Ubiquity of relative regular sequences and proper sequences

K-Theory ◽  
1994 ◽  
Vol 8 (1) ◽  
pp. 81-106 ◽  
Author(s):  
Mihai Cipu ◽  
Mario Fiorentini
Keyword(s):  
Regular Sequences

The Main Case for Regular Sequences

2001 ◽  
pp. 96-104
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

The Main Case for Generic Regular Sequences

2001 ◽  
pp. 85-95
Author(s):  
Günter Scheja ◽  
Uwe Storch
Keyword(s):  
Regular Sequences

scholarly journals Some New Methods in the Theory of $m$-Quasi-Invariants

10.37236/1877 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
J. Bell ◽  
A. M. Garsia ◽  
N. Wallach
Keyword(s):  
Symmetric Functions ◽  
Free Module ◽  
Finitely Generated ◽  
Graded Algebras ◽  
New Approach ◽  
Elementary Symmetric Functions ◽  
New Methods ◽  
Regular Sequences

We introduce here a new approach to the study of $m$-quasi-invariants. This approach consists in representing $m$-quasi-invariants as $N^{tuples}$ of invariants. Then conditions are sought which characterize such $N^{tuples}$. We study here the case of $S_3$ $m$-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions $e_1,e_2,e_3$ which explains certain observed properties of $S_3$ $m$-quasi-invariants. We also use basic results on finitely generated graded algebras to derive some general facts about regular sequences of $S_n$ $m$-quasi-invariants

scholarly journals Regular sequences and synchronized sequences in abstract numeration systems

2022 ◽  
Vol 101 ◽  
pp. 103475
Author(s):  
Émilie Charlier ◽  
Célia Cisternino ◽  
Manon Stipulanti
Keyword(s):  
Regular Sequences ◽  
Numeration Systems

scholarly journals Proregular sequences, local cohomology, and completion

2003 ◽  
Vol 92 (2) ◽  
pp. 161 ◽  
Author(s):  
Peter Schenzel
Keyword(s):  
Noetherian Ring ◽  
Local Cohomology ◽  
Čech Complex ◽  
Regular Sequences ◽  
Local Cohomology Modules ◽  
Derived Functors ◽  
Adic Completion ◽  
Cech Complex ◽  
Cohomology Modules ◽  
The Ideal

As a certain generalization of regular sequences there is an investigation of weakly proregular sequences. Let $M$ denote an arbitrary $R$-module. As the main result it is shown that a system of elements $\underline x$ with bounded torsion is a weakly proregular sequence if and only if the cohomology of the Čech complex $\check C_{\underline x} \otimes M$ is naturally isomorphic to the local cohomology modules $H_{\mathfrak a}^i(M)$ and if and only if the homology of the co-Čech complex $\mathrm{RHom} (\check C_{\underline x}, M)$ is naturally isomorphic to $\mathrm{L}_i \Lambda^{\mathfrak a}(M),$ the left derived functors of the $\mathfrak a$-adic completion, where $\mathfrak a$ denotes the ideal generated by the elements $\underline x$. This extends results known in the case of $R$ a Noetherian ring, where any system of elements forms a weakly proregular sequence of bounded torsion. Moreover, these statements correct results previously known in the literature for proregular sequences.

scholarly journals Syzygetic ideals, regular sequences, and a question of Simis

1989 ◽  
Vol 121 (2) ◽  
pp. 310-314 ◽  
Author(s):  
Javier Barja ◽  
Antonio G Rodicio
Keyword(s):  
Regular Sequences

scholarly journals Regular Sequences of Quasi-Nonexpansive Operators and Their Applications

2018 ◽  
Vol 28 (2) ◽  
pp. 1508-1532 ◽  
Author(s):  
Andrzej Cegielski ◽  
Simeon Reich ◽  
Rafał Zalas
Keyword(s):  
Regular Sequences ◽  
Nonexpansive Operators

An Investigation of the ‘Chronometer’ Factor in Bird Navigation

1955 ◽  
Vol 32 (1) ◽  
pp. 39-58
Author(s):  
G. V. T. MATTHEWS
Keyword(s):  
Local Time ◽  
The Sun ◽  
The West ◽  
Orientation Data ◽  
Regular Sequences

1. An investigation was made of that part of the sun navigation hypothesis which proposes that birds detect longitude displacement by comparing home time (provided by an internal ‘chronometer’) with local time (estimated from the highest point of the sun arc). 2. Shearwaters were exposed for 4 days, and pigeons for ten days, to an artificial day 3 hr. in advance of normal. This did not result in any confusion of their orientation when released to the east. 3. More drastic treatment was then used, pigeons being subjected to 4-5 days of irregular light/dark sequences, followed by 5-11 days of regular sequences, advanced or retarded with respect to normal. 4. In tests from the west (2), east and north after this treatment, the ‘chronometers’ had apparantly been affected and the birds showed a definite tendency to fly in the predicted false direction--east after an advanced day, west after a retarded one. 5. Variations in the time-in-sight, and in the proportion of the more rapid returns supported the conclusions drawn from the orientation data. In a minority (25%) of the birds, the evidence suggests that the ‘chronometers’ were not affected. 6. It is concluded that these new results, taken with those produced previously, strongly support the suggestion that a form of complete, bico-ordinate sun navigation is used by birds.

Sign in / Sign up

Export Citation Format

Share Document