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pro vyhledávání: '"George R. Barnes"'
Autor:
Inessa Levi, George R. Barnes
Publikováno v:
Semigroup Forum. 70:81-96
A subset U of a semigroup S is a generating set for S if every element of S may be written as a finite product of elements of U. The rank of S is the size of a minimal generating set of S, and the idempotent rank of S is the size of a minimal generat
Publikováno v:
The Journal of General Education. 53:20-36
This paper discusses the method and results of an evaluation of general education mathematics courses. Students at the University of Louisville were surveyed in the first week of the Fall 2000 semester to determine their expectations for their mathem
Publikováno v:
Social Networks. 25:161-174
The techniques developed in this paper suggest an objective standard for the process that refines the generation of interaction semigroups associated with social networks. A constructed interaction semigroup S is assessed with respect to measurements
Autor:
Inessa Levi, George R. Barnes
Publikováno v:
Communications in Algebra. 31:1753-1763
The rank of a finite semigroup is the minimal size of its generating set. Let T n be the semigroup of all total transformations of the set {1, 2,…, n}, and let 𝒪 n be the subsemigroup of T n of all the order-preserving transformations whose imag
Publikováno v:
The Journal of Mathematical Sociology. 25:139-161
Current semigroup models of social systems assume that the system is uniform, that is all the units and all the connections in the system have the same influence. Obviously most social structures are not uniform; some units and connections between so
Publikováno v:
Journal of Applied Probability. 35:824-832
The purpose of this paper is to study the asymptotic properties of Markov chains on semigroups. In particular, the structure of transition matrices representing random walks on finite semigroups is examined. It is shown that the transition matrices a
Publikováno v:
Social Networks. 20:179-196
This paper uses the mathematical structure of algebraic semigroups to model interpersonal relationships. The basis for the model is the periodic surveys administered to each member of a social network. The model uses individual preference to uncover
Publikováno v:
The Journal of Mathematical Sociology. 21:295-323
This paper addresses the development of a semigroup model of social networks. Data matrices which represent the perceived relationships between members of a social network are used to construct a (possibly infinite) data semigroup of derived relation
Publikováno v:
Proceedings of the 2003 SIAM International Conference on Data Mining.
Autor:
Robert Whitley, George R. Barnes
Publikováno v:
Transactions of the American Mathematical Society. 211:339-351
We introduce and discuss the oscillation of an operator T mapping L p ( S , Σ , μ ) {L^p}(S,\Sigma ,\mu ) into a Banach space. We establish results relating the oscillation, a “local norm", to the norm of the operator. Also using the oscillation