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Artificial intelligence approaches for tumor phenotype stratification from single-cell transcriptomic data. [PDF]
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Fuzzy Sets and Systems, 2014
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Fang-Fang Pan, Sheng-Wei Han
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Fang-Fang Pan, Sheng-Wei Han
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Canadian Journal of Mathematics, 1985
For us an “algebra” is a finitary “universal algebra” in the sense of G. Birkhoff [9]. We are concerned in this paper with algebras whose endomorphisms are determined by small subsets. For example, an algebra A is rigid (in the strong sense) if the only endomorphism on A is the identity idA. In this case, the empty set determines the endomorphism set E(
Bankston, Paul, Schutt, Richard
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For us an “algebra” is a finitary “universal algebra” in the sense of G. Birkhoff [9]. We are concerned in this paper with algebras whose endomorphisms are determined by small subsets. For example, an algebra A is rigid (in the strong sense) if the only endomorphism on A is the identity idA. In this case, the empty set determines the endomorphism set E(
Bankston, Paul, Schutt, Richard
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Journal of Cybernetics, 1976
Abstract Virtually all algebraic approaches to formal language theory involve an intervening notion of machine, and it is the machine theory which is treated algebraically. The present article details a direct algebraic treatment of context-free languages by means of the recently-developed theory of hetrogeneous algebras.
Hatcher, W. S., Rus, T.
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Abstract Virtually all algebraic approaches to formal language theory involve an intervening notion of machine, and it is the machine theory which is treated algebraically. The present article details a direct algebraic treatment of context-free languages by means of the recently-developed theory of hetrogeneous algebras.
Hatcher, W. S., Rus, T.
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International Journal of Algebra and Computation, 2000
A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L.
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A ternary algebra is a bounded distributive lattice with additonal operations e and ~ that satisfies (a+b)~=a~b~, a~~=a, e≤a+a~, e~= e and 0~=1. This article characterizes free ternary algebras by giving necessary and sufficient conditions on a set X of free generators of a ternary algebra L, so that X freely generates L.
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On Polynomial Algebras and Free Algebras
Canadian Journal of Mathematics, 1968It is well known that given the polynomial algebra (for definitions, see §2), an algebra of type τ, and a sequence a of elements of , one can define a congruence relation θa of such that the factor algebra is isomorphic to the subalgebra of generated by a, and the isomorphism is given in a very simple way.
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Czechoslovak Mathematical Journal, 2003
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2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2012
We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all of them when seen as isomorphic with the set of natural numbers.
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We describe arithmetic computations in terms of operations on some well known free algebras (S1S, S2S and ordered rooted binary trees) while emphasizing the common structure present in all of them when seen as isomorphic with the set of natural numbers.
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Canadian Journal of Mathematics, 1968
By a PQ (product-quotients) algebra, we mean a non-empty set together with three single-valued and not necessarily associative operations ., / , \ that we shall treat as product, right quotient, and left quotient although we require no relation between them. The theory of binary systems provides the following examples:A.
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By a PQ (product-quotients) algebra, we mean a non-empty set together with three single-valued and not necessarily associative operations ., / , \ that we shall treat as product, right quotient, and left quotient although we require no relation between them. The theory of binary systems provides the following examples:A.
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