In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
In this note we study fields $F$ with the property that the simple transcendental extension $F(u)$ of $F$ is isomorphic to some subfield of $F$ but not isomorphic to $F$. Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
We study the stability of average optimal control of general discrete-time Markov processes. Under certain ergodicity and Lipschitz conditions the stability index is bounded by a constant times the Prokhorov distance between distributions of random vectors determinating the "original and the perturbated" control processes.
King and Korf \cite{KingKorf01} introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called \emph{free lunch in the limit} which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory - it depends on the underlying probability measure more than through its null sets. However, we show that the interesting pricing results obtained by conjugate duality are still valid if it is only assumed that the market admits no free lunch rather than no free lunch in the limit.
A topological duality for monadic n-valued Luk asiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de L ukasiewicz nvalente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of Q-distributive lattices and Q-homomorphims, it coincides with the duality obtained by R. Cignoli in 1991. A new characterization of congruences by means of certain closed and involutive subsets of the associated space is also obtained. This allowed us to describe subdirectly irreducible algebras in this variety, arriving by a different method at the results established by Abad.
We provide a necessary and sufficient condition under which a generalized ordered topological product (GOTP) of two GO-spaces is monotonically Lindelöf.
The paper gives an overview of feature selection techniques in statistical pattern recognition with particular emphasis on methods developed within the Institute of Information Theory and Automation research team throughout recent years. Besides discussing the advances in methodology since times of Perez's pioneering work the paper attempts to put the methods into a taxonomical framework. The methods discussed include the latest variants of the optimal algorithms, enhanced sub-optimal techniques and the simultaneous semi-parametric probability density function modelling and feature space selection method. Some related issues are illustrated on real data by means of the Feature Selection Toolbox software.
Solar engine is discussed as integration of solar collector with linear heat loss and Curzon-Ahlborn engine is considered. This simple endoreversible model is used to discuss some applications of results of endoreversible heat engine in the field of solar engine. Optimum operating temperature of the solar collector and relevant maximum overall efficiency of solar engine is calculated, the results being compared with those by the models where Carnot and Curzon-Ahlborn efficiences were used. Conclusions obtained for endoreversible model are used for simple optimal design of solar engine. The size of heat engine for a given solar collector is optimized. The investment costs of solar collector and heat engine per unit of output power are used as optimization criterion. and Obsahuje seznam literatury