In this paper, we are mainly concerned with characterizing matrices that map every bounded sequence into one whose Banach core is a subset of the statistical core of the original sequence.
We present simple proofs that spaces of homogeneous polynomials on Lp[0, 1] and ℓp provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976)., Seán Dineen, Jorge Mujica., and Obsahuje seznam literatury
It is shown that a Banach-valued Henstock-Kurzweil integrable function on an m-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function f : [0, 1]2 −→ R and a continuous function F : [0, 1]2 −→ R such that
(P)∫ x0{ (P) ∫ y 0 f(u, v) dv } du = (P) ∫ y 0 { (P) ∫ x 0 f(u, v) du } dv = F(x, y) for all (x, y) ∈ [0, 1]2.
A generalized $MV$-algebra $\mathcal A$ is called representable if it is a subdirect product of linearly ordered generalized $MV$-algebras. Let $S$ be the system of all congruence relations $\rho $ on $\mathcal A$ such that the quotient algebra $\mathcal A/\rho $ is representable. In the present paper we prove that the system $S$ has a least element.
This paper focused on predicting the bank erosion through the Bank Assessment for Non-point source Consequences of sediment (BANCS) model on the Tŕstie water stream, located in the western Slovakia. In 2014, 18 experimental sections were established on the stream. These were assessed through the Bank Erosion Hazard Index (BEHI) and the Near Bank Stress (NBS) index. Based on the data we gathered, we constructed two erosion prediction curves. One was for BEHI categories low and moderate, and one for high, very high, and extreme BEHI. Erosion predicted through the model correlated strongly with the real annual bank erosion – for low and moderate BEHI, the R2 was 0.51, and for
high, very high and extreme BEHI, the R2 was 0.66. Our results confirmed that the bank erosion can be predicted with sufficient precision on said stream through the BANCS model.