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## Miniversal deformations of matrices of bilinear forms

Dmytryshyn, Andrii R.; Futorny, Vyacheslav; Sergeichuk, Vladimir V.
Fonte: ELSEVIER SCIENCE INC; NEW YORK Publicador: ELSEVIER SCIENCE INC; NEW YORK
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence. (C) 2011 Elsevier Inc. All rights reserved.; CNPq [301743/2007-0]; CNPq; FAPESP; Fapesp [2010/50347-9, 05/59407-6, 2010/07278-6]

## Simulating Deformations of MR Brain Images for Validation of Atlas-based Segmentation and Registration Algorithms

Xue, Zhong; Shen, Dinggang; Karacali, Bilge; Stern, Joshua; Rottenberg, David; Davatzikos, Christos
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
26.87%
Simulated deformations and images can act as the gold standard for evaluating various template-based image segmentation and registration algorithms. Traditional deformable simulation methods, such as the use of analytic deformation fields or the displacement of landmarks followed by some form of interpolation, are often unable to construct rich (complex) and/or realistic deformations of anatomical organs. This paper presents new methods aiming to automatically simulate realistic inter- and intra-individual deformations. The paper first describes a statistical approach to capturing inter-individual variability of high-deformation fields from a number of examples (training samples). In this approach, Wavelet-Packet Transform (WPT) of the training deformations and their Jacobians, in conjunction with a Markov Random Field (MRF) spatial regularization, are used to capture both coarse and fine characteristics of the training deformations in a statistical fashion. Simulated deformations can then be constructed by randomly sampling the resultant statistical distribution in an unconstrained or a landmark-constrained fashion. The paper also describes a model for generating tissue atrophy or growth in order to simulate intra-individual brain deformations. Several sets of simulated deformation fields and respective images are generated...

## Residual Shear Deformations in the Coronary Artery

Wang, Ruoya; Gleason, Rudolph L.
Fonte: American Society of Mechanical Engineers Publicador: American Society of Mechanical Engineers
Tipo: Artigo de Revista Científica
EN
Relevância na Pesquisa
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Quantifying arterial residual deformations is critical for understanding the stresses and strains within the arterial wall during physiological and pathophysiological conditions. This study presents novel findings on residual shear deformations in the left anterior descending coronary artery. Residual shear deformations are most evident when thin, long axial strips are cut from the artery. These strips deform into helical configurations when placed in isotonic solution. A residual shear angle is introduced as a parameter to quantify the residual shear deformations. Furthermore, a stress analysis is performed to study the effects of residual shear deformations on the intramural shear stress distribution of an artery subjected to pressure, axial stretch, and torsion using numerical simulation. The results from the stress analyses suggest that residual shear deformations can significantly modulate the intramural shear stress across the arterial wall.

## Um estudo das alterações dos parâmetros de transformadores oriundas de deformações nos enrolamentos: uma contribuição para o diagnóstico de vida útil; A study of transformer parameter changes caused by deformations in windings: a contribution to lifetime diagnosis

Saraiva, Elise
POR
Relevância na Pesquisa
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Esta tese tem como objetivo estudar as alterações que possam ocorrer nos parâmetros de transformador quando algum tipo de deformação incidir em seus enrolamentos. Para a verificação de tais efeitos, optou-se por analisar possíveis variações em parâmetros elétricos, magnéticos e mecânicos as quais podem indicar um decaimento na vida útil de tal equipamento. Para o desenvolvimento de tal estudo optou-se por utilizar duas ferramentas computacionais para modelar o transformador: o software ATP (Alternative Transient Program) e o programa FLUX em sua versão 3D, o qual emprega o método de elementos finitos. Deformações serão aplicadas nos modelos e análises realizadas para a verificação dos parâmetros supracitados. De posse de tais análises e de técnicas já utilizadas para a detecção de deformações mecânicas nos enrolamentos de transformadores, será apresentada uma metodologia computacional para a realização de tal diagnóstico, antes que este tipo de falha possa retirar o transformador de operação. ______________________________________________________________________________ ABSTRACT; This thesis aims to study the changes that may occur in transformer parameters when any type of deformation is caused in its windings. To verify such effects...

