In our earlier paper [9], generalizing the well known notion of graceful graphs, a $(p,m,n)$-signed graph $S$ of order $p$, with $m$ positive edges and $n$ negative edges, is called graceful if there exists an injective function $f$ that assigns to its $p$ vertices integers $0,1,\dots ,q = m+n$ such that when to each edge $uv$ of $S$ one assigns the absolute difference $|f(u) - f(v)|$ the set of integers received by the positive edges of $S$ is $\lbrace 1,2,\dots ,m\rbrace $ and the set of integers received by the negative edges of $S$ is $\lbrace 1,2,\dots ,n\rbrace $. Considering the conjecture therein that all signed cycles $Z_k$, of admissible length $ k \ge 3$ and signed structures, are graceful, we establish in this paper its truth for all possible signed cycles of lengths $ 0,2$ or $3\hspace{4.44443pt}(\@mod \; 4)$ in which the set of negative edges forms a connected subsigraph.
The article explores the frequency and intensity of childcare provided by grandparents. It uses the 2006/2007 SHARE data for 12 countries with a special focus on the Czech Republic. Past research usually distinguishes between the North-European model with high frequency and low intensity grand-parenting and the Southern-European model with low frequency and high intensity grand-parenting. This article shows that the Czech Republic - along with Germany and Austria - cannot be easily classified into these two broad patterns. Czech grandparents tend to participate in childcare with low frequency and low intensity, particularly in the case of children under 3 years of age. Low maternal labor force participation is used as an argument explaining this finding., Dana Hamplová., and Obsahuje bibliografii
V českém prostředí se latinsky psaná příležitostná poezie nejvíce rozvíjela během 16. století. Jde o básnické texty různorodého rozsahu psané k rozmanitým životním událostem (narozeniny, ukončení studia, cesta do ciziny, sňatek, narození dítěte, úmrtí). Tato oblast humanistického básnictví má vzory v antice, odkud také většina jejích žánrů pochází, a to především z období pozdní římské literatury. Většina z nich si uchovala svou podobu přes středověk až do doby humanismu. Druhy příležitostné poezie jsou definovány v poetikách a rétorikách různých období. Normativnost neolatinské humanistické literatury tedy dává možnost tyto jednotlivé žánry zkoumat a popisovat z hlediska genologického. K nejoblíbenějším žánrům příležitostné poezie (lze-li soudit dle četnosti výskytu) patřila epithalamia a epicedia. Epithalamium čili svatební píseň je blahopřáním k sňatku. Studie analyzuje epithalamia vzniklá v období pozdního humanismu (přelom 16. a 17. století) především z hlediska tematického a motivického, všímá si jejich zajímavých aspektů a také některých pozoruhodnějších realizací žánru, příkladů, v nichž autoři usilovali o jistou míru originality a vymanění se z dobové konvence. and In the Bohemian Lands occasional verse written in Latin developed mostlyin the sixteenth century. It comprises poetic texts of various lengths writtenfor important events in life, such as birthdays, the completion of studies, departures for, or returns from, journeys to foreign lands, weddings, births,or deaths. This branch of humanist poetry employs models from classicalantiquity, which is also where most of its sub-genres come from, mainly inthe period of late Roman literature. Most preserved their form throughoutthe Middle Ages and into the period of humanism. The kinds of occasionalverse are defined in works on poetics and rhetoric of various periods. Thenormative nature of Neo-Latin humanist literature therefore makes it possibleto investigate the individual sub-genres and describe them in terms of genretheory. Among the most popular sub-genres of occasional verse (if one canjudge fairly from the number of poems written) are epithalamia and epicedia.The article analyzes epithalamia written in the latter part of the humanistperiod (the late sixteenth and early seventeenth centuries), concerned chieflywith themes and motifs, and considers interesting aspects and remarkableexamples in which the poets seek to achieve a measure of originality and tofree themselves from the conventions of the times.
In this work, oscillatory behaviour of solutions of a class of fourth-order neutral functional difference equations of the form ∆ 2 (r(n)∆2 (y(n) + p(n)y(n − m))) + q(n)G(y(n − k)) = 0 is studied under the assumption ∑∞ n=0 n ⁄ r(n) < ∞. New oscillation criteria have been established which generalize some of the existing results in the literature.