In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated.
The paper is a reflection on the role of practical wisdom in ethics. By explaining and trying to understand the essence of practical wisdom, the author has endeavoured to determine whether it can be treated as a central ethical category, and if so, then why. In these analyses, author has referred to the concept of Aristotle, universally acknowledged as the classical one. Characterizing and describing that concept, she tries to answer three questions: 1) What is practical wisdom? 2) What function does it perform in ethics? 3) What is the relationship between practical wisdom and other ethical categories? The article is divided into four parts. Each of them concerns different aspects of the analysis of practical wisdom. As a result, the author has come to several important conclusions: Practical wisdom 1) enables appropriate action, i.e. success in action; 2) refers not only to the means-to-ends relationship, but refers to the end itself; 3) is imperative, because it tells what to do; 4) referring to the unusual situation, it allows to understand that every general principle is limited; 5) it is the intellectual ability to recognize how to achieve happiness., Příspěvek je úvahou o úloze praktické moudrosti v etice. Vysvětlením a pokusem o pochopení podstaty praktické moudrosti se autor snažil určit, zda může být považován za centrální etickou kategorii, a pokud ano, pak proč. V těchto analýzách se autor zmiňuje o pojetí Aristotela, všeobecně uznávaném jako klasický. Charakterizuje a popisuje tento koncept a snaží se odpovědět na tři otázky: 1) Co je praktická moudrost? 2) Jakou funkci plní v etice? 3) Jaký je vztah mezi praktickou moudrostí a ostatními etickými kategoriemi? Článek je rozdělen do čtyř částí. Každá z nich se týká různých aspektů analýzy praktické moudrosti. V důsledku toho autor dospěl k několika důležitým závěrům: Praktická moudrost 1) umožňuje vhodné kroky, tj úspěch v akci; 2) odkazuje nejen na vztah mezi prostředky, ale odkazuje na samotný konec; 3) je nezbytné, protože říká, co má dělat; 4) s odkazem na neobvyklou situaci umožňuje pochopit, že každý obecný princip je omezen; 5) je to intelektuální schopnost rozpoznat, jak dosáhnout štěstí., and Karolina Rozmarynowska
This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either $\mathbb{R}$ or $\mathop {\mathrm sl}(2,\mathbb{R})$ or $\operatorname{so} (3)$ are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to $n+1$, where $n$ is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For $\mathbb{R}$-Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf theorem for flat connections) saying that the index sum is independent of the choice of a connection. Multiplying this index sum by the orientation class of $M$, we get the Euler class of this Lie algebroid. Some integral formulae for indices are given.
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