Singular Poisson equations on Finsler-Hadamard manifolds

In the first part of the paper we study the reflexivity of Sobolev spaces on non-compact and not necessarily reversible Finsler manifolds. Then, by using direct methods in the calculus of variations, we establish uniqueness, location and rigidity results for singular Poisson equations involving the Finsler-Laplace operator on Finsler-Hadamard manifolds having finite reversibility constant.Comment: Published in: Calc. Var. Partial Differential Equations 54 (2015), no. 2, 1219-124

Család és politika az Anjou-korban : Lackfiak és Szécsiek (1308-1359) = Family and policy in Angevin era : Lackfi's and Szécsi's (1308-1359)

In this study I examine two families in the Angevin era between 1308 (Szécsi’s first appearance in the elite) to 1359 (death of Lack from kindred Hermán). They had baronial dignities at royal court: Lackfi’s were masters of horses (from 1326 until 1396), many members of the Szécsi family were the stewards under reign Charles I and Louis I of Hungary. I analysed these two families and I focused to the first and second generation. In the end we can see which were differences between them and their king’s personal policy with elite. In the elite there was main changes between first years and the middle of the 14th century

Ghrelin Decreases Firing Activity of Gonadotropin-Releasing Hormone (GnRH) Neurons in an Estrous Cycle and Endocannabinoid Signaling Dependent Manner.

The orexigenic peptide, ghrelin is known to influence function of GnRH neurons, however, the direct effects of the hormone upon these neurons have not been explored, yet. The present study was undertaken to reveal expression of growth hormone secretagogue receptor (GHS-R) in GnRH neurons and elucidate the mechanisms of ghrelin actions upon them. Ca(2+)-imaging revealed a ghrelin-triggered increase of the Ca(2+)-content in GT1-7 neurons kept in a steroid-free medium, which was abolished by GHS-R-antagonist JMV2959 (10µM) suggesting direct action of ghrelin. Estradiol (1nM) eliminated the ghrelin-evoked rise of Ca(2+)-content, indicating the estradiol dependency of the process. Expression of GHS-R mRNA was then confirmed in GnRH-GFP neurons of transgenic mice by single cell RT-PCR. Firing rate and burst frequency of GnRH-GFP neurons were lower in metestrous than proestrous mice. Ghrelin (40nM-4μM) administration resulted in a decreased firing rate and burst frequency of GnRH neurons in metestrous, but not in proestrous mice. Ghrelin also decreased the firing rate of GnRH neurons in males. The ghrelin-evoked alterations of the firing parameters were prevented by JMV2959, supporting the receptor-specific actions of ghrelin on GnRH neurons. In metestrous mice, ghrelin decreased the frequency of GABAergic mPSCs in GnRH neurons. Effects of ghrelin were abolished by the cannabinoid receptor type-1 (CB1) antagonist AM251 (1µM) and the intracellularly applied DAG-lipase inhibitor THL (10µM), indicating the involvement of retrograde endocannabinoid signaling. These findings demonstrate that ghrelin exerts direct regulatory effects on GnRH neurons via GHS-R, and modulates the firing of GnRH neurons in an ovarian-cycle and endocannabinoid dependent manner