## Nearly Ordinary Galois Deformations over Arbitrary Number Fields

Calegari, Frank; Mazur, Barry C.
Fonte: Cambridge University Press Publicador: Cambridge University Press
Tipo: Artigo de Revista Científica
EN_US
Relevância na Pesquisa
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Let $$K$$ be an arbitrary number field, and let $$\rho: Gal(K \bar/K) \rightarrow GL_2(E)$$ be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of $$\rho$$. When $$K$$ is totally real and rho is modular, results of Hida imply that the nearly ordinary deformation space associated to rho contains a Zariski dense set of points corresponding to "automorphic" Galois representations. We conjecture that if $$K$$ is not totally real, then this is never the case, except in three exceptional cases, corresponding to (1) "base change", (2) "CM" forms, and (3) "Even" representations. The latter case conjecturally can only occur if the image of $$\rho$$ is finite. Our results come in two flavours. First, we prove a general result for Artin representations, conditional on a strengthening of Leopoldt's conjecture. Second, when $$K$$ is an imaginary quadratic field, we prove an unconditional result that implies the existence of "many" positive dimensional components (of certain deformation spaces) that do not contain infinitely many classical points. Also included are some speculative remarks about "$$p$$-adic functorality", as well as some remarks on how our methods should apply to n-dimensional representations of Gal$$(Q \bar/Q)$$ when $$n \lt 2$$.; Mathematics

## Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes

Mavlyutov, Anvar
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We generalized the construction of deformations of affine toric varieties of K. Altmann and our previous construction of deformations of weak Fano toric varieties to the case of arbitrary toric varieties by introducing the notion of Minkowski sum decompositions of polyhedral complexes. Our construction embeds the original toric variety into a higher dimensional toric variety where the image is given by a prime binomial complete intersection ideal in Cox homogeneous coordinates. The deformations are realized by families of complete intersections. For compact simplicial toric varieties with at worst Gorenstein terminal singularities, we show that our deformations span the infinitesimal space of deformations by Kodaira-Spencer map. For Fano toric varieties, we show that their deformations can be constructed in higher-dimensional Fano toric varieties related to the Batyrev-Borisov mirror symmetry construction.

## Equisingular Deformations of Plane Curves in Arbitrary Characteristic

Campillo, Antonio; Greuel, Gert-Martin; Lossen, Christoph
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization and of the equation and show that the base space of its semiuniveral deformation is smooth in both cases. Our approach through deformations of the parametrization is elementary and we show that equisingular deformations of the parametrization form a linear subfunctor of all deformations of the parametrization. This gives additional information, even in characteristic zero, the case which was treated by J. Wahl. The methods and proofs extend easily to good characteristic, that is, when the characteristic does not divide the multiplicity of any branch of the singularity. In bad characteristic, however, new phenomena occur and we are naturally led to consider weakly trivial respectively weakly equisingular deformations, that is, those which become trivial respectively equisingular after a finite and dominant base change. The semiuniversal base space for weakly equisingular deformations is, in general, not smooth but becomes smooth after a finite and purely inseparable base extension. For the proof of this fact we introduce some constructions which may have further applications in the theory of singularities in positive characteristic.; Comment: 56 pages

## Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory

van Tongeren, Stijn J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and indicate that this structure can be realized on the gauge theory side by considering theories on various noncommutative spaces. We then conjecture that these are the gauge theory duals of our strings, modulo subtleties involving singularities. We support this conjecture by a brane construction for two jordanian examples, corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also discuss kappa-Minkowski type deformations of AdS_5 x S^5, one of which may be the gravity dual of gauge theory on spacelike kappa-Minkowski space.; Comment: v4, presentation reorganized, physics unchanged, 32 pages

## Infinitesimal deformations of the model $\mathbb{Z}_3$-filiform Lie algebra

Navarro, Rosa
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In this work it is considered the vector space composed by the infinitesimal deformations of the model $\mathbb{Z}_3$-filiform Lie algebra $L^{n,m,p}$. By using these deformations all the $\mathbb{Z}_3$-filiform Lie algebras can be obtained, hence the importance of these deformations. The results obtained in this work together to those obtained in [Integrable deformations of nilpotent color Lie superalgebras, J. Geom. Phys. 61(2011)1797-1808] and [Corrigendum to Integrable deformations of nilpotent color Lie superalgebras, J. Geom. Phys. 62(2012)1571], leads to compute the total dimension of the mentioned space of deformations.; Comment: arXiv admin note: substantial text overlap with arXiv:1202.5466

## Decomposition of deformations of thin rods. Application to nonlinear elasticity

Blanchard, Dominique; Griso, Georges
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order $\delta$, which takes into account the specific geometry of such beams. A deformation $v$ is split into an elementary deformation and a warping. The elementary deformation is the analog of a Bernoulli-Navier's displacement for linearized deformations replacing the infinitesimal rotation by a rotation in SO(3) in each cross section of the rod. Each part of the decomposition is estimated with respect to the $L^2$ norm of the distance from gradient $v$ to SO(3). This result relies on revisiting the rigidity theorem of Friesecke-James-M\"uller in which we estimate the constant for a bounded open set star-shaped with respect to a ball. Then we use the decomposition of the deformations to derive a few asymptotic geometrical behavior: large deformations of extensional type, inextensional deformations and linearized deformations. To illustrate the use of our decomposition in nonlinear elasticity, we consider a St Venant-Kirchhoff material and upon various scaling on the applied forces we obtain the $\Gamma$-limit of the rescaled elastic energy. We first analyze the case of bending forces of order $\delta^2$ which leads to a nonlinear inextensional model. Smaller pure bending forces give the classical linearized model. A coupled extensional-bending model is obtained for a class of forces of order $\delta^2$ in traction and of order $\delta^3$ in bending.

