Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
A number of new results that say how to transfer the entailment relation between two different finite generators of a quasi-variety of algebras is presented. As their consequence, a well-known result saying that dualisability of a quasi-variety is independent of the generating algebra is derived. The transferral of endodualisability is also considered and the results are illustrated by examples.
Necessary and sufficient conditions are given for the existence of state and output transformations, that bring single-input single-output nonlinear state equations into the observer form. The conditions are formulated in terms of differential one-forms, associated with an input-output equation of the system. An algorithm for transformation of the state equations into the observer form is presented and illustrated by an example.
We show how we can transform the H∞ and H2 control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for H∞ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal H2 controller.
Článek se zabývá některými důsledky otevřené vědy z perspektivy komunikace vědy a filosofie komunikace. Kromě čistě komunikačních a filosofických témat se text věnuje i otázkám tykajícím se procesu popularizace vědy prostřednictvím sociálních médií (zejména Twitteru a blogů). Článek se sestává ze tří oddílů: první navrhuje definici komunikace vědy a sociálních médií; druhý zkoumá proměnu komunikace vědy v éře internetu a zabývá se vlivem sociálních médií na komunikaci vědy; třetí a závěrečný oddíl přináší několik případových studií a filosofických postřehů. Nejdůležitějším, zde dosaženým závěrem je tvrzení, že sociální media vědu a vědeckou komunikaci proměnila. Twitter a blogy jakožto nové nástroje vědecké komunikace mohou být užitečné a smysluplné pro vědu i společnost. Sociální média mohou být navíc použita k usnadnění širšího zapojení občanů do diskusí o vědě., The aim of the present article is to discuss several consequences of the Open Science from a perspective of science communication and philosophy of communication. Apart from the purely communicative and philosophical issues, the paper deals with the questions that concern the science popularization process through social media (especially Twitter and blogs). The article consists of three sections: the first one suggests a definition of science communication and social media, the second examines the transformation of science in the Age of the Internet and considers the influence of social media on science communication, the third and final one presents some case studies and philosophical observations. The most important conclusion to be reached here is that the social media have changed science and science communication. Twitter and blogs as novelty tools of science communication can be useful and meaningful for both science and society. Furthermore, social media can be used to facilitate broader involvement of citizens in the discussion about science., and Emanuel Kulczycki.
The paper describes the general form of an ordinary differential equation of an order $n+1$ $(n\ge 1)$ which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form \[ f\biggl (s, w_{00}v_0, \ldots , \sum _{j=0}^n w_{n j}v_j\biggr )=\sum _{j=0}^n w_{n+1 j}v_j + w_{n+1 n+1}f(x,v, v_1, \ldots , v_n), \] where $w_{n+1 0}=h(s, x, x_1, u, u_1, \ldots , u_n)$, $ w_{n+1 1}=g(s, x, x_1, \ldots , x_n, u, u_1, \ldots , u_n)$ and $w_{i j}=a_{i j}(x_1, \ldots , x_{i-j+1}, u, u_1, \ldots , u_{i-j})$ for the given functions $a_{i j}$ is solved on $\mathbb R$, $ u\ne 0.$.
We suggest a nonparametric version of the probability weighted empirical characteristic function (PWECF) introduced by Meintanis {et al.} \cite{meiswaall2014} and use this PWECF in order to estimate the parameters of arbitrary transformations to symmetry. The almost sure consistency of the resulting estimators is shown. Finite-sample results for i.i.d. data are presented and are subsequently extended to the regression setting. A real data illustration is also included.