The Experts below are selected from a list of 36714 Experts worldwide ranked by ideXlab platform
Martha Guzmanpartida - One of the best experts on this subject based on the ideXlab platform.
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the s convolution with singular kernels in the Euclidean Case and the product domain Case
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Josefina Alvarez, Martha GuzmanpartidaAbstract:Abstract We characterize those tempered distributions which are S ′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean Case and the product domain Case. In the Euclidean Case, we consider a class of kernels that includes Riesz kernels, Calderon–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hormander multipliers. In the product domain Case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n -dimensional Hilbert kernel.
Josefina Alvarez - One of the best experts on this subject based on the ideXlab platform.
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Optimal codomains for the Laplace operator and the product Laplace operator
Journal of Function Spaces and Applications, 2007Co-Authors: Josefina Alvarez, Lloyd Edgar S. MoyoAbstract:An optimal codomain for an operator P (∂) with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P (∂)S=T. We identify optimal codomains for the Laplace operator in the Euclidean Case and for the product Laplace operator in the product domain Case. The convolution is understood in the sense of the S′-convolution.
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The S′-convolution with singular kernels in the Euclidean Case and the product domain Case
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Josefina Alvarez, Martha Guzmán-partidaAbstract:Abstract We characterize those tempered distributions which are S ′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean Case and the product domain Case. In the Euclidean Case, we consider a class of kernels that includes Riesz kernels, Calderon–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hormander multipliers. In the product domain Case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n -dimensional Hilbert kernel.
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the s convolution with singular kernels in the Euclidean Case and the product domain Case
Journal of Mathematical Analysis and Applications, 2002Co-Authors: Josefina Alvarez, Martha GuzmanpartidaAbstract:Abstract We characterize those tempered distributions which are S ′-convolvable with a given class of singular convolution kernels. We study both, the Euclidean Case and the product domain Case. In the Euclidean Case, we consider a class of kernels that includes Riesz kernels, Calderon–Zygmund singular convolution kernels, finite part distributions defined by hypersingular convolution kernels, and Hormander multipliers. In the product domain Case, we consider a class of singular kernels introduced by Fefferman and Stein as a generalization of the n -dimensional Hilbert kernel.
Gregory Faye - One of the best experts on this subject based on the ideXlab platform.
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Pattern Formation for the Swift-Hohenberg Equation on the Hyperbolic Plane
Journal of Dynamics and Differential Equations, 2015Co-Authors: Pascal Chossat, Gregory FayeAbstract:In this paper we present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincare disc \(\mathbb{D }\). Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of \(\mathbb{D }\) also called H-planforms in reference with the “planforms” introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of \(\mathbb{D }\) and periodic in the “transverse” direction. We highlight our theoretical results with a selection of numerical simulations.
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pattern formation for the swift hohenberg equation on the hyperbolic plane
Journal of Dynamics and Differential Equations, 2015Co-Authors: Pascal Chossat, Gregory FayeAbstract:In this paper we present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincare disc \(\mathbb{D }\). Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of \(\mathbb{D }\) also called H-planforms in reference with the “planforms” introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of \(\mathbb{D }\) and periodic in the “transverse” direction. We highlight our theoretical results with a selection of numerical simulations.
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pattern formation for the swift hohenberg equation on the hyperbolic plane
arXiv: Mathematical Physics, 2013Co-Authors: Pascal Chossat, Gregory FayeAbstract:We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincar\'e disc D. Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of D also called H-planforms in reference with the "planforms" introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of D and periodic in the "transverse" direction. We highlight our theoretical results with a selection of numerical simulations.
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Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
arXiv: Mathematical Physics, 2013Co-Authors: Pascal Chossat, Gregory FayeAbstract:We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincar\'e disc D. Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of D also called H-planforms in reference with the "planforms" introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of D and periodic in the "transverse" direction. We highlight our theoretical results with a selection of numerical simulations.
Eugene Levner - One of the best experts on this subject based on the ideXlab platform.
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A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean Case
Discrete Applied Mathematics, 2009Co-Authors: Vladimir Kats, Eugene LevnerAbstract:In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an m-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric Case, O(m^5logm).
