The Experts below are selected from a list of 117 Experts worldwide ranked by ideXlab platform
Dieter H. Mayer - One of the best experts on this subject based on the ideXlab platform.
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On the thermodynamic formalism for the Gauss map
Communications in Mathematical Physics, 1991Co-Authors: Dieter H. MayerAbstract:We study the generalized transfer Operator of the Gauss map Tx=(1/x) mod 1 on the unit interval. This Operator, which for β=1 is the familiar Perron-Frobenius Operator of T , can be defined for Re β>1/2 as a Nuclear Operator either on the Banach space A _∞( D ) of holomorphic functions over a certain disc D or on the Hilbert space of functions belonging to some Hardy class of functions over the half plane H _−1/2. The spectra of on the two spaces are identical. On the space is isomorphic to an integral Operator with kernel the Bessel function $$\mathfrak{F}_{2\beta - 1} (2\sqrt {st} )$$ and hence to some generalized Hankel transform. This shows that has real spectrum for real β>1/2. On the space A _∞( D ) the Operator can be analytically continued to the entire β-plane with simple poles at $$\beta = \beta _k = (1 - k)/2,k = 0,1,2,...$$ and residue the rank 1 Operator $$\mathcal{N}^{(k)} f = \tfrac{1}{2}(1/k!)f^{(k)} (0)$$ . From this similar analyticity properties for the Fredholm determinant of and hence also for Ruelle's zeta function follow. Another application is to the function $$\zeta _M (\beta ) = \sum\limits_{n = 1}^\infty {[n]^\beta } $$ , where [ n ] denotes the irrational [n]=(n+(n ^2+4)^1/2)/2. ζ M ( β ) extends to a meromorphic function in the β-plane with the only poles at β=±1 both with residue 1.
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On the thermodynamic formalism for the gauss map
Communications in Mathematical Physics, 1990Co-Authors: Dieter H. MayerAbstract:We study the generalized transfer Operator ℒ_ β f ( z )= $$\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{z + n}}} \right)^{2\beta } \times f\left( {1/\left( {z + n} \right)} \right)} $$ of the Gauss map Tx=(1/x) mod 1 on the unit interval. This Operator, which for β=1 is the familiar Perron-Frobenius Operator of T , can be defined for Re β>1/2 as a Nuclear Operator either on the Banach space A _∞( D ) of holomorphic functions over a certain disc D or on the Hilbert space ℋ _Reβ ^(2) ( H _-1/2 of functions belonging to some Hardy class of functions over the half plane H _−1/2. The spectra of −_ β on the two spaces are identical. On the space ℋ _Reβ ^(2) ( H _-1/2 ℒ_ β is isomorphic to an integral Operator K _ β with kernel the Bessel function $$\mathfrak{F}_{2\beta - 1} (2\sqrt {st} )$$ and hence to some generalized Hankel transform. This shows that ℒ_ β has real spectrum for real β>1/2. On the space A _∞( D ) the Operator ℒ_ β can be analytically continued to the entire β-plane with simple poles at β = β _ k =(1- k )/2, k =0, 1, 2,..., and residue the rank 1 Operator N ^( k ) f =1/2(1/ K !) f ^( k )(0) . From this similar analyticity properties for the Fredholm determinant det (1-ℒ_ β ) of ℒ_ β and hence also for Ruelle's zeta function follow. Another application is to the function $$\zeta _{\rm M} (\beta ) = \sum\limits_{n = 1}^\infty {\left[ n \right]^\beta } $$ , where [ n ] denotes the irradional [ n ]=( n +( n ^2+4)^1/2)/2.ζ_ M ( β ) extends to a meromorphic function in the β-plane with the only poles at β=±1 both with residue 1.
Jérôme Paméla - One of the best experts on this subject based on the ideXlab platform.
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Preparation for tritiated waste management of fusion facilities: Interim storage WAC
Fusion Engineering and Design, 2016Co-Authors: Christelle Decanis, Daniel Canas, F. Derasse, Jérôme PamélaAbstract:Abstract Considering the high mobility of tritium through the package in which it is contained, the new 50-year storage concepts proposed by the French Alternative Energies and Atomic Energy Commission (CEA) currently provide a solution adapted to the management of waste with tritium concentrations higher than the accepted limits in the disposals. The 50-year intermediate storage corresponds to 4 tritium radioactive periods i.e., a tritium reduction by a factor 16. This paper details the approach implemented to define the waste acceptance criteria (WAC) for an interim storage facility that not only takes into account the specificity of tritium provided by the reference scheme for the management of tritiated waste in France, but also the producers’ needs, the safety analysis of the facility and Andra’s disposal requirements. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is also a way to check in advance, during the design phase of the waste treatment chain, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.): the results obtained are shown. It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.
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Methodology to prepare the tritiated waste management : Defining WAC for an interim storage facility
2015Co-Authors: Christelle Decanis, Daniel Canas, F. Derasse, Jérôme PamélaAbstract:Considering the high mobility of tritium through the package in which it is contained, the new 50-year storage concepts proposed by the CEA currently provide a solution adapted to the management of waste with high tritium concentrations. The 50-year intermediate storage corresponds to 4 tritium radioactive periods i.e. a tritium reduction by a factor 16.The waste acceptance criteria (WAC) for this interim storage concept will take into account the criteria applicable at Andra disposal centers, the reference scheme for the management of tritiated waste in France, and the safety of the facility. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is a way to check in advance, during the design phase, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.). It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.This paper details how the work done by the CEA has led to a storage facility project that not only takes into account the specificity of tritium, but also the producers' needs and Andra's disposal requirements. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is also a way to check in advance, during the design phase of the waste treatment chain, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.): the results obtained are shown. It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.
