5. Equivalence Relations
... Examples from Linear Algebra Linear algebra provides several examples of important and interesting equivalence relations. To set the stage, let ℝm×n denote the set of m×n matrices with real entries. First recall that the following are row operations on a matrix: 1. Multiply a row by a non-zero real ...
... Examples from Linear Algebra Linear algebra provides several examples of important and interesting equivalence relations. To set the stage, let ℝm×n denote the set of m×n matrices with real entries. First recall that the following are row operations on a matrix: 1. Multiply a row by a non-zero real ...
Representations of GL_2(A_Q^\infty)
... tool in the study of smooth representations of TD groups. The idea is simple through the following analogy: Hecke algebras are to TD groups as group algebras are to finite groups. Namely, the Hecke algebra H (G) of a TD group G is made so that, essentially Repsm (G) = Modsm (H (G)) where the supersc ...
... tool in the study of smooth representations of TD groups. The idea is simple through the following analogy: Hecke algebras are to TD groups as group algebras are to finite groups. Namely, the Hecke algebra H (G) of a TD group G is made so that, essentially Repsm (G) = Modsm (H (G)) where the supersc ...
Functional Dependencies in a Relational Database and
... We now give Codd’s definition. Assume that 9 is a database relation, and that each column of 9 has a unique “column name.” If A,, .. ., A,, B,, ..., Br are among the column names of 9 (they need not be distinct), then we say that A,, . . ., A, determine B,, . . ., B, (or B,, . . ., B, depend on A,, ...
... We now give Codd’s definition. Assume that 9 is a database relation, and that each column of 9 has a unique “column name.” If A,, .. ., A,, B,, ..., Br are among the column names of 9 (they need not be distinct), then we say that A,, . . ., A, determine B,, . . ., B, (or B,, . . ., B, depend on A,, ...
Euclidian Roles in Description Logics
... For example, in [2] the Description Logic RIQ is extended with several role axioms, like reflexive and irreflexive role axioms, disjoint role axioms and simple negation on roles. These extensions has motivated us to investigate possibilities of extending Description Logics with other role axioms. In ...
... For example, in [2] the Description Logic RIQ is extended with several role axioms, like reflexive and irreflexive role axioms, disjoint role axioms and simple negation on roles. These extensions has motivated us to investigate possibilities of extending Description Logics with other role axioms. In ...
On the homology and homotopy of commutative shuffle algebras
... Acknowledgement: I thank Teimuraz Pirashvili for several helpful discussions. The idea, that all common homology theories of commutative algebras should agree in the setting of symmetric sequences is due to him. John Rognes asked whether commutative shuffle algebras are divided power algebras in a s ...
... Acknowledgement: I thank Teimuraz Pirashvili for several helpful discussions. The idea, that all common homology theories of commutative algebras should agree in the setting of symmetric sequences is due to him. John Rognes asked whether commutative shuffle algebras are divided power algebras in a s ...
