We construct a class of special homogeneous Moran sets, called {mk}-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of {mk}k\geqslant 1, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of ho- mogeneous Moran sets to assume the minimum value, which expands earlier works., Xiaomei Hu., and Obsahuje seznam literatury
In the present in vitro experiments we examined FSH- and ghrelin-induced changes in ovarian hormone secretion by transgenic rabbits. Fragments of ovaries isolated from adult transgenic (carrying mammary gland-specific mWAP-hFVIII gene) and non-transgenic rabbits from the same litter were cultured with and without FSH or ghrelin (both at 0, 1, 10 or 100 ng/ml medium). The secretion of progesterone (P4), estradiol (E2) and insulin-like growth factor I (IGF-I) was assessed by RIA. It was observed that ovaries isolated from transgenic rabbits secreted much less P4, E2 and IGF-I than the ovaries of non-transgenic animals. In control animals FSH reduced E2 (at doses 1-100 ng/ml medium) and IGF-I (at 1-100 ng/ml), but not P4 secretion, whereas ghrelin promoted P4 (at 1 ng/ml) and IGF-I (at 100 ng/ml), but not E2 output. In transgenic animals, the effects were reversed: FSH had a stimulatory effect on E2 (at 100 ng/ml) and ghrelin had an inhibitory effect on P4 (at 10 ng/ml). No differences in the pattern of influence of FSH on P4 and IGF-I and of ghrelin on E2 and IGF-I were found between control and transgenic animals. The present observations suggest that 1) both FSH and ghrelin are involved in rabbit ovarian hormone secretion, 2) transgenesis in rabbits is associated with a reduction in ovarian secretory activity, and 3) transgenesis can affect the response of ovarian cells to hormonal regulators., A. V. Sirotkin, P. Chrenek, K. Darlak, F. Valenzuela, Ž. Kuklová., and Obsahuje bibliografii a bibliografické odkazy
Some enhancements to the approximation of one-variable functions with respect to an orthogonal basis are considered. A two-step approximation scheme is presented here. In the first step, a constant bias is extracted from the approximated function, while in the second, the function with extracted bias is approximated in a usual way. Later, these two components are added together. First of all we prove that a constant bias extracted from the function decreases the error. We demonstrate how to calculate that bias. Secondly, in a minor contribution, we show how to choose basis from a selected set of orthonormal functions to achieve minimum error. Finally we prove that loss of orthonormality due to truncation of the argument range of the basis functions does not effect the overall error of approximation and the expansion coefficients' correctness. We show how this feature can be used. Our attention is focused on Hermite orthonormal functions. An application of the obtained results to ECG data compression is presented.
Some stronger and equivalent metrics are defined on M, the set of all bounded normal operators on a Hilbert space H and then some topological properties of M are investigated.
Let L1 = −Δ + V be a Schrödinger operator and let L2 = (−Δ)2 + V2 be a Schrödinger type operator on \mathbb{R}^{n}\left ( n\geqslant 5 \right ) where V≠ 0 is a nonnegative potential belonging to certain reverse Hölder class Bs for s\geqslant n/2. The Hardy type space H_{L2}^{1} is defined in terms of the maximal function with respect to the semigroup \left\{ {{e^{ - t{L_2}}}} \right\} and it is identical to the Hardy space H_{L2}^{1} established by Dziubański and Zienkiewicz. In this article, we prove the Lp-boundedness of the commutator Rb = bRf - R(bf) generated by the Riesz transform R = {\nabla ^2}L_2^{ - 1/2} , where b \in BM{O_\theta }(\varrho ) , which is larger than the space BMO\left (\mathbb{R}^{n} \right ). Moreover, we prove that Rb is bounded from the Hardy space H_{L2}^{1} into weak L_{weak}^1 (\mathbb{R}^n )., Yu Liu, Jing Zhang, Jie-Lai Sheng, Li-Juan Wang., and Obsahuje seznam literatury
Let λ1(Q) be the first eigenvalue of the Sturm-Liouville problem y ′′ − Q(x)y + λy = 0, y(0) = y(1) = 0, 0 < x < 1. We give some estimates for mα,β,γ = inf Q∈Tα,β,γ λ1(Q) and Mα,β,γ = sup Q∈Tα,β,γ λ1(Q), where Tα,β,γ is the set of real-valued measurable on [0, 1] x α(1 − x) β -weighted Lγ-functions Q with non-negative values such that ∫ 1 0 x α(1 − x) βQ γ (x) dx = 1 (α, β, γ ∈ ℝ, γ ≠ 0).
We consider the Sturm-Liouville problem with symmetric boundary conditions and an integral condition. We estimate the first eigenvalue λ1 of this problem for different values of the parameters.
We provide a characterization of continuous images of Radon-Nikodým compacta lying in a product of real lines and model on it a method for constructing natural examples of such continuous images.
This paper is a contribution to the theoretical foundations of data mining. More precisely, we contribute to a part of data mining allowing us to search for associations among attributes that can be expressed in the form of natural language sentences. The theoretical background and also a method for mining such associations was published recently in [V. Novák et al., Mining pure linguistic associations from numerical data, Int. Journal of Approximate Reasoning 48 (2008), 4 -- 22]. We elaborated other mathematical representations of the model presented in the mentioned paper in order to extend its applicability.
A grant project for the period 2003-2005, supported by the Grant Agency of the Czech Republic, was set up to determine properties of seismic waves and the structure of the uppermost part of the Earth´s crust in the territory of northern Moravia and Silesia. Quarry blasts and mining induced seismic events served as seismic sources. Permanent, temporary and portable seismic stations were used for the monitoring of these seismic events. During the experiments local microearthquakes were also detected and localized. For the complex evaluation of seismic wave features, data of the CELEBRATION 2000 and SUDETES 2003 refraction experiments were incorporated, as well. The velocity-depth dependence of body waves was searched by joint inversions of travel times of Pg/Sg phases. A special feature of the wave trains, generated by quarry blasts, was a pronounced dispersive character of short-period Rayleigh surface waves. These waves enabled us to establish their dispersion curves, on the basis of which the structure of superficial layers was determined down to a depth of several hundreds of meters., Karel Holub, Jaromír Knejzlík, Bohuslav Růžek, Jana Rušajová and Oldřich Novotný., and Obsahuje bibliografii