Using Parameterized Canonical Representations to Resolve Conflicts and Achieve Interoperability between Relational and Object Databases

1996 ◽  
pp. 155-185
Author(s):  
Ya-hui Chang ◽  
Louiqa Raschid
Keyword(s):  
Canonical Representations ◽  
Object Databases

scholarly journals On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

On temporal modeling in the context of object databases

1993 ◽  
Vol 22 (3) ◽  
pp. 8-15 ◽  
Author(s):  
Niki Pissinou ◽  
Kia Makki ◽  
Yelena Yesha
Keyword(s):  
Temporal Modeling ◽  
Object Databases

Canonical representations of fingers and dots trigger an automatic activation of number semantics: an EEG study on 10-year old children

2021 ◽  
pp. 107874
Author(s):  
Cathy Marlair ◽  
Aliette Lochy ◽  
Margot Buyle ◽  
Christine Schiltz ◽  
Virginie Crollen
Keyword(s):  
Canonical Representations ◽  
Automatic Activation

Towards Deductive Object Databases

1995 ◽  
Vol 1 (1) ◽  
pp. 19-39 ◽  
Author(s):  
Elisa Bertino ◽  
Giovanna Guerrini ◽  
Danilo Montesi
Keyword(s):  
Object Databases

scholarly journals The de Rham Cohomology through Hilbert Space Methods

2019 ◽  
pp. 455-465
Author(s):  
Ihsane Malass ◽  
Nikolai Tarkhanov
Keyword(s):  
Hilbert Space ◽  
Elliptic Boundary ◽  
Differential Forms ◽  
Adjoint Operator ◽  
Lagrange Equations ◽  
De Rham Cohomology ◽  
Elliptic Boundary Value ◽  
De Rham ◽  
Canonical Representations ◽  
The Neumann Problem

We discuss canonical representations of the de Rham cohomology on a compact manifold with boundary. They are obtained by minimising the energy integral in a Hilbert space of differential forms that belong along with the exterior derivative to the domain of the adjoint operator. The corresponding Euler- Lagrange equations reduce to an elliptic boundary value problem on the manifold, which is usually referred to as the Neumann problem after Spencer

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