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Content available remote Marczewski–Burstin representations vs. Bernstein and Dense subsets
EN
We find values of superposition of Marczewski–Burstin operation and operation of finding Bernstein sets. Several counterexamples of Marczewski–Burstin systems are given.
EN
The present study consisted of two experiments. The goal of the first experiment was to establish the just noticeable differences for the fundamental frequency of the vowel /u/ by using the 2AFC method. We obtained the threshold value for 27 cents. This value is larger than the motor reaction values which had been observed in previous experiments (e.g. 9 or 19 cents). The second experiment was intended to provide neurophysiological confirmation of the detection of shifts in a frequency, using event-related potentials (ERPs). We concentrated on the mismatch negativity (MMN) - the component elicited by the change in the pattern of stimuli. Its occurrence is correlated with the discrimination threshold. In our study, MMN was observed for changes greater than 27 cents - shifts of ±50 and 100 cents (effect size - Cohen’s d = 2.259). MMN did not appear for changes of ±10 and 20 cents. The results showed that the values for which motor responses can be observed are indeed lower than those for perceptual thresholds.
EN
For each pointclass Γ ⊆ P(2ω) define U[Γ] as the collection of all X⊆ 2ω such that the preimage f− 1(X) belongs to Γ for each continuous f : 2ω → 2ω. We study the properties of and possible rela-tionships among the classes U[Γ], where Γ ranges over the σ-algebras (l), (m), the completely Ramsey sets, and the sets with the Baire property. We also prove some results about cardinal coefficients of U[Γ] for the general case of Marczewski-Burstin representable σ-algebras Γ. We finish by posing some unsolved problems.
4
Content available remote On Borel version of uniformly completely Ramsey sets
EN
We study the Borel versions of uniformly completely Ramsey null sets. We give general theorems on game-defined classes of sigma-ideals.
PL
W artykule przedstawiono metody i urządzenia do zapobiegania tworzenia się niepożądanych osadów szczególnie kamienia kotłowego w kotłach i innych wymiennikach cieplnych metodą inną od klasycznie stosowanych sposobów urabiania wody, tj. przy pomocy aparatury wytwarzającej pole ultradźwięków, co gwarantuje, jak wykazuje doświadczenie eksploatacyjne, usunięcie m.in. istniejącego kamienia kotłowego i zapobiega tworzeniu nowych osadów. Aparatura jest produktem rosyjskim, ale może być osiągalna na naszym rynku.
EN
The paper presents methods and equipment for preventing of building up unwanted deposits particularly of boiler scale in boilers and other heat exchangers using a different method from the applied classical ways of water treatment. Suggested is the application of various ultrasonic appliances creating an ultrasonic field, what guarantees as service experience shows a. removal of exiting boiler scale and prevents from forming of new deposits. The appliance is of Russian production but can be available on our market.
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