2015/1
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- ItemContinuous functions over discrete partial orders(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2015) 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.
- ItemTopographic spaces over ordered monoids(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2015) 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.
- ItemA note on finite generated subsemigroups of T(X,Y)(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2015) 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 ).
- ItemMathematical analysis of continuous time active and adaptive dynamics of artificial neural network in star shape(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2015) 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.
- ItemA game of asymmetric information between a therapist and a mentally ill patient(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2015) Haugen, K. K.; Vatne, S.In this paper, we follow up research of Vatne [23] related to how mentally ill patients could (and perhaps should) be treated. We propose, model, and ana- lyze a simple sequential game of incomplete and asymmetric information where the patient moves rst, signaling behavior which is observed by the therapist with lack or limited knowledge of the actual patient type. We assume greatly approximated strategy spaces both for patient and therapist, but will still claim that our results increase knowledge of this important relation. Knowledge that may be critically important in continued improved treatment of patients with mental illness.