A subset of the plane is called a two point set if it intersects any line in exactly two points. We give constructions of two point sets possessing some additional properties. Among these properties we consider: being a Hamel base, belonging to some $\sigma $-ideal, being (completely) nonmeasurable with respect to different $\sigma $-ideals, being a $\kappa $-covering. We also give examples of properties that are not satisfied by any two point set: being Luzin, Sierpiński and Bernstein set. We also consider natural generalizations of two point sets, namely: partial two point sets and $n$ point sets for $n=3,4,\ldots , \aleph _0,$ $\aleph _1.$ We obtain consistent results connecting partial two point sets and some combinatorial properties (e.g. being an m.a.d. family).
We give some explicit values of the constants $C_{1}$ and $C_{2}$ in the inequality $C_{1}/{\sin (\frac{\pi }{p})}\le \left| P\right| _{p}\le C_{2}/{\sin (\frac{\pi }{p})}$ where $\left| P\right| _{p}$ denotes the norm of the Bergman projection on the $L^{p}$ space.
Effects of low-frequency electromagnetic fields (LF EMF) on the
activation of different tissue recovery processes have not yet
been fully understood. The detailed quantification of LF EMF
effects on the angiogenesis were analysed in our experiments by
using cultured human and mouse endothelial cells. Two types of
fields were used in the tests as follows: the LF EMF with
rectangular pulses, 340-microsecond mode at a frequency of
72 Hz and peak intensity 4 mT, and the LF EMF with sinusoidal
alternating waveform 5 000 Hz, amplitude-modulated by means
of a special interference spectrum mode set to a frequency linear
sweep from 1 to 100 Hz for 6 s and from 100 Hz to 1 Hz return
also for 6 s, swing period of 12 second. Basic parameters of
cultured cells measured after the LF EMF stimulus were viability
and proliferation acceleration. Both types of endothelial cells
(mouse and human ones) displayed significant changes in the
proliferation after the application of the LF EMF under conditions
of a rectangular pulse mode. Based on the results, another test
of the stimulation on a more complex endothelial-fibroblast
coculture model will be the future step of the investigation.
The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in $2$-normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.
In this paper, following the methods of Connor \cite {connor}, we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely \cite {moe}) to $\mu $-statistical convergence and convergence in $\mu $-density using a two valued measure $\mu $. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $\mu $ called the (APO$_2$) condition, inspired by the (APO) condition of Connor \cite {jc}. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure $\mu $ has the condition (APO$_2$).
One of the limiting factors in decreasing the systematic error of laser ranging is the influence of the atmospheric refraction. Two colour ranging may contribute useful information for more precise refraction factor modelling and calculation. We will describe two wavelength experiment using streak camera as a high resolution detector for ground target distance measurement.
The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is reflected in the vagueness of the very term indispensability, which is essential to the Argument. The paper will remind of a recent definition of the concept of indispensability of a mathematical object, reveal its deficiency and propose an improvement of this definition. Following this, we will deal with one of the consequences of the arbitrary employment of the concept of indispensability of a mathematical theory. We will propose a definition of this concept as well, in accordance with the common intuition about it. Eventually, on the basis of these two definitions, the paper will describe the relation between these two concepts, in the attempt to clarify the conceptual apparatus of the EIA., Současní platonisté ve filozofii matematiky argumentují, že matematické objekty existují. Jedním z argumentů, které toto stanovisko podporují, je tzv. Enhanced Indispensability Argument (EIA). Cílem tohoto příspěvku je poukázat na obtíže spojené s EIA. První z nich je obsažena v vágní formulaci Argumentu, což je důvod, proč nelze stanovit ani přibližný rozsah nastavených objektů, jejichž existence je uvedena argumentem. Druhý problém se odráží v neurčitosti samotného pojmu nepostradatelnost, která je pro argument nezbytná. Příspěvek bude připomínat nedávnou definici pojmu nepostradatelnost matematického objektu, odhalit jeho nedostatek a navrhnout zlepšení této definice. Poté budeme se zabývat jedním z důsledků svévolného zaměstnávání konceptu nepostradatelnosti matematické teorie. Navrhneme také definici této koncepce v souladu se společnou intuicí. Nakonec, na základě těchto dvou definic, bude článek popsat vztah mezi těmito dvěma pojmy, ve snaze objasnit koncepční aparát EIA., and Vladimir Drekalović
A refined common generalization of known theorems (Arhangel’skii, Michael, Popov and Rančin) on the Fréchetness of products is proved. A new characterization, in terms of products, of strongly Fréchet topologies is provided.
In many natural language processing applications two or more models usually have to be involved for accuracy. But it is difficult for minor models, such as “backoff” taggers in part-of-speech tagging, to cooperate smoothly with the major probabilistic model. We introduce a two-stage approach for model selection between hidden Markov models and other minor models. In the first stage, the major model is extended to give a set of candidates for model selection. Parameters weighted hidden Markov model is presented using weighted ratio to create the candidate set. In the second stage, heuristic rules and features are used as evaluation functions to give extra scores to candidates in the set. Such scores are calculated using a diagnostic likelihood ratio test based on sensitivity and specificity criteria. The selection procedure can be fulfilled using swarm optimization technique. Experiment results on public tagging data sets show the applicability of the proposed approach.
This conference took place 3-7 March 2008 and was held in the Emauzy Abbey. ALICE is the acronym for A Large Ion Collider Experiment, one of the largest experiments in the world devoted to research in the physics of matter on an infinitely small scale. Hosted at CERN, this project involves the international collaboratin of more than 1000 physicists, engineers and technicians from 300 countries. Together they are contributing to the resolution of one of the latest challenges in fundamental physics recounting the birth of matter. and Michal Šumbera, Vojtěch Petráček, Petr Závada.