The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Lawrence E Wilson - One of the best experts on this subject based on the ideXlab platform.
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Corrigendum to “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132]
Journal of Algebra, 2012Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract An error in the proof of Theorem 19, in “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132] is corrected.
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corrigendum to the multiplicative Jordan Decomposition in group rings ii j algebra 316 1 2007 109 132
Journal of Algebra, 2012Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract An error in the proof of Theorem 19, in “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132] is corrected.
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the multiplicative Jordan Decomposition in group rings ii
Journal of Algebra, 1998Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract We classify the finite 2-groups G whose integral group rings Z [ G ] have the multiplicative Jordan Decomposition property. In addition to those cases already known, these include three further cases of order thirty-two and no others. We also give a theorem which severely restricts the structure of those finite groups G with Z [ G ] having this property which are not of order 2 a 3 b for some a , b .
Robert Rettinger - One of the best experts on this subject based on the ideXlab platform.
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a reference correction of effective Jordan Decomposition
Theory of Computing Systems \ Mathematical Systems Theory, 2006Co-Authors: Xizhong Zheng, Robert RettingerAbstract:In our paper "Effective Jordan Decomposition" (Theory of Computing Systems, 38 (2005), 189-209; DOI: 10.1007/s00224-004-1193-z) there is a reference error. The referenced paper [15] should be "M. Josephy. Composing functions of bounded variation. Proc. Amer. Math. Soc. 83:354-356, 1981". The result mentioned in our paper (second paragraph of page 194) belongs of course to Josephy instead of Young. We apologize for this mistake.
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effective Jordan Decomposition
Theory of Computing Systems \ Mathematical Systems Theory, 2005Co-Authors: Xizhong Zheng, Robert RettingerAbstract:The Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper investigates the effective version of Jordan Decomposition and discusses the properties of variation of computable real functions. First we show that the effective version of Jordan Decomposition does not hold in general. Then we give a sufficient and necessary condition for computable real functions of bounded variation which have an effective Jordan Decomposition. Applying this condition, we construct a computable real function which has a computable modulus of absolute continuity (hence of bounded variation) but is not effectively Jordan decomposable. Finally, we prove a version of this result restricted to polynomial time which answers negatively an open question of Ko in [8].
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STACS - On the Effective Jordan Decomposability
Lecture Notes in Computer Science, 2003Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:The classical Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan Decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functions. Using this condition, we prove further that there is a computable real function which has even a computable modulus of absolute continuity (hence is of bounded variation) but it is not a difference of any two computable increasing functions. The polynomial time version of this result holds too and this gives a negative answer to an open question of Ko in [6].
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On the effective Jordan decomposability
Lecture Notes in Computer Science, 2003Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:The classical Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan Decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functions. Using this condition, we prove further that there is a computable real function which has even a computable modulus of absolute continuity (hence is of bounded variation) but it is not a difference of any two computable increasing functions. The polynomial time version of this result holds too and this gives a negative answer to an open question of Ko in [6].
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Effectively Absolute Continuity and Effective Jordan Decomposability
Electronic Notes in Theoretical Computer Science, 2002Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:Abstract Classically, any absolute continuous real function is of bounded variation and hence can always be expressed as a difference of two increasing continuous functions (so-called Jordan Decomposition). The effective version of this result is not true. In this paper we give a sufficient and necessary condition for computable real functions which can be expressed as two computable increasing functions (effectively Jordan decomposable, or EJD for short). Using this condition, we prove further that there is a computable real function which has a computable modulus of absolute continuity but is not EJD. The polynomial time version of this result holds accordingly too and this gives a negative answer to an open question of Ko in [6].
Ryan C Vinroot - One of the best experts on this subject based on the ideXlab platform.
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galois group action and Jordan Decomposition of characters of finite reductive groups with connected center
Journal of Algebra, 2019Co-Authors: Bhama Srinivasan, Ryan C VinrootAbstract:Abstract Let G be a connected reductive group with connected center defined over F q , with Frobenius morphism F. Given an irreducible complex character χ of G F with its Jordan Decomposition, and a Galois automorphism σ ∈ Gal ( Q ‾ / Q ) , we give the Jordan Decomposition of the image χ σ of χ under the action of σ on its character values.
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galois group action and Jordan Decomposition of characters of finite reductive groups with connected center
arXiv: Representation Theory, 2018Co-Authors: Bhama Srinivasan, Ryan C VinrootAbstract:Let $\mathbf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism F. Given an irreducible complex character $\chi$ of $\mathbf{G}^F$ with its Jordan Decomposition, and a Galois automorphism $\sigma \in \mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$, we give the Jordan Decomposition of the image ${^\sigma \chi}$ of $\chi$ under the action of $\sigma$ on its character values.