Julio Delgado - One of the best experts on this subject based on the ideXlab platform.
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The Trace of Nuclear Operators on L ^ p (μ) for σ-Finite Borel Measures on Second Countable Spaces
Integral Equations and Operator Theory, 2010Co-Authors: Julio DelgadoAbstract:Let Ω be a second countable topological space and μ be a σ −finite measure on the Borel sets $${\mathcal{M}}$$ . Let T be a Nuclear Operator on $${L^p({\Omega},{\mathcal{M}},\mu) }$$ , 1 < p
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The Trace of Nuclear Operators on L p (μ) for σ-Finite Borel Measures on Second Countable Spaces
Integral Equations and Operator Theory, 2010Co-Authors: Julio DelgadoAbstract:Let Ω be a second countable topological space and μ be a σ−finite measure on the Borel sets \({\mathcal{M}}\). Let T be a Nuclear Operator on \({L^p({\Omega},{\mathcal{M}},\mu) }\), 1 < p < ∞, in this work we establish a formula for the trace of T. A preliminary trace formula is established applying the general theory of traces on Operator ideals introduced by Pietsch and a characterization of Nuclear Operators for σ−finite measures. We also use the Doob’s maximal theorem for martingales with the purpose of studying the kernel k(x, y) of T on the diagonal.
Christelle Decanis - One of the best experts on this subject based on the ideXlab platform.
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Preparation for tritiated waste management of fusion facilities: Interim storage WAC
Fusion Engineering and Design, 2016Co-Authors: Christelle Decanis, Daniel Canas, F. Derasse, Jérôme PamélaAbstract:Abstract Considering the high mobility of tritium through the package in which it is contained, the new 50-year storage concepts proposed by the French Alternative Energies and Atomic Energy Commission (CEA) currently provide a solution adapted to the management of waste with tritium concentrations higher than the accepted limits in the disposals. The 50-year intermediate storage corresponds to 4 tritium radioactive periods i.e., a tritium reduction by a factor 16. This paper details the approach implemented to define the waste acceptance criteria (WAC) for an interim storage facility that not only takes into account the specificity of tritium provided by the reference scheme for the management of tritiated waste in France, but also the producers’ needs, the safety analysis of the facility and Andra’s disposal requirements. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is also a way to check in advance, during the design phase of the waste treatment chain, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.): the results obtained are shown. It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.
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Methodology to prepare the tritiated waste management : Defining WAC for an interim storage facility
2015Co-Authors: Christelle Decanis, Daniel Canas, F. Derasse, Jérôme PamélaAbstract:Considering the high mobility of tritium through the package in which it is contained, the new 50-year storage concepts proposed by the CEA currently provide a solution adapted to the management of waste with high tritium concentrations. The 50-year intermediate storage corresponds to 4 tritium radioactive periods i.e. a tritium reduction by a factor 16.The waste acceptance criteria (WAC) for this interim storage concept will take into account the criteria applicable at Andra disposal centers, the reference scheme for the management of tritiated waste in France, and the safety of the facility. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is a way to check in advance, during the design phase, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.). It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.This paper details how the work done by the CEA has led to a storage facility project that not only takes into account the specificity of tritium, but also the producers' needs and Andra's disposal requirements. This will lead to define a set of waste specifications that describe the generic criteria such as acceptable waste forms, general principles and specific issues, e.g. conditioning, radioactive content, tritium content, waste tracking system, and quality control. This approach is also a way to check in advance, during the design phase of the waste treatment chain, how the future waste could be integrated into the overall waste management routes and identify possible key points that need further investigations (design changes, selection of materials, etc.): the results obtained are shown. It supports the Nuclear Operator to ensure the compliance of the future waste packages with the disposal acceptance criteria.
Franz Hanauska - One of the best experts on this subject based on the ideXlab platform.
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On the distribution of the discrete spectrum of Nuclearly perturbed Operators in Banach spaces
Indian Journal of Pure and Applied Mathematics, 2015Co-Authors: Michael Demuth, Franz HanauskaAbstract:Let Z _0 be a bounded Operator in a Banach space X with purely essential spectrum and K a Nuclear Operator in X . We construct a holomorphic function the zeros of which coincide with the discrete spectrum of Z _0+ K and derive a Lieb-Thirring type inequality. We obtain estimates for the number of eigenvalues in certain regions of the complex plane and an estimate for the asymptotics of the eigenvalues approaching to the essential spectrum of Z _0.
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On the distribution of the discrete spectrum of Nuclearly perturbed Operators in Banach spaces
arXiv: Spectral Theory, 2013Co-Authors: Michael Demuth, Franz HanauskaAbstract:Let Z_0 be a bounded Operator in a Banach space X with purely essential spectrum and K a Nuclear Operator in X. Using methods of complex analysis we study the discrete spectrum of Z_0+K and derive a Lieb-Thirring type inequality. We obtain estimates for the number of eigenvalues in certain regions of the complex plane and an estimate for the asymptotics of the eigenvalues approaching to the essential spectrum of Z_0
