On a functional equation related to two-variable weighted quasi-arithmetic means

In this paper, we are going to describe the solutions of the functional equation $$\varphi\Big(\frac{x+y}{2}\Big)(f(x)+f(y))=\varphi(x)f(x)+\varphi(y)f(y)$$ concerning the unknown functions $\varphi$ and $f$ defined on an open interval. In our main result only the continuity of the function $\varphi$ and a regularity property of the set of zeroes of $f$ are assumed. As application, we determine the solutions of the functional equation $$G(g(u)-g(v))=H(h(u)+h(v))+F(u)+F(v)$$ under monotonicity and differentiability conditions on the unknown functions $F,G,H,g,h$

Implications between generalized convexity properties of real functions

Motivated by the well-known implications among $t$-convexity properties of real functions, analogous relations among the upper and lower $M$-convexity properties of real functions are established. More precisely, having an $n$-tuple $(M_1,\dots,M_n)$ of continuous two-variable means, the notion of the descendant of these means (which is also an $n$-tuple $(N_1,\dots,N_n)$ of two-variable means) is introduced. In particular, when all the means $M_i$ are weighted arithmetic, then the components of their descendants are also weighted arithmetic means. More general statements are obtained in terms of the generalized quasi-arithmetic or Matkowski means. The main results then state that if a function $f$ is $M_i$-convex for all $i\in\{1,\dots,n\}$, then it is also $N_i$-convex for all $i\in\{1,\dots,n\}$. Several consequences are discussed

A Prod kromoszómális fehérje heterokromatin kondenzációban és génregulációban betöltött szerepének jellemzése ecetmuslicában = Function of the Drosophila Prod chromosomal protein in heterochromatin condensation and gene regulation

Mivel a vizsgált Prod fehérje óriáskromoszómák immunofestésein kozekvens telomerikus lokalizációt mutatott megvizsgáltuk, hogy mi lehet a telomerikus funkciója. A Drosophila telomerei 3 elküleníthető egységből állnak: 1., A szabad DNS véget védő capping fehérje komplexből, 2., Az emlősök telomerázával analóg módon a kromoszómákat a replikációs rövidüléstől megvédő (azokat folyton hosszabbító) retro-transzpozon (HeT-A) repeatekből, 3., Szubtelomerikus heterokromatinból (TAS). TAS deléciós törzsek és hosszú HeT-A retrotranszpozon repeatet tertalmazó törzsek immunofestése arra utalt, hogy a Prod fehérje minden bizonnyal a HeT-A repeatekhez kötődik. Ezután in vivo és in vitro DNS-fehérje kötési kísérletekkel igazoltuk, hogy a Prod fehérje valóban közvetlenül kötődik a HeT-A retrotranszpozonok promóteréhez, minden bizonnyal egy fehérje komplex részeként. Kvantitatív real-time PCR-rel kimutattuk, hogy a promóter kötés transzkripciós szuppressziót von maga után, mivel prod/+ heterozigóta mutánsokban 6,5-szeresére emelkedik a HeT-A transzkripciós szintje a vad típushoz képest. Élesztő kettős-hibrid kísérlettel 6 db. a Prod fehérjéhez kötődő fehérje partnert azonosítottunk. Ezek közül legérdekesebb a Pliohomeoticlike egy Polycomb csoportba tartozó DNS-kötő fehérje, amely szupresszor komplexekből ismert. Vizsgálni fogjuk ezen fehérje kölcsönhatások in vivo jelentőségét. | Immunofluorescence localization of the Prod protein on salivary gland polytene chromosomes showed, a clear labeling of all telomeres. In Drosophila melanogaster, three telomeric domains can be distinguished by DNA sequence and by proteins associated with them: 1., The end of the chromosomal DNA molecule (cap), 2., The retrotransposon array (HeT-A), and 3., The subtelomeric repetitive region, TAS. Immunolocalization of Prod on giant chromosomes of strains carrying deletions of TAS, and strains carrying an extra long HeT-A array, showed that Prod is most probably associated with the HeT-A array. In vivo and in vitro protein-DNA binding experiments confirmed that Prod binds directly to the HeT-A promoters, most probably as part of a protein complex, and is a suppressor of HeT-A transcription. Latter was verified by compering the HeT-A transcription level between prod/+ heterozygous and wild type flies, where wild type exhibited 6.5 times lower HeT-A transcript levels than prod/+. Yeast-2-hybrid experiments identified 6 new protein partners of Prod, one of them -Pliohomeoticlike- is known to be member of suppressor protein complexes. We will test the possible interaction of these proteins on telomeres and other chromosome loci

