mathematics 22, no. 11 (November 2011): 1661–81. http://dx.doi.org/10.1142/s0129167x11007331.

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Let G = H2n + 1 be the 2n + 1-dimensional Heisenberg group and H be a connected Lie subgroup of G. Given any discontinuous subgroup Γ ⊂ G for G/H, a precise union of open sets of the resulting deformation space [Formula: see text] of the natural action of Γ on G/H is derived since the paper of Kobayshi and Nasrin [Deformation of Properly discontinuous action of ℤk and ℝk+1, Internat. J. Math.17 (2006) 1175–1190]. We determine in this paper when exactly this space is endowed with a smooth manifold structure. Such a result is only known when the Clifford–Klein form Γ\G/H is compact and Γ is abelian. When Γ is not abelian or H meets the center of G, the parameter and deformation spaces are shown to be semi-algebraic and equipped with a smooth manifold structure. In the case where Γ is abelian and H does not meet the center of G, then [Formula: see text] splits into finitely many semi-algebraic smooth manifolds and fails to be a Hausdorff space whenever Γ is not maximal, but admits a manifold structure otherwise. In any case, it is shown that [Formula: see text] admits an open smooth manifold as its dense subset. Furthermore, a sufficient and necessary condition for the global stability of all these deformations to hold is established.

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GOTO, RYUSHI. "MODULI SPACES OF TOPOLOGICAL CALIBRATIONS, CALABI–YAU, HYPERKÄHLER, G2 and SPIN(7) STRUCTURES." International Journal of Mathematics 15, no. 03 (May 2004): 211–57. http://dx.doi.org/10.1142/s0129167x04002296.

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This paper focuses on a geometric structure defined by a system of closed exterior differential forms and develops a new approach to deformation problems of geometric structures. We obtain a criterion for unobstructed deformations from a cohomological point of view (Theorem 1.7). Further we show that under a cohomological condition, the moduli space of the geometric structures becomes a smooth manifold of finite dimension (Theorem 1.8). We apply our approach to the geometric structures such as Calabi–Yau, HyperKähler, G2 and Spin(7) structures and then obtain a unified construction of smooth moduli spaces of these four geometric structures. We generalize the Moser's stability theorem to provide a direct proof of the local Torelli type theorem in these four geometric structures (Theorem 1.10).

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34

Seyed Bolouri, Seyed Ehsan, Chun IL Kim, and Seunghwa Yang. "Linear theory for the mechanics of third-gradient continua reinforced with fibers resistance to flexure." Mathematics and Mechanics of Solids 25, no. 4 (December 16, 2019): 937–60. http://dx.doi.org/10.1177/1081286519893408.

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A linear model, framed in the setting of the second strain gradient theory, is presented for the mechanics of an elastic solid reinforced with fibers resistant to flexure. The kinematics and bending resistance of the fibers are formulated via the second and third gradient of the continuum deformation. The corresponding Euler equations and admissible boundary conditions are then obtained by means of iterated integration by parts and variational principles arising in the third gradient of virtual displacement. In particular, within the prescription of superposed incremental deformations, we derive a compatible linear model from which a complete analytical solution describing the deformations of fiber composites is obtained. The proposed linear model predicts smooth and dilatational shear angle distributions over the domain of interest, which are also aligned with the results obtained from the corresponding nonlinear theory.

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35

Shigetomi, Shota, and Kenji Kajiwara. "Explicit formulas for isoperimetric deformations of smooth and discrete elasticae." JSIAM Letters 13 (2021): 80–83. http://dx.doi.org/10.14495/jsiaml.13.80.

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36

Falach, Lior, and Reuven Segev. "Reynolds transport theorem for smooth deformations of currents on manifolds." Mathematics and Mechanics of Solids 20, no. 6 (October 9, 2014): 770–86. http://dx.doi.org/10.1177/1081286514551503.

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37

Piovani, Riccardo, and Tommaso Sferruzza. "Deformations of Strong Kähler with torsion metrics." Complex Manifolds 8, no. 1 (January 1, 2021): 286–301. http://dx.doi.org/10.1515/coma-2020-0120.

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Abstract Existence of strong Kähler with torsion metrics, shortly SKT metrics, on complex manifolds has been shown to be unstable under small deformations. We find necessary conditions under which the property of being SKT is stable for a smooth curve of Hermitian metrics {ω t } t which equals a fixed SKT metric ω for t = 0, along a differentiable family of complex manifolds {M t } t .

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38

Drézet, Jean-Marc. "Reachable sheaves on ribbons and deformations of moduli spaces of sheaves." International Journal of Mathematics 28, no. 12 (November 2017): 1750086. http://dx.doi.org/10.1142/s0129167x17500860.