## Infinitesimal deformations of double covers of smooth algebraic varieties

Cynk, Slawomir; van Straten, Duco
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety. The space of all infinitesimal deformations has a representation as a direct sum of two subspaces. One is isomorphic to the space of simultaneous deformations of the branch locus and the base of the double covering. The second summand is the subspace of deformations of the double covering which induce trivial deformations of the branch divisor. The main result of the paper is a description of the effect of imposing singularities in the branch locus. As a special case we study deformations of Calabi--Yau threefolds which are non--singular models of double cover of the projective 3--space branched along an octic surface. We show that in that case the number of deformations can be computed explicitly using computer algebra systems. This gives a method to compute the Hodge numbers of these Calabi--Yau manifolds. In this case the transverse deformations are resolutions of deformations of double covers of projective space but not double covers of a blow--up of projective space. In the paper we gave many explicit examples.; Comment: 15 pages

## Deformations of nonsingular Poisson varieties and Poisson invertible sheaves

Kim, Chunghoon
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.83%
In this paper, we study deformations of nonsingular Poisson varieties, deformations of Poisson invertible sheaves and simultaneous deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend flat deformation theory of nonsingular varieties and invertible sheaves. In an appendix, we study deformations of Poisson vector bundles. We identify first-order deformations and obstructions.; Comment: appendix added (deformations of Poisson vector bundles)

## Simultaneous Deformations of Lie Algebroids and Lie Subalgebroids

Ji, Xiang
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie algebroids and a second one to control the deformations of Lie subalgebroids. We also combine these two $L_\infty$-algebras into one to control the simultaneous deformations of a Lie algebroid and its Lie subalgebroids. The results generalize the deformation theory of Lie algebra and Lie subalgebras. Applications of our results include deformations of foliations, deformations of complex structures and deformations of homomorphisms of Lie algebroids.

## Massless conformal fields, AdS_{d+1}/CFT_d higher spin algebras and their deformations

Fernando, Sudarshan; Gunaydin, Murat
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Extending our earlier work in d = 4, 5 and 6 dimensions, we study the minimal unitary representation (minrep) of SO(d,2) and its deformations obtained by quantization of its geometric quasiconformal realization in higher dimensions. We show that there is a one-to-one correspondence between the minrep of SO(d,2) and its deformations and massless conformal fields in Minkowskian spacetimes in d dimensions. The minrep describes a massless conformal scalar field, and its deformations describe massless conformal fields of higher spin. The generators of Joseph ideal vanish identically as operators for the quasiconformal realization of the minrep and its enveloping algebra yields directly the standard bosonic $AdS_{(d+1)}/CFT_d$ higher spin algebra. For deformed minreps the generators of certain deformations of Joseph ideal vanish as operators and their enveloping algebras lead to deformations of the standard bosonic higher spin algebra. In odd dimensions there is a unique deformation of the higher spin algebra corresponding to the spinor singleton. In even dimensions one finds infinitely many deformations of the higher spin algebra labelled by the eigenvalues of Casimir operator of the little group SO(d-2) for massless representations.; Comment: 41 pages; LaTeX file; Minor improvements in presentation; Typos corrected. arXiv admin note: text overlap with arXiv:1409.2185

## Electric-magnetic Duality and Deformations of Three-Dimensional CFT's

de Haro, Sebastian; Gao, Peng
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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SL(2,Z) duality transformations in asymptotically AdS4 x S^7 act non-trivially on the three-dimensional SCFT of coincident M2-branes on the boundary. We show how S-duality acts away from the IR fixed point. We develop a systematic method to holographically obtain the deformations of the boundary CFT and show how electric-magnetic duality relates different deformations. We analyze in detail marginal deformations and deformations by dimension 4 operators. In the case of massive deformations, the RG flow relates S-dual CFT's. Correlation functions in the CFT are computed by varying magnetic bulk sources, whereas correlation functions in the dual CFT are computed by electric bulk sources. Under massive deformations, the boundary effective action is generically minimized by massive self-dual configurations of the U(1) gauge field. We show that a self-dual choice of boundary conditions exists, and it corresponds to the self-dual topologically massive gauge theory in 2+1 dimensions. Thus, self-duality in three dimensions can be understood as a consequence of electric-magnetic invariance in the bulk of AdS4.; Comment: 59 pages, 1 figure. Version to appear in Phys. Rev. D

## Deformations of compact holomorphic Poisson submanifolds

Kim, Chunghoon
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.9%
In this paper, we study deformations of compact holomorphic Poisson submanifolds which extend Kodaira's series of papers on semi-regularity (deformations of compact complex submanifolds of codimension 1), deformations of compact complex submanifolds of arbitrary codimensions, and stability of compact complex submanifolds in the context of holomorphic Poisson deformations. We also study simultaneous deformations of holomorphic Poisson structures and holomorphic Poisson submanifolds on a fixed underlying compact complex manifold. In appendices, we present deformations of Poisson closed subschemes in the language of functors of Artin rings which is the algebraic version of deformations of holomorphic Poisson submanifolds. We identify first-order deformations and obstructions.

