We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others. The Lyapunov function used does not involve the use of signum functions as used by others.
We define an ultra $LI$-ideal of a lattice implication algebra and give equivalent conditions for an $LI$-ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $LI$-ideal.
A mistake concerning the ultra $LI$-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an $LI$-ideal to be an ultra $LI$-ideal are given. Moreover, the notion of an $LI$-ideal is extended to $MTL$-algebras, the notions of a (prime, ultra, obstinate, Boolean) $LI$-ideal and an $ILI$-ideal of an $MTL$-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in $MTL$-algebra: (1) prime proper $LI$-ideal and Boolean $LI$-ideal, (2) prime proper $LI$-ideal and $ILI$-ideal, (3) proper obstinate $LI$-ideal, (4) ultra $LI$-ideal.
Recently, more and more efforts are directed towards developing new imaging and drug-delivery options based on various nanoparticles, exploiting their unique properties. Here, ultra-small gold nanoparticles functionalized with widely used polyethylene glycol and its amine-terminated form were tested in respect of their potential interactions with human immune cells (cell line and primary cells). The results showed that differently terminated ultrasmall gold nanoparticles represent an interesting theranostic platform as they are harmless to immune cells (not inducing cytotoxicity and severe immune response) and on the other hand, they can serve as imaging and/or drug delivery agents using e.g. monocytes/ macrophages as “Trojan horses” to deliver these nanoparticles across the blood-brain barrier and diagnose or treat pathologies of the central nervous system.
Mnoho skupin živočichů disponuje zrakem citlivým na tzv. ultrafialové světlo. Jednou z takových skupin jsou i různí opylovači, kteří nám dobře známé květy mohou vidět v trochu odlišných barvách, než my. Na květech rostlin totiž často existují vzory patrné pouze v ultrafialové části spektra, které jsou pro člověka neviditelné. V první části seriálu o výskytu a významu těchto vzorů u rostlin se zabývá historií odhalování citlivosti živočichů na ultrafialové světlo, přibližuje otázky, jak funguje zrak a jakým způsobem ultrafialové zbarvení na povrchu organismů vzniká., The vision of many animal groups is sensitive to the so-called ultraviolet (UV) light. These groups include various pollinators, which may see flowers that are quite familiar to us in a different coloration. That is because flowers often feature patterns visible only in the UV part of the spectrum, and thus invisible to humans. This series deals with the occurrence of such patterns and their significance for plants. The first part recounts the history of discovering the sensibility of animals to UV light, expounds on the way how vision works, explains the origin of UV coloration on organismal surfaces., and Pavel Pecháček.
Význam ultrafialových znaků v životě různých organismů byl dlouho opomíjen především z toho důvodu, že UV paprsky jsou pro lidský zrak za normálních okolností neviditelné. Jedna z možností, jak si můžeme ultrafialovou podobu živočichů či rostlin zviditelnit, je použití speciálně upraveného klasického či digitálního fotoaparátu. Druhý díl seriálu o ultrafialových vzorech na květech rostlin se zabývá vývojem techniky záznamu UV podoby různých organismů a popisem získávání fotografií, které doprovázejí tento text. Druhá část článku je věnována vybraným druhům našich nejběžnějších rostlin a charakterizaci jejich ultrafialových znaků., The significance of UV characteristics for the life of various organisms has been neglected for a long time. It stems mainly from the fact, that under normal circumstances, UV rays are invisible to the human eye. One of the ways to make the UV appearance of animals or plants visible is to use a specially adjusted classic or digital camera. This second paper deals with the UV patterns on flowers. It focuses on the development of techniques which allow us to capture the UV appearance of various organisms, and provides a methodology with which the accompanying photos were taken. The article also presents selected species of common native plants, with a description of their UV characteristics., and Pavel Pecháček.