The Experts below are selected from a list of 66 Experts worldwide ranked by ideXlab platform
Michio Yoshiwaki - One of the best experts on this subject based on the ideXlab platform.
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Relative Derived Dimensions for cotilting modules
Journal of Algebra, 2017Co-Authors: Michio YoshiwakiAbstract:Abstract For a Noetherian ring R and a cotilting R-module T of injective Dimension at least 1, we prove that the Derived Dimension of R with respect to the category X T is precisely the injective Dimension of T by applying Auslander–Buchweitz theory and Ghost Lemma. In particular, when R is a commutative Noetherian Cohen–Macaulay local ring with a canonical module ω R and dim R ≥ 1 , the Derived Dimension of R with respect to the category of maximal Cohen–Macaulay modules is precisely dim R .
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Relative Derived Dimensions for cotilting modules
arXiv: Representation Theory, 2016Co-Authors: Michio YoshiwakiAbstract:For a Noetherian ring $R$ and a cotilting $R$-module $T$ of injective Dimension at least $1$, we prove that the Derived Dimension of $R$ with respect to the category $\mathcal{X}_T$ is precisely the injective Dimension of $T$ by applying Auslander-Buchweitz theory and Ghost Lemma. In particular, when $R$ is a commutative Noetherian local ring with a canonical module $\omega_R$ and $\dim R\ge1$, the Derived Dimension of R with respect to the category of maximal Cohen-Macaulay modules is precisely $\dim R$.
Peter J.t. Verheijen - One of the best experts on this subject based on the ideXlab platform.
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Influence of noise on power-law scaling functions and an algorithm for Dimension estimations
Physical Review E, 1997Co-Authors: Hans Oltmans, Peter J.t. VerheijenAbstract:The influence of Gaussian noise on power-law scaling functions of interpoint distances has been investigated. These functions appear in the estimation of the correlation Dimension a of the attractor of a chaotic dynamical system, where the relative number of pairwise distances smaller than r ~correlation integral! theoretically scales as r a . Assuming the noise added to each measurement is independent and the distribution of the distances is governed completely by the power-law scaling rule in the noise-free case, the scaling functions of the perturbed distances have been calculated exactly. By considering the limiting cases for small and large distances, a method is presented to estimate the variance of the added noise and approximations of the scaling functions, which are suitable for data analysis, are Derived. Dimension estimation can be improved by applying a nonlinear fit procedure to histograms of interpoint distances instead of the usual linear regression on log-log plots. @S1063-651X~97!04506-6#
Pu Zhang - One of the best experts on this subject based on the ideXlab platform.
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Algebras of Derived Dimension Zero
Communications in Algebra, 2008Co-Authors: Xiao-wu Chen, Pu ZhangAbstract:We prove that a finite-Dimensional algebra over an algebraically closed field is of Derived Dimension 0 if and only if it is an iterated tilted algebra of Dynkin type.
Hans Oltmans - One of the best experts on this subject based on the ideXlab platform.
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Influence of noise on power-law scaling functions and an algorithm for Dimension estimations
Physical Review E, 1997Co-Authors: Hans Oltmans, Peter J.t. VerheijenAbstract:The influence of Gaussian noise on power-law scaling functions of interpoint distances has been investigated. These functions appear in the estimation of the correlation Dimension a of the attractor of a chaotic dynamical system, where the relative number of pairwise distances smaller than r ~correlation integral! theoretically scales as r a . Assuming the noise added to each measurement is independent and the distribution of the distances is governed completely by the power-law scaling rule in the noise-free case, the scaling functions of the perturbed distances have been calculated exactly. By considering the limiting cases for small and large distances, a method is presented to estimate the variance of the added noise and approximations of the scaling functions, which are suitable for data analysis, are Derived. Dimension estimation can be improved by applying a nonlinear fit procedure to histograms of interpoint distances instead of the usual linear regression on log-log plots. @S1063-651X~97!04506-6#
M. Rostami - One of the best experts on this subject based on the ideXlab platform.
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An observation on Krull and Derived Dimensions of some topological lattices
2011Co-Authors: M. Rostami, Ilda Inácio RodriguesAbstract:Let $(L, \le)$, be an algebraic lattice. It is well-known that $(L, \le)$ with its topological structure is topologically scattered if and only if $(L, \le)$ is ordered scattered with respect to its algebraic structure. In this note we prove that, if $L$ is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then $L$ has Krull-Dimension if and only if $L$ has Derived Dimension. We also prove the same result for $\operatorname{\it spec} L$, the set of all prime elements of $L$. Hence the Dimensions on the lattice and on the spectrum coincide.
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On Dimensions of Spectral Spaces of Finite Lattices
2009Co-Authors: M. RostamiAbstract:In this note we prove that the Krull Dimension of a finite distributive lattice (L, ≤) coincide with the inductive Dimension and the Derived Dimension of the spectral space of L.