## On the equi-normalizable deformations of singularities of complex plane curves

Kerner, Dmitry
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.87%
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic deformations. We restrict primarily to the deformations of singularities with smooth branches. A natural invariant of the singular type is introduced: the dual graph. It imposes severe restrictions on the possible collisions/deformations. And allows to prove some bounds on the variation of classical invariants in equi-normalizable families. We consider in details deformations of ordinary multiple points, the deformations of a singularity into the collections of ordinary multiple points and deformations of the type $x^p+y^{pk}$ into the collections of $A_k$'s.; Comment: Final version. To appear in Manuscripta

## Late Alpine deformations, Neotectonic evolution and Active Tectonics of the southern border of Central Balkan Mountain: a new contribution.

Shanov, Stefan; Sanz de Galdeano, Carlos; Galindo-Zaldívar, Jesús; Radulov, Alexander; Nikolov, Gabriel; Azañón, José Miguel; Yaneva, M.
Tipo: Artículo Formato: 10752 bytes; application/octet-stream
ENG
Relevância na Pesquisa
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10 pages, 3 figures, 1 table.; The published till now data and interpretations show the dominant role of the active faults in the structures of Karlovo and Sheynovo grabens and along the southern slope of the Central Balkan Mountain. The new investigations along the southern border of the Balkan Mountain included studies of faulting and fracturing at micro and mezzo-levels. A quantity of striae on slickensides and shear joints were measured. Thin sections have been prepared from five samples collected from outcrops of the surface of thrusting of the big granite over-thrust. The microscope analyses have shown that the process of thrusting was in low-temperature conditions. The secondary deformations at micro-level are reflections of the next tectonic impacts. Geophysical information has been also analysed (data from the seismic profiling, as well as reinterpretations of the gravity field). The tectonic stress fields from the Early-Alpine time till now have been reconstructed. For the first time it has been proved the existence of deformations from the Atean phase (Late Miocene) along the southern slope of the Balkan Mountains. This stress field is characterised by sub-horizontal and NE—SW directed axis s3 and axis s1 varying from subvertical to NW—SE direction. The youngest tectonic stress field has dominant N—S extension. The main conclusion of the study is that it was not possible to find proves for the existence of significant fault extended along the southern slope of the Balkan Mountains. A combination of fault structures is present...

## Elastocapillarity: adhesion and large deformations of thin sheets

Wagner, Till Jakob Wenzel
Fonte: University of Cambridge; Department of Applied Mathematics and Theoretical Physics Publicador: University of Cambridge; Department of Applied Mathematics and Theoretical Physics
Tipo: Thesis; doctoral; PhD
EN
Relevância na Pesquisa
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This thesis is concerned with the deformation and adhesion of thin elastic sheets that come into contact with an underlying substrate. The focus of this work is on the interplay between material and geometric properties of a system and how this interplay determines the equilibrium states of sheet and substrate, particularly in the regime of geometrically nonlinear deformations. We first consider the form of an elastic sheet that is partially adhered to a rigid substrate, accounting for deflections with large slope: the Sticky Elastica. Starting from the classical Euler Elastica we provide numerical results for the profiles of such blisters and present asymptotic expressions that go beyond the previously known, linear, approximations. Our theoretical predictions are confirmed by desktop experiments and suggest a new method for the measurement of material properties for systems undergoing large deformations. With the aim to gain better understanding of the initial appearance of blisters we next investigate the deformation of a thin elastic sheet floating on a liquid surface. We show that, after the appearance of initial wrinkles, the sheet delaminates from the liquid over a finite region at a critical compression, forming a delamination blister. We determine the initial blister size and the evolution of blister size with continuing compression before verifying our theoretical results with experiments at a macroscopic scale. We next study theoretically the deposition of thin sheets onto a grooved substrate...

## BITUMINOUS MIX RESPONSE TO PLASTIC DEFORMATIONS: COMPARISON OF THE SPANISH NLT-173 AND UNE-EN 12697-22 WHEEL-TRACKING TESTS

GARCÍA-TRAVÉ,GEMA; MARTINEZ-ECHEVARRIA,MARIA JOSÉ; RUBIO GÁMEZ,MARÍA DEL CARMEN; MORENO NAVARRO,FERNANDO