Karlin (Samuel) and McGregor (James). -- The classification of birth and death processes. Transactions of the American Mathematical Society, vol. 86, 1957, pp. 366--400. Home/Search Document Not in Database Summary Related Articles Check |
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A Categorical Manifesto - Goguen (1991) (20 citations) (Correct)
....B there corresponds a natural transformation F ) G. Although this looks like a mere definition of the phrase natural translation, it can nevertheless be very useful in practice. It is also interesting that this concept was the historical origin of category theory, since Eilenberg and Mac Lane [11] used it to formalise the notion of an equivalence of homology theories, and then found that for this definition to make sense, they had to define functors, and for functors to make sense, they had to define categories. This history also explains why homology theory so often appears in ....
Samuel Eilenberg and Saunders Mac Lane. General theory of natural equivalences. Transactions of the American Mathematical Society, 58:231--294, 1945.
Tossing Algebraic Flowers down the Great Divide - Goguen (1999) (2 citations) (Correct)
....This is an insight from mathematics. The journey through this paper has already encountered several cases where morphisms are important: initial extensions for constraint programming (in Section 2.9) data constraints (in Section 2.4) and inclusion systems (Section 2. 4) Eilenberg and Mac Lane [25] gave this insight a more definite and systematic form with the invention of category theory. explanations. The zoo illustrates how algebraic semiotics can be applied to syntax, understanding stories, and much more. 3.4 Fuzzy Logic and Information Theory Many people have had the intuition ....
Samuel Eilenberg and Saunders Mac Lane. General theory of natural equivalences. Transactions of the American Mathematical Society, 58:231--294, 1945.
Birth-Death Processes, Lattice Path Combinatorics, Continued.. - France Self-citation (Birth) (Correct)
....j (t) j 1 p j 1 (t) p j (0) ffi j;0 : 1) Although finite dimensional versions are easy and reduce to combinations of exponentials, it is precisely the infinite dimensional character of the system that renders its analysis interesting. In a series of important papers, Karlin and McGregor [10, 11] have developed a general connection between the fundamental system (1) and an associated family of orthogonal polynomials. Later, Jones and Magnus constructed a direct continued fraction representation; see [8, 9] This summary is an account of Guillemin s lecture (see [5, 6] as well as of ....
Karlin (Samuel) and McGregor (James). -- The classification of birth and death processes. Transactions of the American Mathematical Society, vol. 86, 1957, pp. 366--400.
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