The Experts below are selected from a list of 2382 Experts worldwide ranked by ideXlab platform
Kalle Karu - One of the best experts on this subject based on the ideXlab platform.
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Vector bundles on toric varieties
Comptes Rendus Mathematique, 2012Co-Authors: Saman Gharib, Kalle KaruAbstract:Abstract Following Sam Payneʼs work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear Multivalued Function. Such Functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Cortinas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X , such that Y has a large Grothendieck group.
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Vector bundles on toric varieties
arXiv: Algebraic Geometry, 2011Co-Authors: Saman Gharib, Kalle KaruAbstract:CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group of perfect complexes and not vector bundles. Since the varieties are not quasi-projective, existence of nontrivial perfect complexes says nothing about the existence of nontrivial vector bundles. We thank Sam Payne for drawing our attention to the error and Christian Haesemeyer for explanations about the K-theory. Abstract: Following Sam Payne's work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear Multivalued Function. Such Functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Corti\~nas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X, such that Y has a large Grothendieck group.
Gabriela Marinoschi - One of the best experts on this subject based on the ideXlab platform.
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Existence for Diffusion Degenerate Problems
Degenerate Nonlinear Diffusion Equations, 2012Co-Authors: Angelo Favini, Gabriela MarinoschiAbstract:In this chapter we present another method for studying the well-posedness of a Multivalued degenerate fast diffusion equation by proposing an appropriate time discretization scheme. We consider that the degeneration of the equation is due to the vanishing of the diffusion coefficient and choose for this problem Robin boundary conditions which contain the Multivalued Function as well.
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Well posedness of a time-difference scheme for a degenerate fastdiffusion problem
Discrete & Continuous Dynamical Systems - B, 2010Co-Authors: Gabriela MarinoschiAbstract:We study a time-difference scheme for a nonlinear degenerate parabolic equation with a transport term. The model generally describes diffusion in porous media with the formation of a free boundary, this being expressed by the presence of a Multivalued Function in the equation. We consider singular boundary conditions which contain the Multivalued Function as well, and prove the stability and the convergence of the scheme, emphasizing the precise nature of the convergence. This approach is aimed to be a mathematical background which justifies the correctness of the numerical algorithm for computing the solution to this type of equations by avoiding the approximation of the Multivalued Function. The theory is illustrated by numerical results which put into evidence both the effects due to the equation degeneration and the formation and advance of the free boundary.
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Convergence of the Finite Difference Scheme for a Fast Diffusion Equation in Porous Media
Numerical Functional Analysis and Optimization, 2008Co-Authors: Cornelia Ciutureanu, Gabriela MarinoschiAbstract:We are concerned with an implicit scheme for the finite difference solution to a nonlinear parabolic equation with a Multivalued coefficient that describes the fast diffusion in a porous medium. The boundary conditions contain the Multivalued Function as well. We prove the stability and the convergence of the scheme, emphasizing the precise nature of convergence in this specific case, and compute the error level of the approximating solution. The method is aimed to simplify the numerical computations for the solutions to equations of this type, without performing an approximation of the Multivalued Function. The theory is illustrated by numerical results.
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The diffusive form of Richards’ equation with hysteresis
Nonlinear Analysis: Real World Applications, 2008Co-Authors: Gabriela MarinoschiAbstract:Abstract Coupling hysteretic hydraulic laws with the pressure form of Richards’ equation, a mathematical model of a hysteretic wetting–drying cycle of a soil is settled. The particularity of the model resides in the blowing-up diffusion coefficient characterizing a strongly nonlinear behavior of the porous medium and in certain relationships between the hydraulic Functions accounting for a sufficiently realistic hysteretic evolution of the envisaged process. The hysteretic effect of the hydraulic laws can be regained in the hysteretic behavior of the Multivalued Function defined as an antiderivative of the diffusivity Function. We investigate the well-posedness of the model in appropriate Functional spaces.
Hiroo Azuma - One of the best experts on this subject based on the ideXlab platform.
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dynamics of the bloch vector in the thermal jaynes cummings model
Physical Review A, 2008Co-Authors: Hiroo AzumaAbstract:In this paper, we investigate the dynamics of the Bloch vector of a single two-level atom which interacts with a single quantized electromagnetic field mode according to the Jaynes-Cummings model, where the field is initially prepared in a thermal state. The time evolution of the Bloch vector $\mathbit{S}(t)$ seems to be in complete disorder because of the thermal distribution of the initial state of the field. Both the norm and the direction of $\mathbit{S}(t)$ oscillate hard and their periods seem infinite. We observe that the trajectory of the time evolution of $\mathbit{S}(t)$ in the two- or three-dimensional space does not form a closed path. To remove the fast frequency oscillation from the trajectory, we take the time average of the Bloch vector $\mathbit{S}(t)$. We examine the histogram of ${\phantom{|}{S}_{z}(n\ensuremath{\Delta}t)|n=0,1,\dots{},N}$ for small $\ensuremath{\Delta}t$ and large $N$. It represents an absolute value of a derivative of the inverse Function of ${S}_{z}(t)$. [When the inverse Function of $y={S}_{z}(t)$ is a Multivalued Function, the histogram represents a summation of the absolute values of its derivatives at points whose real parts are equal to $y$ on the Riemann surface.] We examine the dependence of the variance of the histogram on the temperature of the field. We estimate the lower bound of the entanglement between the atom and the field.
José Santos-victor - One of the best experts on this subject based on the ideXlab platform.
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Online learning of single-and Multivalued Functions with an infinite mixture of linear experts
Neural computation, 2013Co-Authors: Bruno Damas, José Santos-victorAbstract:We present a supervised learning algorithm for estimation of generic input-output relations in a real-time, online fashion. The proposed method is based on a generalized expectation-maximization approach to fit an infinite mixture of linear experts IMLE to an online stream of data samples. This probabilistic model, while not fully Bayesian, can efficiently choose the number of experts that are allocated to the mixture, this way effectively controlling the complexity of the resulting model. The result is an incremental, online, and localized learning algorithm that performs nonlinear, multivariate regression on multivariate outputs by approximating the target Function by a linear relation within each expert input domain and that can allocate new experts as needed. A distinctive feature of the proposed method is the ability to learn Multivalued Functions: one-to-many mappings that naturally arise in some robotic and computer vision learning domains, using an approach based on a Bayesian generative model for the predictions provided by each of the mixture experts. As a consequence, it is able to directly provide forward and inverse relations from the same learned mixture model. We conduct an extensive set of experiments to evaluate the proposed algorithm performance, and the results show that it can outperform state-of-the-art online Function approximation algorithms in single-valued regression, while demonstrating good estimation capabilities in a Multivalued Function approximation context.
Saman Gharib - One of the best experts on this subject based on the ideXlab platform.
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Vector bundles on toric varieties
Comptes Rendus Mathematique, 2012Co-Authors: Saman Gharib, Kalle KaruAbstract:Abstract Following Sam Payneʼs work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear Multivalued Function. Such Functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Cortinas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X , such that Y has a large Grothendieck group.
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Vector bundles on toric varieties
arXiv: Algebraic Geometry, 2011Co-Authors: Saman Gharib, Kalle KaruAbstract:CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group of perfect complexes and not vector bundles. Since the varieties are not quasi-projective, existence of nontrivial perfect complexes says nothing about the existence of nontrivial vector bundles. We thank Sam Payne for drawing our attention to the error and Christian Haesemeyer for explanations about the K-theory. Abstract: Following Sam Payne's work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear Multivalued Function. Such Functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Corti\~nas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X, such that Y has a large Grothendieck group.