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A primitive multiple curve is a Cohen–Macaulay irreducible projective curve [Formula: see text] that can be locally embedded in a smooth surface, and such that [Formula: see text] is smooth. In this case, [Formula: see text] is a line bundle on [Formula: see text]. If [Formula: see text] is of multiplicity 2, i.e. if [Formula: see text], [Formula: see text] is called a ribbon. If [Formula: see text] is a ribbon and [Formula: see text], then [Formula: see text] can be deformed to smooth curves, but in general a coherent sheaf on [Formula: see text] cannot be deformed in coherent sheaves on the smooth curves. It has been proved in [Reducible deformations and smoothing of primitive multiple curves, Manuscripta Math. 148 (2015) 447–469] that a ribbon with associated line bundle [Formula: see text] such that [Formula: see text] can be deformed to reduced curves having two irreducible components if [Formula: see text] can be written as [Formula: see text] where [Formula: see text] are distinct points of [Formula: see text]. In this case we prove that quasi-locally free sheaves on [Formula: see text] can be deformed to torsion-free sheaves on the reducible curves with two components. This has some consequences on the structure and deformations of the moduli spaces of semi-stable sheaves on [Formula: see text].

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39

Khalfoun, Hafedh, Nizar Ben Fraj, and Meher Abdaoui. "Cohomology of 𝔞𝔣𝔣(m|1) acting on the space of superpseudodifferential operators on the supercircle S1|m." Asian-European Journal of Mathematics 11, no. 04 (August 2018): 1850057. http://dx.doi.org/10.1142/s1793557118500572.

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We investigate the first differential cohomology space associated with the embedding of the affine Lie superalgebra [Formula: see text] on the [Formula: see text]-dimensional supercircle [Formula: see text] in the Lie superalgebra [Formula: see text] of superpseudodifferential operators with smooth coefficients, where [Formula: see text]. Following Ovsienko and Roger, we give explicit expressions of the basis cocycles. We study the deformations of the structure of the [Formula: see text]-module [Formula: see text]. We prove that any formal deformation is equivalent to its infinitesimal part.

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BANAGL, MARKUS, and LAURENTIU MAXIM. "DEFORMATION OF SINGULARITIES AND THE HOMOLOGY OF INTERSECTION SPACES." Journal of Topology and Analysis 04, no. 04 (December 2012): 413–48. http://dx.doi.org/10.1142/s1793525312500185.

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While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity, we show that the first author's cohomology of intersection spaces is stable under smooth deformations in all degrees except possibly the middle, and in the middle degree precisely when the monodromy action on the cohomology of the Milnor fiber is trivial. In many situations, the isomorphism is shown to be a ring homomorphism induced by a continuous map. This is used to show that the rational cohomology of intersection spaces can be endowed with a mixed Hodge structure compatible with Deligne's mixed Hodge structure on the ordinary cohomology of the singular hypersurface. Regardless of monodromy, the middle degree homology of intersection spaces is always a subspace of the homology of the deformation, yet itself contains the middle intersection homology group, the ordinary homology of the singular space, and the ordinary homology of the regular part.

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BEN ABDELGHANI, LEILA, MICHAEL HEUSENER, and HAJER JEBALI. "DEFORMATIONS OF METABELIAN REPRESENTATIONS OF KNOT GROUPS INTO SL(3, C)." Journal of Knot Theory and Its Ramifications 19, no. 03 (March 2010): 385–404. http://dx.doi.org/10.1142/s0218216510007887.

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Let K be a knot in S3 and X its complement. We study deformations of reducible metabelian representations of the knot group π1(X) into SL(3, C) which are associated to a double root of the Alexander polynomial. We prove that these reducible metabelian representations are smooth points of the representation variety and that they have irreducible non metabelian deformations.

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Kaloghiros, Anne-Sophie, and Andrea Petracci. "On toric geometry and K-stability of Fano varieties." Transactions of the American Mathematical Society, Series B 8, no. 19 (July 16, 2021): 548–77. http://dx.doi.org/10.1090/btran/82.

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We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano 3 3 -fold with obstructed deformations. In one case, the K-moduli spaces and stacks are reducible near the closed point associated to the toric Fano 3 3 -fold, while in the other they are non-reduced near the closed point associated to the toric Fano 3 3 -fold. Second, we study K-stability of the general members of two deformation families of smooth Fano 3 3 -folds by building degenerations to K-polystable toric Fano 3 3 -folds.

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43

Ha, In Young, Matthias Wilms, and Mattias Heinrich. "Semantically Guided Large Deformation Estimation with Deep Networks." Sensors 20, no. 5 (March 4, 2020): 1392. http://dx.doi.org/10.3390/s20051392.

