scholarly journals Решеточная структура в пространстве ограниченных гомоморфизмов между топологическими решеточно упорядоченными кольцами

2019 ◽  
Author(s):  
O. Zabeti
Keyword(s):  
Lattice Structure ◽  
Bounded Operators ◽  
Topological Ring ◽  
Topological Structures ◽  
Riesz Spaces ◽  
Topological Lattice ◽  
Bounded Group

Suppose X is a topological ring. It is known that there are three classes of bounded group homomorphisms on X whose topological structures make them again topological rings. First, we show that if X is a Hausdorff topological ring, then so are these classes of bounded group homomorphisms on X. Now, assume that X is a locally solid lattice ring. In this paper, our aim is to consider lattice structure on these classes of bounded group homomorphisms more precisely, we show that, under some mild assumptions, they are locally solid lattice rings. In fact, we consider bounded order bounded homomorphisms on X. Then we show that under the assumed topology, they form locally solid lattice rings. For this reason, we need a version of the remarkable RieszKantorovich formulae for order bounded operators in Riesz spaces in terms of order bounded homomorphisms on topological lattice groups.

scholarly journals A few remarks on bounded homomorphisms acting on topological lattice groups and topological rings

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2897-2905
Author(s):  
Omid Zabeti
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Lattice Structures ◽  
Fatou Property ◽  
Topological Structures ◽  
Lattice Group ◽  
Topological Lattice ◽  
Bounded Group ◽  
Different Types ◽  
Necessary And Sufficient

Suppose G is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on G which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for completeness of different types of bounded group homomorphisms between topological rings have been obtained, as well.

Some characterizations of Riesz spaces in the sense of strongly order bounded operators

Positivity ◽  
2019 ◽  
Vol 24 (1) ◽  
pp. 117-127
Author(s):  
Seyed AliReza Jalili ◽  
Mohammad Bagher Farshbaf Moghimi ◽  
Kazem Haghnejad Azar ◽  
Abbas Najati ◽  
Razi Alavizadeh ◽  
...  
Keyword(s):  
Bounded Operators ◽  
Riesz Spaces

scholarly journals Study of Dynamic Brittle Fracture of Composite Lamina Using a Bond-Based Peridynamic Lattice Model

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Jushang Guo ◽  
Weicheng Gao ◽  
Zhenyu Liu ◽  
Xiongwu Yang ◽  
Fengshou Li
Keyword(s):  
Brittle Fracture ◽  
Lattice Model ◽  
Composite Laminates ◽  
Lattice Structure ◽  
Numerical Implementation ◽  
Energy Equivalence ◽  
Topological Lattice ◽  
Proposed Model ◽  
Dynamic Brittle Fracture ◽  
Orthogonal Anisotropy

We proposed a bond-based peridynamic lattice model for simulating dynamic brittle fracture of 2D composite lamina. Material orthogonal anisotropy was represented by rotating topological lattice structure instead of fiber directions. Analytical derivation and numerical implementation of the proposed model were given based on energy equivalence. Benchmark composite lamina tests are used to validate the capability of modeling dynamic fracture of the method. The peridynamic lattice model is found to be robust and successful in modeling dynamic brittle fracture of 2D composite lamina and can be extended to composite laminates by applying 3D lattice structure.

scholarly journals A note on the relationship between three classes of operators on Riesz spaces

2019 ◽  
Vol 57 (2) ◽  
pp. 77-85
Author(s):  
Liang Hong
Keyword(s):  
Bounded Operators ◽  
Riesz Spaces ◽  
Prior Literature ◽  
Continuous Operators ◽  
The Relationship

Abstract Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.

scholarly journals A NOTE ON LATTICE OPERATIONS OF RIESZ SPACES OF ORDER BOUNDED OPERATORS

1990 ◽  
Vol 21 (4) ◽  
pp. 395-398
Author(s):  
BORIS LAVRIČ
Keyword(s):  
Weak Form ◽  
Riesz Space ◽  
Linear Operators ◽  
Spectral Theorem ◽  
Bounded Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Spaces

Let $L$, $M$ be Archimedean Riesz spaces with $M$ Dedekind complete, and let $\mathcal L_b(L,M )$ be the Riesz space of order bounded linear operators from $L$ into $M$. A theorem of Abramovic [1] on lattice operations of $\mathcal L_b(L,M )$ is generalized on Riesz spaces $L$ in which a weak form of Freudenthal's spectral theorem [4] holds.

Structural analysis of the photosynthetic membrane from Ectothiorhodospira halochloris

1983 ◽  
Vol 41 ◽  
pp. 740-741
Author(s):  
H. Engelhardt ◽  
R. Guckenberger ◽  
W. Baumeister
Keyword(s):  
Lattice Structure ◽  
Bacterial Species ◽  
Hexagonal Lattice ◽  
Reaction Centre ◽  
Photosynthetic Membrane ◽  
Rhodopseudomonas Viridis ◽  
Photosynthetic Membranes ◽  
Ectothiorhodospira Halochloris ◽  
Main Components

Bacterial photosynthetic membranes contain, apart from lipids and electron transport components, reaction centre (RC) and light harvesting (LH) polypeptides as the main components. The RC-LH complexes in Rhodopseudomonas viridis membranes are known since quite seme time to form a hexagonal lattice structure in vivo; hence this membrane attracted the particular attention of electron microscopists. Contrary to previous claims in the literature we found, however, that 2-D periodically organized photosynthetic membranes are not a unique feature of Rhodopseudomonas viridis. At least five bacterial species, all bacteriophyll b - containing, possess membranes with the RC-LH complexes regularly arrayed. All these membranes appear to have a similar lattice structure and fine-morphology. The lattice spacings of the Ectothiorhodospira haloohloris, Ectothiorhodospira abdelmalekii and Rhodopseudomonas viridis membranes are close to 13 nm, those of Thiocapsa pfennigii and Rhodopseudomonas sulfoviridis are slightly smaller (∼12.5 nm).

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