scholarly journals An integrability criterion for a projective limit of Banach distributions

2022 ◽  
pp. 104453
Author(s):  
Fernand Pelletier
Keyword(s):  
Projective Limit ◽  
Integrability Criterion

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

scholarly journals Material’s Perception Strategy in Terms of Adaptive Re-use Within the Computational, and Parametricism Context

2019 ◽  
Vol 2 (4) ◽  
pp. 294
Author(s):  
Sarah Mansour
Keyword(s):  
Material Culture ◽  
New Technology ◽  
Projective Limit ◽  
Evidence Based ◽  
Physical Domain ◽  
Defining Moment ◽  
The Past ◽  
Structural Plan ◽  
Set Up

Creativity has been assigned to the design or drawing, with materials most often being specified as a result of design rather than being considered a driver of it. Designers empowered by new technology now consider form as it is defined by identifiable systems. This evidence based, parametric methodology is a response to two decades of digitally-derived projects, often produced simply for their novelty. The best work results when the architect has combined respect for the old with a skilled progressive command of the new. Material culture is portrayed as the physical confirmation and articulation of a culture in its relics and design. In the time that we comprehend the thought of material culture not just as having importance for investigations of the past. yet in addition getting a projective limit. we may now be at a critical defining moment.. As computation starts to significantly change our origination of the material, so in architecture this will defy the set up connection between the procedures of design and the physical fabrication of the constructed medium . Obviously, computation was brought into design & architecture the greater part a century back. furthermore, expanding digitization has since plagued all parts of the field . As though, it has remained emphatically impacted by the theoretical isolation of the procedures of design and making that has overwhelmed structural plan thinking since the Renaissance, and it is just now that creators are starting to deal with the computational void as never again disconnecting from the physical domain.

Square Integrable Representations and the Standard Module Conjecture for General Spin Groups

2009 ◽  
Vol 61 (3) ◽  
pp. 617-640 ◽  
Author(s):  
Wook Kim
Keyword(s):  
Half Plane ◽  
Spin Groups ◽  
Standard Module ◽  
Square Integrability ◽  
Integrability Criterion

Abstract.In this paper we study square integrable representations and L -functions for quasisplit general spin groups over a p-adic field. In the first part, the holomorphy of L -functions in a half plane is proved by using a variant formof Casselman's square integrability criterion and the Langlands–Shahidi method. The remaining part focuses on the proof of the standard module conjecture. We generalize Muić's idea via the Langlands–Shahidimethod towards a proof of the conjecture. It is used in the work of M. Asgari and F. Shahidi on generic transfer for general spin groups.

On the Injective and Projective Limit of Complexes

1965 ◽  
Vol 8 (3) ◽  
pp. 291-305
Author(s):  
Krishna Tewari
Keyword(s):  
Commutative Ring ◽  
Projective Limit ◽  
Covariant Functor ◽  
Projective System ◽  
Directed Set

Let R be a commutative ring with unit. Let (Aα, φ βα) (α ≤ β) (resp. (Bα, ψαβ) (α ≤ β)) be an infective (resp. projective) system of R-algebras indexed by a directed set I; let ((Xα, dα), fβα) (α ≤ β) (resp. ((Yα, δα), gαβ) (α≤β)) be an injective (resp. projective) system of complexes, indexed by the same set I, such that for each αϵI, (Xα, dα) (resp. (Yα, δα)) is a complex over Aα (resp. over Bα). The purpose of this paper is to show that the covariant functor from the category of all such injective systems of complexes and complex homomorphisms over the R-algebra Aα is such that it associates with an injective system ((Uα, dα), hβα) of universal complexes a universal complex over Aα whereas the same is not true of the covariant functor the category of all such projective systems of complexes and their maps.

scholarly journals Singularity confinement as an integrability criterion

2019 ◽  
Vol 52 (20) ◽  
pp. 205201 ◽  
Author(s):  
Takafumi Mase ◽  
Ralph Willox ◽  
Alfred Ramani ◽  
Basil Grammaticos
Keyword(s):  
Singularity Confinement ◽  
Integrability Criterion

scholarly journals Projective limit of infinite Radon measures

1978 ◽  
Vol 25 (3) ◽  
pp. 328-331 ◽  
Author(s):  
Susumu Okada ◽  
Yoshiaki Okazaki
Keyword(s):  
Projective Limit ◽  
Radon Measures ◽  
Self Consistent

AbstractWe show that for any self-consistent sequentially maximal system {μα} of infinite (perhaps non-σ-finite) Radon measures, the projective limit of {μα} exists.

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