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Deformable image registration is still a challenge when the considered images have strong variations in appearance and large initial misalignment. A huge performance gap currently remains for fast-moving regions in videos or strong deformations of natural objects. We present a new semantically guided and two-step deep deformation network that is particularly well suited for the estimation of large deformations. We combine a U-Net architecture that is weakly supervised with segmentation information to extract semantically meaningful features with multiple stages of nonrigid spatial transformer networks parameterized with low-dimensional B-spline deformations. Combining alignment loss and semantic loss functions together with a regularization penalty to obtain smooth and plausible deformations, we achieve superior results in terms of alignment quality compared to previous approaches that have only considered a label-driven alignment loss. Our network model advances the state of the art for inter-subject face part alignment and motion tracking in medical cardiac magnetic resonance imaging (MRI) sequences in comparison to the FlowNet and Label-Reg, two recent deep-learning registration frameworks. The models are compact, very fast in inference, and demonstrate clear potential for a variety of challenging tracking and/or alignment tasks in computer vision and medical image analysis.

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Radchenko, Vladimir P., and Dmitry M. Shishkin. "The Method of Reconstruction of Residual Stresses in a Prismatic Specimen with a Notch of a Semicircular Profile after Advanced Surface Plastic Deformation." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 20, no. 4 (2020): 478–92. http://dx.doi.org/10.18500/1816-9791-2020-20-4-478-492.

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The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method. For model calculations, experimental data on the distribution of residual stresses in a smooth beam made of EP742 alloy after ultrasonic mechanical hardening were used. The effect of the notch radius and beam thickness on the nature and magnitude of the distribution of the residual stress tensor components in the region of the stress concentrator is studied. For the normal longitudinal component of the residual stress tensor, which plays an important role in the theory of high-cycle fatigue, it was found that if the radius of a semicircular notch is less than the thickness of the hardened layer (area of material compression), an increase (in modulus) of this component of residual stresses occurs in the smallest section of the part (in the volume immediately adjacent to the bottom of the concentrator). If the depth of the notch is greater than the thickness of the hardened layer, then a decrease (in magnitude) of this value is observed in comparison with a smooth hardened sample. It is shown that in a reinforced notched beam, the deflection value due to induced self-balanced residual stresses is less than in a smooth beam. Experimental verification of the developed numerical method is done for a surface-hardened smooth beam made of EP742 alloy.

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Basdouri, Imed, Issam Bartouli, and Jean Lerbet. "Deforming 𝔥-trivial the Lie algebra Vect(S1) inside the Lie algebra of pseudodifferential operators Ψ𝒟𝒪." International Journal of Geometric Methods in Modern Physics 14, no. 06 (May 4, 2017): 1750082. http://dx.doi.org/10.1142/s0219887817500827.

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In this paper, we consider the action of Vect(S1) by Lie derivative on the spaces of pseudodifferential operators [Formula: see text]. We study the [Formula: see text]-trivial deformations of the standard embedding of the Lie algebra Vect(S1) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle [Formula: see text]. We classify the deformations of this action that become trivial once restricted to [Formula: see text], where [Formula: see text] or [Formula: see text]. Necessary and sufficient conditions for integrability of infinitesimal deformations are given.

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46

Betina, Adel. "Ramification of the Eigencurve at Classical RM Points." Canadian Journal of Mathematics 72, no. 1 (March 7, 2019): 57–88. http://dx.doi.org/10.4153/cjm-2018-029-4.

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AbstractJ. Bellaïche and M. Dimitrov showed that the $p$-adic eigencurve is smooth but not étale over the weight space at $p$-regular theta series attached to a character of a real quadratic field $F$ in which $p$ splits. In this paper we prove the existence of an isomorphism between the subring fixed by the Atkin–Lehner involution of the completed local ring of the eigencurve at these points and a universal ring representing a pseudo-deformation problem. Additionally, we give a precise criterion for which the ramification index is exactly 2. We finish this paper by proving the smoothness of the nearly ordinary and ordinary Hecke algebras for Hilbert modular forms over $F$ at the overconvergent cuspidal Eisenstein points, being the base change lift for $\text{GL}(2)_{/F}$ of these theta series. Our approach uses deformations and pseudo-deformations of reducible Galois representations.

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Ilten, Nathan, and Charles Turo. "Deformations of smooth complete toric varieties: obstructions and the cup product." Algebra & Number Theory 14, no. 4 (June 21, 2020): 907–26. http://dx.doi.org/10.2140/ant.2020.14.907.

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Baladi, Viviane, and Daniel Smania. "Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps." Annales scientifiques de l'École normale supérieure 45, no. 6 (2012): 861–926. http://dx.doi.org/10.24033/asens.2179.

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Galaktionov, V. A. "Nonlinear dispersion equations: Smooth deformations, compactions, and extensions to higher orders." Computational Mathematics and Mathematical Physics 48, no. 10 (October 2008): 1823–56. http://dx.doi.org/10.1134/s0965542508100084.

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Ran, Ziv. "Incidence stratifications on Hilbert schemes of smooth surfaces, and an application to Poisson structures." International Journal of Mathematics 27, no. 01 (January 2016): 1650006. http://dx.doi.org/10.1142/s0129167x16500063.

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Given a smooth curve on a smooth surface, the Hilbert scheme of points on the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural log-resolution, namely the stratified blowup. As a consequence, the induced Poisson structure on the Hilbert scheme of a Poisson surface has unobstructed deformations.

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