Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 86 for “"Integrability"”.
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Integrability from Chern-Simons theories
This thesis details my work exploring connections between integrable systems and Chern-Simons theories. It is divided into two parts. The first concerns the application of 4d Chern-Simons theory to describe integrable models with boundary, while the second concerns relations between holomorphic …
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Integrability in random conformal geometry
Liouville quantum gravity (LQG) is a random surface arising as the scaling limit of random planar maps. Schramm-Loewner evolution (SLE) is a random planar curve describing the scaling limits of interfaces in many statistical physics models. Liouville conformal field theory (LCFT) is the quantum …
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Open strings and analytic non-integrability
… theory instead. Based on this concept the integrability, or rather non-integrability of a gauge theory system can be determined using semi-classical string solutions. Integrability has become a coveted property in a system. It indicates that the system can be solved fully. Since there is no …
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Vortices, Painlevé integrability and projective geometry
… in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the …
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Complete integrability and geometrically induced representations
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Advancing integrability for strings in AdS3/CFT2
In this thesis we develop techniques of integrability in the study of dualities between two-dimensional conformal field theories and theories of closed strings on three-dimensional Anti-de Sitter background geometries. For several years after integrability was first applied to the 3d/2d dualities, …
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A study of integrability conditions for irrotational dust spacetimes
… waves interacting with matter), both imply integrability conditions in the exact non-linear case. The integrability conditions for the divergence-free magnetic Weyl tensor are identically satisfied in the linearized perturbation case, but are non-trivial in the exact non-linear case. This …
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Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… and unstable manifolds and the loss of complete integrability. Consequently, the system admits spatially chaotic solutions and a multiplicity of multimodal homoclinic solutions exist. Poincare sections associated with the loss of integrability are displayed. Homoclinic solutions are computed and …
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On the Integrability of Derivatives of Holomorphic and M-Subharmonic Inner Functions In the Unit Ball of Cn
<p>Let Bn be the unit ball in Cn. If f is a bounded holomorphic function, we say that f is inner provided that its modulus has a radial limit of 1 almost everywhere on Sn where Sn is the unit sphere.</p> <p>If a > -1 and p > 0 then Apa denotes the weighted Bergman space of all holomorphic functions …
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Regularity theory for nonlocal equations
… it is only possible to obtain higher integrability, in our nonlocal setting we are able to also prove a substantial amount of higher differentiability. Therefore, our results are in some sense of purely nonlocal type, following a recent trend of such results in the literature.<br /><br …
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Searching for self-duality in non-maximally supersymmetric backgrounds
… are of great interest due to their link to integrability. Fermionic T-duality has played a pivotal role in proving that the maximally supersymmetric background AdS₅ × S⁵ is self-dual. This background is also known to be integrable, therefore, when it was shown to be self-dual, the hypothesis …
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Some problems in the dynamics of spatially extended systems
… sine-Gordon equation and the ""Painleve test of integrability."" We present results of our numerical studies of the d.c. driven, damped sine-Gordon equation. We also present a nonperturbative proof of the persistence of soliton-like (""soliton"") and antisoliton-like (""antisoliton"") solutions …
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Lebesgue ▼-Measure and Riemann ▼-Integration
… the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, a …
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EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
… Sobolev-Hilbert H-space, as it only needs square integrability of the gradients of the functions involved. Our results generalize exactly certain well-known results on Laplace's spherical harmonics in classical mathematical physics.
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Rational matrix differential operators and integrable systems of PDEs
A key feature of integrability for systems of evolution PDEs ut = F(u), where F lies in a differential algebra of functionals V and u = (U1, ... , ul) depends on one space variable x and time t, is to be part of an infinite hierarchy of generalized symmetries. Recall that V carries a Lie algebra …
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On extended supersymmetry in two and four dimensions.
… aspects. On they way we use various methods of integrability, conformal filed theories and string theory to achieve our goals. We start with describing physics of two dimensional N = 2 sigma models, geometry of their target spaces, their BPS spectra, and how they can de derived from four …
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Equivariant Deformations of Horospherical Surfaces
… indicate how the Goursat transformation law and integrability conditions for the "spin curve" of a horospherical surface are analogous to the Lorentz transformation law and equations of motion for the wavefunction of a massless fermion.
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On Inflationary cosmological models
… do not find exact solutions because of the non-integrability of the field equations, but we can investigate their global properties (and hence their stability) by means of methods of the theory of dynamical systems.
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Integrable symmetric fields in computational design : from stable woven shells to seamless parameterizations
… formulation of an exact formulation of discrete integrability which extends to symmetric frame fields in volumes. The key insight of our work was the introduction of a new "mixed-moment" representation for symmetric frames to the geometry processing literature. We prove that this representation …
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Continuous and quad-graph integrable models with a boundary: Reflection maps and 3D-boundary consistency
… method developed by Fokas. The notion of integrability is argued by constructing an explicit generating function for conserved quantities. Then, by adapting a mirror image technique, an inverse scattering method with an integrable boundary is constructed in order to obtain N-soliton …
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