2015/1http://hdl.handle.net/11012/630822021-03-06T13:47:35Z2021-03-06T13:47:35ZContinuous functions over discrete partial ordersPfaltz, J. L.http://hdl.handle.net/11012/630882016-08-24T01:01:06Z2015-01-01T00:00:00ZContinuous functions over discrete partial orders
Pfaltz, J. L.
This paper examines the properties of structure preserving morphisms f over discrete partial orders. It employs concepts of continuity and path homomor- phisms. It will conclude that no single constraint on f will be sufficient, and it will also conclude that a convexity constraint on f −1 seems to be essential. We employ closure lattices to help reach this conclusion.
2015-01-01T00:00:00ZA note on finite generated subsemigroups of T(X,Y)Lekkoksung N.Koppitz, J.http://hdl.handle.net/11012/630862016-08-24T01:01:05Z2015-01-01T00:00:00ZA note on finite generated subsemigroups of T(X,Y)
Lekkoksung N.; Koppitz, J.
It is well known that a countable set of transformations on an innite set X is contained in a two-generated subsemigroup of the full transformation semigroup on X. If Y X, then T(X; Y ), the set of all transformations on X with an image in Y , forms a semigroup of transformations with restricted range, as shown in 1975 by Symons [10]. In this paper, we give a sucient and necessary condition for a countable subset of T(X; Y ) to be contained in a three-generated subsemigroup of T(X; Y ).
2015-01-01T00:00:00ZMathematical analysis of continuous time active and adaptive dynamics of artificial neural network in star shapeKřivan, M.http://hdl.handle.net/11012/630852016-08-24T01:01:06Z2015-01-01T00:00:00ZMathematical analysis of continuous time active and adaptive dynamics of artificial neural network in star shape
Křivan, M.
The present paper gives a detailed mathematical description of continuous time active and adaptive dynamics of an articial neural network, based on adaptive resonance theory and consisting in solving systems of dierential equations. The mathematical description uses the example of a simple star-shaped arti ial neural network for two dierently parameterized cases of general equations including the evaluation of both learning methods and both their functions.
2015-01-01T00:00:00ZTopographic spaces over ordered monoidsPavlík, J.http://hdl.handle.net/11012/630872016-08-24T01:01:07Z2015-01-01T00:00:00ZTopographic spaces over ordered monoids
Pavlík, J.
A topography on a set is considered to be a collection of features described by two valuations: distance and elevation. Spaces with such structure will be studied on a general level, with generalized metric (gem) and pseudometric (pseudogem). We show many pseudogem distances and characteristics, particularly those related to the elevation function. We focus on paths in the topographic images and cohesiveness (generalized continuity) of their compositions with the elevation function. Special emphasis is also placed on the spaces arising from the digital geometry and, therefore, oering applications in image processing.
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