Chaos theory and social science: a methodological analysis

Der vorliegende Beitrag prüft die Relevanz der Chaos-Theorie für die Sozialwissenschaften. Die Anwendung von Chaos-Modellen zur Analyse von sozialen Phänomenen wirft einige wichtige methodologische Fragen auf. Chaos-Modelle sind nicht-lineare mathematische Modelle. Bei ihrer Anwendung auf soziale Probleme diskutieren die Autoren hauptsächlich die Frage der internen und externen Validität. Das Fazit der Ausführungen läßt sich wie folgt zusammenfassen: Den Sozialwissenschaften ist wenig mit der Anwendung elaborierter mathematischer Modelle gedient, wenn das theoretische Verständnis und Wissen über die zugrundeliegenden dynamischen Prozesse unzureichend ist. Erst wenn diese Voraussetzung erfüllt ist, lassen sich Modelle der Chaos Theorie in die Sozialwissenschaften mit Nutzen einbringen. (pmb)'This article investigates the relevance of chaos theory for social science. The application of chaos models in the analysis of social phenomena is accompanied by some important scientific problems. First, whether observations of social phenomena are generated by nonlinear dynamics cannot be ascertained beyond considerable doubt, especially when these observations contain measurement errors; i.e., there is a problem of external validity. Secondly, and more important, as a theory of irregular cyclical social behaviour is lacking inductive-statistical theory-formation about such behaviour, which is based on fitting a mathematical model of chaos to observations of social phenomena, is impossible unless additional information is used concerning the context and circumstances wherein the social phenomena occur; i.e., the internal validity of any theoretical explanation that is derived from only a fitted mathematical model (of chaos) cannot be assessed. So, research into the suggestion derived from mathematical chaos theory that irregular cycles may be present in the development of social phenomena over time requires theory-formation about irregular cyclical social behaviour on the basis of established theoretical insights and empirical evidence instead of fitting sophisticated mathematical models of chaos to observations of social phenomena.' (author's abstract

ON THE EMBEDDING OF GROUPS AND DESIGNS IN A DIFFERENCE BLOCK DESIGN

A difference BIBD is a balanced incomplete block design on a group which isconstructed by transferring a regular perfect difference system by a subgroup of its point set. There is an obvious bijection between these BIBDs and some copies of their point sets as two sets. In this paper, we investigate the algebraic structure of these block designs by definning a group-isomorphism between them and their point sets. It has done by defning some relations between the independent-graphs of difference BIBDs and some Cayley graphs of their point sets. It is shown that some Cayley graphs are embedded in the independent-graph of difference BIBDs as a spanning sub-graphs. Due to find these relations, we find out a configuration ordering on these BIBDs, also we achieve some results about the classification of these BIBDs. All in this paper are on difference BIBDs with even numbers of the points

Hypertensive disorders in twin pregnancy

Objective: To compare the incidence and severity of pregnancy-induced hypertensive disorders in twin pregnancy and in singleton gestation. Study design: Case-control study in the setting of a University Hospital. Each pregnancy of a consecutive series of 187 twin pregnancies attending the antenatal clinic and booked before a gestational age of 24 weeks was matched for maternal age, parity, and gestational age at delivery with a singleton pregnancy delivered in the same year. Primary end points of the analysis of the course and outcome of pregnancy were pregnancy-induced hypertension and proteinuric pre-eclampsi. Results: In the twin pregnancy group, 21% of patients met the criteria for the diagnosis of a pregnancy-induced hypertensive disorder, compared with 13% in the singleton pregnancy group (P < 0.05). The difference was due to a significantly higher incidence of pregnancy-induced hypertension in twin (15%) than in singleton (6%) pregnancy (P < 0.05), in particular in nulliparous women. The incidence of pre-eclampsia was similar in twin (6%) and singleton pregnancies (6.5%), without a difference in severity and in the occurrence of the HELLP syndrome. Conclusion: The incidence of non-proteinuric pregnancy-induced hypertension, but not of proteinuric pre-eclampsia, is increased in twin pregnancy

Proof of Concept of Novel Visuo-Spatial-Motor Fall Prevention Training for Old People

Falls in the geriatric population are one of the most important causes of disabilities in this age group. Its consequences impose a great deal of economic burden on health and insurance systems. This study was conducted by a multidisciplinary team with the aim of evaluating the effect of visuo-spatial-motor training for the prevention of falls in older adults. The subjects consisted of 31 volunteers aged 60 to 92 years who were studied in three groups: (1) A group under standard physical training, (2) a group under visuo-spatial-motor interventions, and (3) a control group (without any intervention). The results of the study showed that visual-spatial motor exercises significantly reduced the risk of falls of the subjects

On some known fixed point results in the complex domain: survey / О некоторых известных результатах о неподвижной точке в комплексном домене: исследование / Neki poznati rezultati iz nepokretne tačke u kompleksnom domenu - istraživanje

In this survey paper, we consider some known results from the fixed point theory with complex domain. The year 1926 is very significant for this subject. This is the beginning of the research and application of the fixed point theory in complex analysis. The Denjoy-Wolf theorem, together with the Banach contraction principle, is one of the main tools in the mathematical analysis. / В данной обзорной статье представлены некоторые известные результаты теорий о неподвижной точке над комплексным доменом. Надо подчеркнуть, что 1962 год является ключевым для данной области. Ведь именно тогда начали проводиться исследования по применению теорий о неподвижной точке в рамках комплексного анализа. Теорема единственности для рядов Вольфа-Данжуа наряду с Банаховым принципом сжатия, становятся главным методом (результатом) математического анализа. / U ovom preglednom radu razmatrani su neki poznati rezultati iz teorije nepokretne tačke nad kompleksnim domenom. Istraživanje i primena teorije nepokretne tačke u kompleksnoj analizi započeti su 1926, godine. Teorema DenjoyWolf, zajedno sa Banahovim principom kontrakcije, jedno je od glavnih oruđa (rezultata) matematičke analize