Two ideals connected with strong right upper porosity at a point

Let $SP$ be the set of upper strongly porous at $0$ subsets of $\mathbb R^{+}$ and let $\hat I(SP)$ be the intersection of maximal ideals $I \subseteq SP$. Some characteristic properties of sets $E\in\hat I(SP)$ are obtained. It is shown that the ideal generated by the so-called completely strongly porous at $0$ subsets of $\mathbb R^{+}$ is a proper subideal of $\hat I(SP).$Comment: 18 page

Evaluation of a Reflection Method on an Open-Ended Coaxial Line and its Use in Dielectric Measurements

This paper describes a method for determining the dielectric constant of a biological tissue. A suitable way to make a dielectric measurement that is nondestructive and noninvasive for the biological substance and broadband at the frequency range of the network analyzer is to use a reflection method on an open ended coaxial line. A coaxial probe in the frequency range of the network analyzer from 17 MHz to 2 GHz is under investigation and also a calibration technique and the behavior of discrete elements in an equivalent circuit of an open ended coaxial line. Information about the magnitude and phase of the reflection coefficient on the interface between a biological tissue sample and a measurement probe is modeled with the aid of an electromagnetic field simulator. The numerical modeling is compared with real measurements, and a comparison is presented.

A compact null set containing a differentiability point of every Lipschitz function

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.Comment: 28 pages; minor modifications throughout; Lemma 4.2 is proved for general Banach space rather than for Hilbert spac

Surfaces Meeting Porous Sets in Positive Measure

Let n>2 and X be a Banach space of dimension strictly greater than n. We show there exists a directionally porous set P in X for which the set of C^1 surfaces of dimension n meeting P in positive measure is not meager. If X is separable this leads to a decomposition of X into a countable union of directionally porous sets and a set which is null on residually many C^1 surfaces of dimension n. This is of interest in the study of certain classes of null sets used to investigate differentiability of Lipschitz functions on Banach spaces

A σ\sigma-porous set need not be σ\sigma-bilaterally porous

summary:A closed subset of the real line which is right porous but is not $\sigma$-left-porous is constructed

Modelling of the turbine blade by new finite element

This publication was supported by the project TE 01020068 of the Technology Agency of the Czech Republic and by the project GA16-04546S.The paper deals with 1D finite element modelling of a turbine blade. The proposed finite element has only 16 degrees of freedom (DOF) and enables to achieve a complex model of turbo-machine with a relatively small DOF number, more details will be described in the article. It is a great advantage but the pre-processing for the blade cross section parameters of the individual blades is a little bit more complicated. This approach means to solve a warping function in chosen cross sections of the blade and simultaneously calculate the geometrical parameters of those cross sections. The second step represents an approximation of the obtained parameters along the axis coordinate ? by means of spline functions. The next step is gradual computation of local finite element matrices and assemblage of the global blade matrices