Local Limit Theorem for the Lorentz Process and Its Recurrence in the Plane

For Young systems, i.e. for hyperbolic systems without/with singularities satisfying Lai-Sang Young's axioms (which imply exponential decay of correlation and the CLT) a local CLT is proven. In fact, a unified version of the local CLT is found, covering among others the absolutely contionuous and the arithmetic cases. For the planar Lorentz process with a finite horizon this result implies a.) the local CLT and b.) the recurrence. For the latter case ($d=2$, finite horizon), combining the global CLT with abstract ergodic theoretic ideas, K. Schmidt, and J.-P. Conze, could already establish recurrence

Újabb adatok az Alinda biplicata (Montagu 1803) héjmorfológiájához, valamint annak klímafüggéséhez (Mollusca, Clausiliidae) : In memoriam malacologus Kovács Gyula (1932‒1996) = New data on the shell morphology of the Alinda biplicata, as well as its microlimata dependence

Abstract: The authors show that the shell sizes of Alinda biplicata are largest in the Bakony Mountains, are the smallest in the Somogy Hilly

Kárpát-medencei adatok a Laciniaria plicata (Draparnaud, 1801) és az Alinda biplicata (Montagu, 1803) héjalaktanához, annak klímafüggéséhez (Mollusca, Clausiliidae) = Data on the shell morphology of the Laciniaria plicata and the Alinda biplicata as well as theirs macroclimate dependence in the Carpathian Basin

The authors point out that the shell size of the Laciniaria plicata and the Alinda biplicata is the largest in the mountains, is the smallest in the lowland regions.The shell morphologic results be connected with climate types (Péczely 1957, 1981), but in case of vegetation zones (Borhidi 2003) we can’t speak about correlation

Data to the morphometry of the species anisus yortex (L.) (Gastropoda, Planorbidae)

The biometry of Anisus vortex (L.): radial growth does riot follow a logarithmic spiral but a power function. Up to whorl-numbers 4 or 5, with the 25-individual groups the deviation of the mode of the Balatonmária material is about 5 p. c. With Anisus vortex the growth-lines smaller in number than with Anisus septemgyratus

A Nyugati-szigethegység csodálatos élővilága (könyvismertető)

Venczel Márton – Sófalvi István A Nyugati-szigethegység csodálatos élővilága Prolog Kiadó, Nagyvárad, 2008, ISBN – 978-973-7746-39-