Sequence space representations of spaces of Whitney functions

2000 ◽  
Vol 37 (1-2) ◽  
pp. 3-12
Author(s):  
Bora Arslan ◽  
Alexander P. Goncharov ◽  
Mefharet Kocatepe
Keyword(s):  
Sequence Space ◽  
Whitney Functions

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

The Cesàro–Gamma operator and its associated sequence space

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Merve İlkhan Kara ◽  
Hadi Roopaei
Keyword(s):  
Sequence Space ◽  
Gamma Operator

Reinforcement Learning in Latent Action Sequence Space

2020 ◽  
Author(s):  
Heecheol Kim ◽  
Masanori Yamada ◽  
Kosuke Miyoshi ◽  
Tomoharu Iwata ◽  
Hiroshi Yamakawa
Keyword(s):  
Reinforcement Learning ◽  
Sequence Space ◽  
Action Sequence

scholarly journals A study on Copson operator and its associated sequence space II

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sequence Spaces ◽  
Matrix Domains

AbstractIn this paper, we investigate some properties of the domains $c(C^{n})$ c ( C n ) , $c_{0}(C^{n})$ c 0 ( C n ) , and $\ell _{p}(C^{n})$ ℓ p ( C n ) $(0< p<1)$ ( 0 < p < 1 ) of the Copson matrix of order n, where c, $c_{0}$ c 0 , and $\ell _{p}$ ℓ p are the spaces of all convergent, convergent to zero, and p-summable real sequences, respectively. Moreover, we compute the Köthe duals of these spaces and the lower bound of well-known operators on these sequence spaces. The domain $\ell _{p}(C^{n})$ ℓ p ( C n ) of Copson matrix $C^{n}$ C n of order n in the sequence space $\ell _{p}$ ℓ p , the norm of operators on this space, and the norm of Copson operator on several matrix domains have been investigated recently in (Roopaei in J. Inequal. Appl. 2020:120, 2020), and the present study is a complement of our previous research.

scholarly journals Heme-binding enables allosteric modulation in an ancient TIM-barrel glycosidase

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Gloria Gamiz-Arco ◽  
Luis I. Gutierrez-Rus ◽  
Valeria A. Risso ◽  
Beatriz Ibarra-Molero ◽  
Yosuke Hoshino ◽  
...  
Keyword(s):  
Sequence Space ◽  
Conformational Flexibility ◽  
Allosteric Modulation ◽  
Heme Binding ◽  
Optimum Temperature ◽  
Glycosidic Bonds ◽  
Glycosidase Activity ◽  
Tim Barrel ◽  
Crystallographic Structures ◽  
Ancestral Protein

AbstractGlycosidases are phylogenetically widely distributed enzymes that are crucial for the cleavage of glycosidic bonds. Here, we present the exceptional properties of a putative ancestor of bacterial and eukaryotic family-1 glycosidases. The ancestral protein shares the TIM-barrel fold with its modern descendants but displays large regions with greatly enhanced conformational flexibility. Yet, the barrel core remains comparatively rigid and the ancestral glycosidase activity is stable, with an optimum temperature within the experimental range for thermophilic family-1 glycosidases. None of the ∼5500 reported crystallographic structures of ∼1400 modern glycosidases show a bound porphyrin. Remarkably, the ancestral glycosidase binds heme tightly and stoichiometrically at a well-defined buried site. Heme binding rigidifies this TIM-barrel and allosterically enhances catalysis. Our work demonstrates the capability of ancestral protein reconstructions to reveal valuable but unexpected biomolecular features when sampling distant sequence space. The potential of the ancestral glycosidase as a scaffold for custom catalysis and biosensor engineering is discussed.

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