On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

CHANGES IN FATTY ACID COMPOSITION OF DIFFERENT MILK PRODUCTS CAUSED BY DIFFERENT TECHNOLOGY

The fatty acid composition of cow’s milk with fat contents of 3.6%, Dalia cheese with fat contents of 44%, butter with fat contents of 80% and margarine with fat contents of 24% was determined after a heat treatment performed on cooking plate and microwave treatment, respectively of different durations. The biggest difference was obtained for oleic acid and elaidic acid since, with the exception of the margarine, in each case proportion of the cis-configurated oleic acid decreased while that of the trans-configurated elaidic acid increased. For all of the other fatty acids in the foodstuffs examined no such differences were obtained regarding change in fatty acid composition whose differences could influence healthy nutrition to considerable extent. Therefore we can take it as a fact that neither heat treatment performed on a traditional cooking plate nor microwave treatment affects considerably the composition of food fats

Trianon és a brit földrajz I. = British Geography and the Trianon Peace Treaty (Part 1)

The ‘dismemberment’ of Hungary as a result of the Treaty of Trianon (1920) was a momentous event. This paper examines the reaction of British geographers to Hungary’s dramatic and extensive loss of territory and much-reduced national sovereignty. It considers two works by British geographers, Marion Newbigin (in 1920) and Alan Ogilvie (in 1922), who attempted to explain Hungary’s situation following the Treaty. To Hungary’s geographers, Trianon ruptured historical associations between nature and nation. Boundaries previously formed upon the Carpathians’ natural geography and the hydrography of the Great Hungarian Plain were now replaced by ethnic considerations, even although these proved difficult to effect in practice as the basis of the new boundaries. The paper explores maps produced by Hungarian geographers, and most notably Pál Teleki’s ‘Ethnographical Map of Hungary’ (1919)—the so-called ‘Carte Rouge’—which attempted to reveal Hungary’s ethnic identity and territorial integrity. The paper then examines Marion Newbigin’s ‘Aftermath: A geographical study of the peace terms’ (1920) and Ogilvie’s ‘Some aspects of boundary settlement at the peace conference’ (1922) as Britain’s geographers tried to explain and justify Trianon in terms of post-war geopolitics, ethnic diversity, and linguistic difference. For Newbigin, Hungary’s ethnic delimitation post-Trianon was largely dictated by the Western powers (principally by the American delegation to the 1919 Paris peace conference). In his work Ogilvie (a member of the British geographical delegation in Paris) shows that the principles on which Trianon was determined were often compromised in practice. The paper shows how the new geography of Europe and Hungary dictated by Trianon elicited different responses from different geographical communities

Soil analyses in the Rothamsted Park grass experiment

 The status of antioxidant superoxide dismutase (SOD) was reported decreased in the liver tissues of diabetic experimental Macaca fascicularis. This study observed effect of Mamordica charantia on the status of SOD in the liver and kidney of diabetic experimental rats. The SOD was localized using immunohistochemical technique.  Male Wistar rats of negative control and diabetes mellitus (DM) group treated with 5 and 10% of M. charantia powder for 28 days. The DM condition was achieved by alloxan (110 mg/kg BW) induction. Charantia powder increased the status of antioxidant SOD in the liver and kidney of diabetic experimental rats. Aplication of M. charantia powder 10% gave better results than that of 5%. The results suggested that M. charantia powder can increase the status of antioxidant in the oxidative stress condition, such as diabetes mellitus

The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete