scholarly journals New Euler-Maclaurin expansions and their application to quadrature over the $s$-dimensional simplex

1979 ◽  
Vol 33 (147) ◽  
pp. 1003-1003
Author(s):  
Elise de Doncker
Keyword(s):  
Dimensional Simplex

scholarly journals On Minimal Absorption Index for an n-Dimensional Simplex

2018 ◽  
Vol 25 (1) ◽  
pp. 140-150 ◽  
Author(s):  
Mikhail V. Nevskii ◽  
Alexey Y. Ukhalov
Keyword(s):  
Absorption Index ◽  
Dimensional Simplex

scholarly journals Faces of 2-Dimensional Simplex of Order and Chain Polytopes

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 851
Author(s):  
Aki Mori
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Explicit Description ◽  
Dimensional Simplex ◽  
Partially Ordered ◽  
The Face ◽  
Finite Partially Ordered Set ◽  
Arbitrary Triangle

Each of the descriptions of vertices, edges, and facets of the order and chain polytope of a finite partially ordered set are well known. In this paper, we give an explicit description of faces of 2-dimensional simplex in terms of vertices. Namely, it will be proved that an arbitrary triangle in 1-skeleton of the order or chain polytope forms the face of 2-dimensional simplex of each polytope. These results mean a generalization in the case of 2-faces of the characterization known in the case of edges.

scholarly journals When is the algebra of regular sets for a finitely additive borel measure a α-algebra?

1982 ◽  
Vol 33 (3) ◽  
pp. 374-385 ◽  
Author(s):  
Thomas E. Armstrong
Keyword(s):  
Borel Measure ◽  
Convex Set ◽  
Additive Measure ◽  
Dimensional Simplex ◽  
Finitely Additive Measure ◽  
Regular Algebra ◽  
Finite Dimensional ◽  
Regular Sets ◽  
Dirac Measures

AbstractIt is shown that hte algebra of regular sets for a finitely additive Borel measure μ on a compact Hausdroff space is a σ-algebra only if it includes the Baire algebra and μ is countably additive onthe σ-algebra of regular sets. Any infinite compact Hausdroff space admits a finitely additive Borel measure whose algebra of regular sets is not a σ-algebra. Although a finitely additive measure with a σ-algebra of regular sets is countably additive on the Baire σ-algebra there are examples of finitely additive extensions of countably additive Baire measures whose regular algebra is not a σ-algebra. We examine the particular case of extensions of Dirac measures. In this context it is shown that all extensions of a {0, 1}-valued countably additive measure from a σ-algebra to a larger σ-algebra are countably additive if and only if the convex set of these extensions is a finite dimensional simplex.

Simple Three-dimensional Simplex Modulator

2014 ◽  
Author(s):  
Hiroshi Yamazaki ◽  
Yasuaki Hashizume ◽  
Takashi Saida
Keyword(s):  
Three Dimensional ◽  
Dimensional Simplex

Dynamical Properties of Quadratic Homeomorphisms of a Finite-Dimensional Simplex

2020 ◽  
Vol 245 (3) ◽  
pp. 398-402
Author(s):  
R. N. Ganikhodzhaev ◽  
M. A. Tadzhieva ◽  
D. B. Eshmamatova
Keyword(s):  
Dimensional Simplex ◽  
Finite Dimensional ◽  
Dynamical Properties

ON DYNAMICS OF ℓ-VOLTERRA QUADRATIC STOCHASTIC OPERATORS

2010 ◽  
Vol 03 (02) ◽  
pp. 143-159 ◽  
Author(s):  
U. A. ROZIKOV ◽  
A. ZADA
Keyword(s):  
Volterra Operator ◽  
Periodic Points ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Volterra Operators ◽  
Quadratic Stochastic Operators

We introduce a notion of ℓ-Volterra quadratic stochastic operator defined on (m - 1)-dimensional simplex, where ℓ ∈ {0,1,…, m}. The ℓ-Volterra operator is a Volterra operator if and only if ℓ = m. We study structure of the set of all ℓ-Volterra operators and describe their several fixed and periodic points. For m = 2 and 3, we describe behavior of trajectories of (m - 1)-Volterra operators. The paper also contains many remarks with comparisons of ℓ-Volterra operators and Volterra ones.

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