scholarly journals THE GYSIN EXACT SEQUENCE FOR S1-EQUIVARIANT SYMPLECTIC HOMOLOGY

2013 ◽  
Vol 05 (04) ◽  
pp. 361-407 ◽  
Author(s):  
FRÉDÉRIC BOURGEOIS ◽  
ALEXANDRU OANCEA
Keyword(s):  
Exact Sequence ◽  
Parameter Space ◽  
Contact Boundary ◽  
Important Ingredient ◽  
Symplectic Homology ◽  
Finite Dimensional ◽  
Type Construction ◽  
Hamiltonian Functions ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

We define S1-equivariant symplectic homology for symplectically aspherical manifolds with contact boundary, using a Floer-type construction first proposed by Viterbo. We show that it is related to the usual symplectic homology by a Gysin exact sequence. As an important ingredient of the proof, we define a parametrized version of symplectic homology, corresponding to families of Hamiltonian functions indexed by a finite dimensional smooth parameter space.

Instabilities of exact, time-periodic solutions of the incompressible Euler equations

2000 ◽  
Vol 404 ◽  
pp. 269-287 ◽  
Author(s):  
JOSEPH A. BIELLO ◽  
KENNETH I. SALDANHA ◽  
NORMAN R. LEBOVITZ
Keyword(s):  
Periodic Solutions ◽  
Linear Stability ◽  
Euler Equations ◽  
Parameter Space ◽  
Spatial Scales ◽  
Inviscid Flow ◽  
Steady Flows ◽  
Periodic Flows ◽  
Finite Dimensional ◽  
Time Periodic Solutions

We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.

scholarly journals An extension of the MILES library with derived Teff, log  g, [Fe/H], and [α/Fe]

2021 ◽  
Author(s):  
A E García Pérez ◽  
P Sánchez-Blázquez ◽  
A Vazdekis ◽  
C Allende Prieto ◽  
A de C Milone ◽  
...  
Keyword(s):  
Star Formation ◽  
Parameter Space ◽  
Important Ingredient ◽  
Chemical Abundances ◽  
Reliable Determination ◽  
Stellar Masses ◽  
Star Formation Histories ◽  
Good Coverage ◽  
Data Reductions

Abstract Extragalactic astronomy and stellar astrophysics are intrinsically related. In fact, the determination of important galaxy properties such as stellar masses, star formation histories or chemical abundances relies on the ability to model their stellar populations. One important ingredient of these models are stellar libraries. Empirical libraries must have a good coverage of Teff, [Z/H], and surface gravity, and have these parameters reliably determined. MILES is one of the most widely used empirical libraries. Here we present an extension of this library with 205 new stars especially selected to cover important regions of the parameter space, including metal poor stars down to [Fe/H] ∼ −1.0. We describe the observations and data reductions as well as a new determination of the stellar parameters, including [α/Fe] ratio. The new MILES library contains 1070 stars with homogeneous and reliable determination of [Fe/H], Teff, log g and [α/Fe] ratio.

The Classification of Algebras by Dominant Dimension

1968 ◽  
Vol 20 ◽  
pp. 398-409 ◽  
Author(s):  
Bruno J. Mueller
Keyword(s):  
Exact Sequence ◽  
Infinite Sequence ◽  
Dominant Dimension ◽  
Finite Dimensional ◽  
Image Position ◽  
Finite Dimensional Algebras

Nakayama proposed to classify finite-dimensional algebras R over a field according to how long an exact sequenceof projective and injective R-R-bimodules Xi they allow. He conjectured that if there exists an infinite sequence of this type, then R must be quasi-Frobenius; and he proved this when R is generalized uniserial (17).

Extensions that are Submodules of their Quotients

1990 ◽  
Vol 33 (1) ◽  
pp. 93-99 ◽  
Author(s):  
F. Okoh ◽  
F. Zorzitto
Keyword(s):  
Exact Sequence ◽  
Short Exact Sequence ◽  
Height Function ◽  
Projective Line ◽  
Finite Dimensional ◽  
Rank One ◽  
Torsion Free

AbstractLet 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.

COMPLETING FUZZY IF-THEN RULE BASES BY MEANS OF SMOOTHING SPLINES

2006 ◽  
Vol 14 (02) ◽  
pp. 235-244 ◽  
Author(s):  
THOMAS VETTERLEIN ◽  
MARTIN ŠTEPNICKA
Keyword(s):  
Fuzzy Sets ◽  
Parameter Space ◽  
Fuzzy Inference ◽  
Smoothing Splines ◽  
Partial Function ◽  
Rule Base ◽  
Parameter Spaces ◽  
Finite Dimensional ◽  
Rule Bases ◽  
Do So

A fuzzy if-then rule base may be viewed as a partial function between universes of fuzzy sets. For the construction of a fuzzy inference module, this partial function needs to be extended to a total one. Here, we propose a new method how to do so, making use of the method of smoothing splines. To this end, we identify the fuzzy sets with elements of a finite-dimensional real parameter space in an approximate way, using Perfilieva's fuzzy transforms. We then determine a function between two such parameter spaces by requiring that it reproduces the rule base as precise as possible and that it minimizes a parameter depending on its smoothness.

scholarly journals Conformal invariance of white noise

1985 ◽  
Vol 98 ◽  
pp. 87-98 ◽  
Author(s):  
Takeyuki Hida ◽  
Ke-Seung Lee ◽  
Sheu-San Lee
Keyword(s):  
Probability Theory ◽  
White Noise ◽  
Parameter Space ◽  
Conformal Invariance ◽  
Rotation Group ◽  
Gaussian Random Fields ◽  
Conformal Group ◽  
Time Parameter ◽  
Infinite Dimensional ◽  
Finite Dimensional

The remarkable link between the structure of the white noise and that of the infinite dimensional rotation group has been exemplified by various approaches in probability theory and harmonic analysis. Such a link naturally becomes more intricate as the dimension of the time-parameter space of the white noise increases. One of the powerful method to illustrate this situation is to observe the structure of certain subgroups of the infinite dimensional rotation group that come from the diffeomorphisms of the time-parameter space, that is the time change. Indeed, those subgroups would shed light on the probabilistic meanings hidden behind the usual formal observations. Moreover, the subgroups often describe the way of dependency for Gaussian random fields formed from the white noise as the time-parameter runs over the basic parameter space.The main purpose of this note is to introduce finite dimensional subgroups of the infinite dimensional rotation group that have important probabilistic meanings and to discuss their roles in probability theory. In particular, we shall see that the conformal invariance of white noise can be described in terms of the conformal group which is a finite dimensional Lie subgroup of the infinite dimensional rotation group.

scholarly journals Erratum to: An exact sequence for contact- and symplectic homology

2015 ◽  
Vol 200 (3) ◽  
pp. 1065-1076 ◽  
Author(s):  
Frédéric Bourgeois ◽  
Alexandru Oancea
Keyword(s):  
Exact Sequence ◽  
Symplectic Homology
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