Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

Kepler-16b: safe in a resonance cell

The planet Kepler-16b is known to follow a circumbinary orbit around a system of two main-sequence stars. We construct stability diagrams in the "pericentric distance - eccentricity" plane, which show that Kepler-16b is in a hazardous vicinity to the chaos domain - just between the instability "teeth" in the space of orbital parameters. Kepler-16b survives, because it is close to the stable half-integer 11/2 orbital resonance with the central binary, safe inside a resonance cell bounded by the unstable 5/1 and 6/1 resonances. The neighboring resonance cells are vacant, because they are "purged" by Kepler-16b, due to overlap of first-order resonances with the planet. The newly discovered planets Kepler-34b and Kepler-35b are also safe inside resonance cells at the chaos border.Comment: 17 pages, including 5 figure

Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Big Line Bundles over Arithmetic Varieties

We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry, which is an analogue of a classical theorem of Siu. An application of this result gives equidistribution of small points over algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also generalize Chambert-Loir's non-archimedean equidistribution

Contrasting pressure evolution of f-electron hybridized states in CeRhIn5 and YbNi3 Ga9 : An optical conductivity study

Optical conductivity [σ (ω)] of CeRhIn5 and YbNi3Ga9 have been measured at external pressures to 10 GPa and at low temperatures to 6 K. Regarding CeRhIn5, at ambient pressure the main feature in σ (ω) is a Drude peak due to free carriers. With increasing pressure, however, a characteristic midinfrared (mIR) peak rapidly develops in σ (ω), and its peak energy and width increase with pressure. These features are consistent with an increased conduction (c)- f electron hybridization at high pressure and show that pressure has tuned the electronic state of CeRhIn5 from very weakly to strongly hybridized ones. As for YbNi3Ga9, in contrast, a marked mIR peak is observed already at ambient pressure, indicating a strong c- f hybridization. At high pressures, however, the mIR peak shifts to lower energy and becomes diminished and seems to merge with the Drude component at 10 GPa. Namely, CeRhIn5 and YbNi3Ga9 exhibit some opposite tendencies in the pressure evolution of σ (ω) and electronic structure. These results are discussed in terms of the pressure evolution of c- f hybridized electronic states in Ce and Yb compounds, in particular in terms of the electron-hole symmetry often considered between Ce and Yb

Utilization of silkworm cocoon waste as a sorbent for the removal of oil from water

ArticleJOURNAL OF HAZARDOUS MATERIALS. 165(1-3):266-270 (2009)journal articl

Next generation organofluorine containing blockbuster drugs

Funding: the National Natural Science Foundation of China (No. 21761132021), the Hungarian Research Foundation (NKFIH No. K 119282), and Ministry of Human Capacities, Hungary grant 20391-3/2018/FEKUSTRAT. The Qinlan Project of Jiangsu Province, and IKERBASQUE, the Basque Foundation for Science are also acknowledged.The role of organo-fluorine compounds in modern health, food and energy related industries is widely-appreciated. The unique properties that fluorine imparts to organic molecules, stemming from its high electronegativity and stability when bound to carbon, finds it increasing being used in the development of new bioactivities. Around 25% of the current blockbuster drugs contain fluorine and this number is increasing to well above 30% for recent FDA approvals. In this Review we highlight a selection of the most successful organo-fluorine drugs, that have achieved blockbuster status, namely, sitagliptin (diabetes), sofosbuvir (hepatitis C), emtricitabine (HIV), glecaprevir/pibrentasvir (hepatitis C), elvitegravir (HIV), dolutegravir (HIV), bictegravir (HIV), efavirenz (HIV), enzalutamide (prostate cancer), aubagio (immunomodulatory) and paliperidone palmitate (schizophrenia). For each compound we discuss their discovery, their relevant disease state and how they are made, emphasizing the source of fluorine-containing moieties, and where known, their mode of action.PostprintPeer reviewe