A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack-McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.
The article delimits emotionality and presents a brief survey of research of emotional interjections. The methodology of the research (the issues of classification of the semantic field of emotionality, semantics of interjections, selection of the analysed texts) is outlined. The core of the paper consists in the characteristics of the five basic types of emotions, described on the basis of the material of interjections: (1) psychical states, e.g. pleasure-displeasure, joy, sadness, relief, surprise etc., (2) egoistic emotions (e.g. fear), (3) altruistic emotions (e.g. liking-antipathy, mistrust, admiration, wrath etc.), (4) esthetical emotions (beauty, disgust), (5) ethical emotions (e.g. pity). The sixth part of the article investigates the displays and consequences of emotions (for example, laughing and crying are expressed by onomatopoeic interjections. The general conclusions of the paper are represented by the findings that emotional interjections often have no inherent meaning, but these interjections are usually polysemic (as one interjection expresses more emotions, e.g. ach, bože), and that some emotions are expressed by a number of synonymous interjections (e.g. ''joy'' jupí, juchú, ach, joj, jé, páni, bože etc.).
This paper proposes a stochastic diffusion model for the spread of a susceptible-infective- removed Kermack–McKendric epidemic (M1) in a population which size is a martingale Nt that solves the Engelbert–Schmidt stochastic differential equation (2). The model is given by the stochastic differential equation (M2) or equivalently by the ordinary differential equation (M3) whose coeffients depend on the size Nt. Theorems on a unique strong and weak existence of the solution to (M2) are proved and computer simulations performed.
The article deals with one type of subordinate clauses expressing causality, namely pronominal-particle clauses in the present Czech. The incorporation of these clauses into the head clause lies in the fact that they express broadly understood causal meanings of adverbial subordinate clauses using primary and secondary prepositions and multiple-word units together with the pronoun to, which anticipates the subordinate clause introduced by the connecting particles že, aby. Data from the Czech National Corpus concerning subordinate clauses of cause (reason), purpose, condition and concession are analysed from the point of view of the Czech language (grammar) system.