We study the problem of existence of orbits connecting stationary points for the nonlinear heat and strongly damped wave equations being at resonance at infinity. The main difficulty lies in the fact that the problems may have no solutions for general nonlinearity. To address this question we introduce geometrical assumptions for the nonlinear term and use them to prove index formulas expressing the Conley index of associated semiflows. We also prove that the geometrical assumptions are generalizations of the well known Landesman-Lazer and strong resonance conditions. Obtained index formulas are used to derive criteria determining the existence of orbits connecting stationary points.
The study aims to present and shed light on lyric philosophy, a philosophical orientation established by the Canadian philosopher Jan Zwicky. It does so in several steps. First, it presents the central idea of the existence of nonverbal lyric thinking and the experiencing of lyric practice in the framework of which the meaning of this world and its individual parts is to be shown to us. It then illustrates these theses by presenting the two main inspirations of lyric philosophy – the philosophy of Ludwig Wittgenstein and gestaltism. It also brings nearer the relationship between lyric philosophy and the philosophical method that is reduced to thinking in words with the help of logical categories. It then focuses on the communication of meaning through metaphorical expression, which Zwicky considers to be a sort of “window” in the “wall” between us and the meaning through which we are able to see meaning. Finally, the study considers lyric philosophy’s problematic areas and relationship with the philosophical tradition and makes an attempt to outline its potential for philosophical research in general. and Studie si klade za cíl představit a osvětlit lyrickou filosofii, filosofický směr založený kanadskou filosofkou Jan Zwickyovou. Činí tak v několika krocích. Nejprve představuje centrální myšlenku existence nonverbálního lyrického myšlení a zakoušení lyrické zkušenosti, v rámci které se nám má ukazovat smysl tohoto světa a jeho jednotlivých částí. Tyto teze poté dokresluje skrze představení dvou hlavních inspirací lyrické filosofie – filosofie Ludwiga Wittgensteina a gestaltismu. Dále přibližuje vztah lyrické filosofie a filosofické metody redukované na myšlení ve slovech za pomoci logických kategorií. Posléze se zaměřuje na komunikaci smyslu skrze metaforické vyjádření, které Zwickyová považuje za jakési „okno“ ve „zdi“ mezi námi a smyslem, skrze které jsme schopni smysl nahlédnout. Nakonec se studie zamýšlí nad problematickými místy lyrické filosofie a jejím vztahem s filosofickou tradicí. V souvislosti s tím se pak pokouší načrtnout její potenciál pro filosofické bádání vůbec.
The paper deals with the modelling of a real gearbox used in cement mill applications and with the sensitivity analysis of its eigenfrequencies with respect to design parameters. The torsional model (including a motor and couplings) based on th finite element method implemented in an in-house MATLAB application is described. The sensitivity analysis of gearbox eigenfrequencies is performed in order to avoid possible dangerous resonance states of the gearbox. The parameters chosen with respect to the sensitivity analysis are used for tuning the gearbox eigenfrequencies outside resonance areas. Two approaches (analytical and numerical) to the sensitivity calculation are discussed. and Obsahuje seznam literatury
This paper deals with the generalized nonlinear third-order left focal problem at resonance (p(t)u ′′(t))′ − q(t)u(t) = f(t, u(t), u′ (t), u′′(t)), t ∈ ]t0, T[, m(u(t0), u′′(t0)) = 0, n(u(T), u′ (T)) = 0, l(u(ξ), u′ (ξ), u′′(ξ)) = 0, where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions by using the topological degree technique as well as some recent generalizations of this technique. Our results are generalizations and extensions of the results of several authors. An application is included to illustrate the results obtained.