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MICAI - A polynomial algorithm for 2-cyclic robotic scheduling
Lecture Notes in Computer Science, 2006Co-Authors: Vladimir Kats, Eugene LevnerAbstract:We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing systems served by computer-controlled robots. The problem is to find the minimum cycle time for the so-called 2-cyclic (or “2-degree”) schedules, in which exactly two parts enter and two parts leave the production line during each cycle. An earlier known polynomial time algorithm for this problem was applicable only to the Euclidean Case, where the transportation times must satisfy the “triangle inequality”. In this paper we study a general non-Euclidean Case. Applying a geometrical approach, we construct a polynomial time algorithm of complexity O(m5 log m).
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A polynomial algorithm for 2-cyclic robotic scheduling
Lecture Notes in Computer Science, 2006Co-Authors: Vladimir Kats, Eugene LevnerAbstract:We solve a single-robot m-machine cyclic scheduling problem arising in flexible manufacturing systems served by computer-controlled robots. The problem is to find the minimum cycle time for the so-called 2-cyclic (or 2-degree) schedules, in which exactly two parts enter and two parts leave the production line during each cycle. An earlier known polynomial time algorithm for this problem was applicable only to the Euclidean Case, where the transportation times must satisfy the triangle inequality. In this paper we study a general non-Euclidean Case. Applying a geometrical approach, we construct a polynomial time algorithm of complexity O(m 5 log m).
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Minimizing the number of vehicles in periodic scheduling: The non-Euclidean Case
European Journal of Operational Research, 1998Co-Authors: Vladimir Kats, Eugene LevnerAbstract:In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed periodically repeating set of tasks where set-up times between tasks do not satisfy the triangle inequality. We reduce this problem to finding the minimal length cycle-cover in a graph. In a special Case, where the set-up times satisfy the triangle inequality, we reduce the scheduling problem to the assignment problem.
Pascal Chossat - One of the best experts on this subject based on the ideXlab platform.
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Pattern Formation for the Swift-Hohenberg Equation on the Hyperbolic Plane
Journal of Dynamics and Differential Equations, 2015Co-Authors: Pascal Chossat, Gregory FayeAbstract:In this paper we present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincare disc \(\mathbb{D }\). Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of \(\mathbb{D }\) also called H-planforms in reference with the “planforms” introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of \(\mathbb{D }\) and periodic in the “transverse” direction. We highlight our theoretical results with a selection of numerical simulations.
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pattern formation for the swift hohenberg equation on the hyperbolic plane
Journal of Dynamics and Differential Equations, 2015Co-Authors: Pascal Chossat, Gregory FayeAbstract:In this paper we present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincare disc \(\mathbb{D }\). Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of \(\mathbb{D }\) also called H-planforms in reference with the “planforms” introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of \(\mathbb{D }\) and periodic in the “transverse” direction. We highlight our theoretical results with a selection of numerical simulations.
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pattern formation for the swift hohenberg equation on the hyperbolic plane
arXiv: Mathematical Physics, 2013Co-Authors: Pascal Chossat, Gregory FayeAbstract:We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincar\'e disc D. Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of D also called H-planforms in reference with the "planforms" introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of D and periodic in the "transverse" direction. We highlight our theoretical results with a selection of numerical simulations.
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Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
arXiv: Mathematical Physics, 2013Co-Authors: Pascal Chossat, Gregory FayeAbstract:We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the Poincar\'e disc D. Different types of patterns are considered: spatially periodic stationary solutions, radial solutions and traveling waves, however there are significant differences in the results with the Euclidean Case. We apply equivariant bifurcation theory to the study of spatially periodic solutions on a given lattice of D also called H-planforms in reference with the "planforms" introduced for pattern formation in Euclidean space. We consider in details the Case of the regular octagonal lattice and give a complete descriptions of all H-planforms bifurcating in this Case. For radial solutions (in geodesic polar coordinates), we present a result of existence for stationary localized radial solutions, which we have adapted from techniques on the Euclidean plane. Finally, we show that unlike the Euclidean Case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf bifurcation to traveling waves which are invariant along horocycles of D and periodic in the "transverse" direction. We highlight our theoretical results with a selection of numerical simulations.