Multifunctional Role of Pacap-Like Peptides in Molluscs

The purpose of this review is to highlight the role of pituitary adenylate cyclase-activating polypeptide (PACAP) in a range of physiological and behavioral processes of gastropod molluscs, Helix and Lymnaea. Since its discovery in 1989 PACAP has become increasingly recognized for its important and diversified roles in the central and peripheral nervous system and in several peripheral organs of a variety of vertebrate and invertebrate species. Twenty-two years after its discovery, PACAP is now one of the most extensively studied of the neuropeptides. This review surveys the importance of PACAP and PACAP-like peptides in invertebrates, focusing mainly on the gastropod molluscs. The relevance of studies on lower vertebrates and invertebrates, which do not have a pituitary gland, is to contribute to the unraveling of fundamental effects of PACAP or PACAP-like peptides and to provide a comparative view

Geological features, geophysical measurements and interpretation at the Telkibánya research area

A lot of geophysical measurements (gravity, geomagnetic, geoelectric, airborne magnetic and radiometric) were carried out in the Tokaj Mountains in the 60’s. They covered partly the Northern part of the Tokaj Mountains, the Telkibánya area too. Later, in 1997 detailed airborne magnetic and radiometric measurements covered the ore perspective part of the Telkibánya area. The well-known surface geology of the Telkibánya volcanic structure allows the interpretation of different geophysical data as indicating volcanic bodies, secondary alterations of volcanic formations and hydrothermal processes. There was only local field geophysical work on the area without a summary program of different time and different kind geophysical exploration works. The biggest one was the paleovolcanic reconstruction of the Tokaj Mountains financed by Hungarian Scientific Research Found (OTKA-022769). Unfortunately the Telkibánya area is located near the state boundary, which was a spatial limit of the old airborne surveys. Now, in this paper we summarize the results of geophysical interpretations of field gravity, airborne magnetic and radiometric data

Impact of Economic and Financial Crisis on Human Resource Function in Four Eastern- European Countries in Light of an Empirical Research in 2009

When the crisis broke out in October 2008, the four countries (Bulgaria, Hungary, Romania and Slovakia) examined were in different situations, and, consequently, the governments of these countries reacted at different times. They did so, however, in very similar ways. Nevertheless, it is particularly important to know how their companies reacted to the crisis, and our study aims to find out what actions companies from these selected countries plan to take concerning the field of Human Resource Management (HRM) in the present financial and economic crisis. With a brief review of the literature, we demonstrate the role of HR in a period of depression, and then we present the findings of our empirical research, which was conducted from November 2008 to February 2009.Keywords: Human Resource Management, Crisis, Bulgaria, Hungary, Romania and Slovakia.

Applicability of friction stir welding in polymeric materials

The applicability of friction stir welding has been studied on polypropylene sheets. The joint strength has been analysed in terms of rotation and translation speed. It has been demonstrated that in addition to the judicious selection of welding parameters the proper construction of the welding tool is also very important. The crystallinity of the seam and its neighbourhood has been analysed by DSC, the structure of the seam border region has been analysed by optical and by scanning electron microscopy. It was found, that the seam has undergone embrittlement, as a result of non-satisfactory homogenization. Having analysed the flow circumstances during welding on seams produced by proper tool geometries it has been demonstrated that homogenization and, consequently the joint strength can be substantially improved