The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Charles A. Weibel - One of the best experts on this subject based on the ideXlab platform.
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The Norm Residue Theorem in Motivic Cohomology
2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It proceeds to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. It then addresses symmetric powers of motives and motivic cohomology operations. The book unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
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The Norm Residue Theorem in Motivic Cohomology - Motivic Classifying Spaces
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter focuses on motivic classifying spaces. It first connects the motives
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The Norm Residue Theorem in Motivic Cohomology - Motives over S
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter shows that the operation φ
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The Norm Residue Theorem in Motivic Cohomology - Rost’s Chain Lemma
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter states and proves Rost's Chain Lemma. The proof (due to Markus Rost) does not use the inductive assumption that BL(n − 1) holds. Throughout this chapter,
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The Norm Residue Theorem in Motivic Cohomology - Existence of Rost Motives
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter fixes a Rost variety
Keith Conrad - One of the best experts on this subject based on the ideXlab platform.
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the mobius function and the Residue Theorem
Journal of Number Theory, 2005Co-Authors: Brian Conrad, Keith ConradAbstract:Abstract A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z [ T ] has infinitely many prime values unless there is a local obstruction. Replacing Z [ T ] with κ [ u ] [ T ] , where κ is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples.
Christian Haesemeyer - One of the best experts on this subject based on the ideXlab platform.
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The Norm Residue Theorem in Motivic Cohomology
2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It proceeds to describe the highly innovative geometric constructions of Markus Rost, including the construction of norm varieties, which play a crucial role in the proof. It then addresses symmetric powers of motives and motivic cohomology operations. The book unites various components of the proof that until now were scattered across many sources of varying accessibility, often with differing hypotheses, definitions, and language.
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The Norm Residue Theorem in Motivic Cohomology - Motivic Classifying Spaces
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter focuses on motivic classifying spaces. It first connects the motives
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The Norm Residue Theorem in Motivic Cohomology - Motives over S
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter shows that the operation φ
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The Norm Residue Theorem in Motivic Cohomology - Rost’s Chain Lemma
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter states and proves Rost's Chain Lemma. The proof (due to Markus Rost) does not use the inductive assumption that BL(n − 1) holds. Throughout this chapter,
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The Norm Residue Theorem in Motivic Cohomology - Existence of Rost Motives
The Norm Residue Theorem in Motivic Cohomology, 2019Co-Authors: Christian Haesemeyer, Charles A. WeibelAbstract:This chapter fixes a Rost variety
Wim Desmet - One of the best experts on this subject based on the ideXlab platform.
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optimal dynamic vibration absorber design for minimizing the band averaged input power using the Residue Theorem
Journal of Sound and Vibration, 2015Co-Authors: R D Amico, Bert Pluymers, Claus Claeys, Wim DesmetAbstract:Abstract This paper deals with an efficient strategy to improve the vibro-acoustic behavior of a structure over frequency bands. Genetic Algorithms are used to identify the optimal resonance frequency and location of Dynamic Vibration Absorbers (DVAs) which minimize the band-averaged input power into a plate, leading to an indirect reduction of the radiated acoustic power and global vibration. Instead of classic numerical quadrature schemes, the Residue Theorem is used to evaluate the band-averaged input power. This results into a considerable reduction of computational effort, as it requires only few function evaluations at complex frequencies, regardless of the analyzed bandwidth. The structural response is simulated by using the Wave Based Method (WBM). Besides an increased convergence rate as compared to classical element-based techniques, the WBM is also free in determining the optimal position of the DVAs, not restricting it to nodal grid locations. Moreover, when point connections are taken into account, only a small part of the WB matrices needs to be recomputed at each iteration, resulting in a strong reduction of the computation time. Numerical examples illustrate the benefits and the efficiency of the proposed optimization strategy.
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design sensitivity analysis and optimization of frequency averaged input power using the Residue Theorem
Computers & Structures, 2014Co-Authors: Roberto Damico, Bert Pluymers, Wim DesmetAbstract:The Residue Theorem is employed in the design optimization of a vibrating structure.The adjoint variable method is used for the design sensitivity computation.Numerical examples demonstrate the computational efficiency of the optimization scheme.High enhancement of the optimization process for the reduction of the radiated sound power. The Residue Theorem is employed in the design optimization of the frequency averaged power injected into a linear second-order system. The dynamic behavior of a vibrating structure is obtained with the finite element method and the frequency averaged input power into the structure is adopted as an objective function. The design sensitivity with respect to each structural element is computed by the adjoint variable method with consideration for the Residue Theorem. The proposed method highly enhances the computational efficiency of the optimization and the design of the optimization leads to substantial reduction of the radiated sound power from the structure.
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a refined use of the Residue Theorem for the evaluation of band averaged input power into linear second order dynamic systems
Journal of Sound and Vibration, 2014Co-Authors: Roberto Damico, Daan Huybrechs, Wim DesmetAbstract:Abstract In a recent work, a strategy was proposed which exploits the Residue Theorem as an efficient tool for evaluating the frequency averaged input power into vibrating systems. In this paper, such a technique is generalised and further insight and improvements are presented. Evaluating band-averages requires the solution of a weighted integral over a real frequency variable. In this paper, the integration path is moved to the complex plane, where the input mobility shows a smoother behaviour. Consequently, a smaller number of quadrature points are needed to perform an accurate integration, which leads to a significant reduction of computational time. In addition, the connection between the use of quadrature rules in the complex plane and weighting functions on real frequencies is considered. Two application examples prove the accuracy of the present strategy for different quadrature rules. Adaptive integration schemes are also investigated.
Brian Conrad - One of the best experts on this subject based on the ideXlab platform.
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the mobius function and the Residue Theorem
Journal of Number Theory, 2005Co-Authors: Brian Conrad, Keith ConradAbstract:Abstract A classical conjecture of Bouniakowsky says that a non-constant irreducible polynomial in Z [ T ] has infinitely many prime values unless there is a local obstruction. Replacing Z [ T ] with κ [ u ] [ T ] , where κ is a finite field, the obvious analogue of Bouniakowsky's conjecture is false. All known counterexamples can be explained by a new obstruction, and this obstruction can be used to fix the conjecture. The situation is more subtle in characteristic 2 than in odd characteristic. Here, we illustrate the general theory for characteristic 2 in some examples.