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Jordan Decomposition and real valued characters of finite reductive groups with connected center
Bulletin of The London Mathematical Society, 2015Co-Authors: Bhama Srinivasan, Ryan C VinrootAbstract:Let $\bf{G}$ be a connected reductive group with connected center defined over $\mathbb{F}_q$, with Frobenius morphism $F$. We parameterize all of the real-valued irreducible complex characters of ${\bf G}^F$ using the Jordan Decomposition of characters.
Alfred W Hales - One of the best experts on this subject based on the ideXlab platform.
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Corrigendum to “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132]
Journal of Algebra, 2012Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract An error in the proof of Theorem 19, in “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132] is corrected.
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corrigendum to the multiplicative Jordan Decomposition in group rings ii j algebra 316 1 2007 109 132
Journal of Algebra, 2012Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract An error in the proof of Theorem 19, in “The multiplicative Jordan Decomposition in group rings, II” [J. Algebra 316 (1) (2007) 109–132] is corrected.
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the multiplicative Jordan Decomposition in group rings ii
Journal of Algebra, 1998Co-Authors: Alfred W Hales, Inder Bir S Passi, Lawrence E WilsonAbstract:Abstract We classify the finite 2-groups G whose integral group rings Z [ G ] have the multiplicative Jordan Decomposition property. In addition to those cases already known, these include three further cases of order thirty-two and no others. We also give a theorem which severely restricts the structure of those finite groups G with Z [ G ] having this property which are not of order 2 a 3 b for some a , b .
Xizhong Zheng - One of the best experts on this subject based on the ideXlab platform.
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a reference correction of effective Jordan Decomposition
Theory of Computing Systems \ Mathematical Systems Theory, 2006Co-Authors: Xizhong Zheng, Robert RettingerAbstract:In our paper "Effective Jordan Decomposition" (Theory of Computing Systems, 38 (2005), 189-209; DOI: 10.1007/s00224-004-1193-z) there is a reference error. The referenced paper [15] should be "M. Josephy. Composing functions of bounded variation. Proc. Amer. Math. Soc. 83:354-356, 1981". The result mentioned in our paper (second paragraph of page 194) belongs of course to Josephy instead of Young. We apologize for this mistake.
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effective Jordan Decomposition
Theory of Computing Systems \ Mathematical Systems Theory, 2005Co-Authors: Xizhong Zheng, Robert RettingerAbstract:The Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper investigates the effective version of Jordan Decomposition and discusses the properties of variation of computable real functions. First we show that the effective version of Jordan Decomposition does not hold in general. Then we give a sufficient and necessary condition for computable real functions of bounded variation which have an effective Jordan Decomposition. Applying this condition, we construct a computable real function which has a computable modulus of absolute continuity (hence of bounded variation) but is not effectively Jordan decomposable. Finally, we prove a version of this result restricted to polynomial time which answers negatively an open question of Ko in [8].
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STACS - On the Effective Jordan Decomposability
Lecture Notes in Computer Science, 2003Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:The classical Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan Decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functions. Using this condition, we prove further that there is a computable real function which has even a computable modulus of absolute continuity (hence is of bounded variation) but it is not a difference of any two computable increasing functions. The polynomial time version of this result holds too and this gives a negative answer to an open question of Ko in [6].
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On the effective Jordan decomposability
Lecture Notes in Computer Science, 2003Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:The classical Jordan Decomposition Theorem says that any real function of bounded variation can be expressed as a difference of two increasing functions. This paper explores the effective version of Jordan Decomposition. We give a sufficient and necessary condition for those computable real functions of bounded variation which can be expressed as a difference of two computable increasing functions. Using this condition, we prove further that there is a computable real function which has even a computable modulus of absolute continuity (hence is of bounded variation) but it is not a difference of any two computable increasing functions. The polynomial time version of this result holds too and this gives a negative answer to an open question of Ko in [6].
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Effectively Absolute Continuity and Effective Jordan Decomposability
Electronic Notes in Theoretical Computer Science, 2002Co-Authors: Xizhong Zheng, Robert Rettinger, Burchard Von BraunmühlAbstract:Abstract Classically, any absolute continuous real function is of bounded variation and hence can always be expressed as a difference of two increasing continuous functions (so-called Jordan Decomposition). The effective version of this result is not true. In this paper we give a sufficient and necessary condition for computable real functions which can be expressed as two computable increasing functions (effectively Jordan decomposable, or EJD for short). Using this condition, we prove further that there is a computable real function which has a computable modulus of absolute continuity but is not EJD. The polynomial time version of this result holds accordingly too and this gives a negative answer to an open question of Ko in [6].
