The minimal base size for a p-solvable linear group

Let $V$ be a finite vector space over a finite field of order $q$ and of characteristic $p$. Let $G\leq GL(V)$ be a $p$-solvable completely reducible linear group. Then there exists a base for $G$ on $V$ of size at most $2$ unless $q \leq 4$ in which case there exists a base of size at most $3$. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of P\'alfy and Wolf is also given.Comment: 11 page

Heme oxygenase 1 (HMOX1) gene expression in hemodialysed uremic patients

The oxidative stress and the released heme molecule of degrading red blood cells during hemodialysis induce the expression of heme oxygenase 1 gene (HMOX1). The goal of our study was to measure the expression of HMOX1 during dialysis and compare it with the common oxidative markers. We established a cRT-PCR (competitive reverse transcriptase PCR) method to measure the mRNA levels. The mRNA levels were calculated to the white blood cell count respectively for each sample. We measured a 1-5-fold increase in the HMOX1 gene expression after the dialysis session, which dropped back to the original value 48 hours after the dialysis. The base level of HMOX1 mRNA of hemodialysed patients before dialysis was in the range of normal controls. The changes in mRNA levels showed significant correlation with the plasma hemoglobin (r=0.72, p<0.001) and plasma bilirubin (r=0.71, p<0.002) changes. We found no correlation between the changes of mRNA levels and other biochemical markers (GSH, GSSG). Our results suggest that the induced HMOX1 expression during hemodialysis is primarily due to the undergoing hemolysis

On a conjecture of Gluck

Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$. A well-known conjecture of D. Gluck claims that if $G$ is solvable then $|G:F(G)|\leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$ is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure.Comment: 16 page

The bottom of the looted cauldron. Part I.

The following study deals with a looted metal sheet artefact probably originating from the Balkan region. Our main goal is to give a preliminary technological characterization of the object by the aid of four different analytical methods (macro- and microscopic observations, Neutron and X-ray Radiography, X-ray Fluorescence Spectroscopy). Using these different techniques together allowed us to characterize this complex metal sheet object more precisely than it would have been possible by traditional archaeological methods. According to our results, it seems that the technological characters of the artefact (e.g. the manufacturing technology, decorations, repair marks) are very similar to the metal sheet cauldrons of the Late Bronze Age and Early Iron Age

The minimal base size for a p-solvable linear group

Let V be a finite vector space over a finite field of order q and of characteristic p. Let G ≤ GL(V) be a p-solvable completely reducible linear group. Then there exists a base for G on V of size at most 2 unless q ≤ 4 in which case there exists a base of size at most 3. The first statement extends a recent result of Halasi and Podoski and the second statement generalizes a theorem of Seress. An extension of a theorem of Pálfy and Wolf is also given. Dedicated to the memory of Ákos Seress

Lokális hidrogéntartalom mérése roncsolásmentes neutronos módszerekkel cirkónium fűtőelemburkolatok hossztengelye mentén

Magas hőmérsékletű felhasadást és oxidációt követően roncsolásmentes neutronos vizsgálatokkal hidrogén-cirkónium elemarányt határoztunk meg E110 és E110G típusú Zr fűtőelem-burkolatok hossztengelye mentén. A neutronos képalkotással kombinált prompt-gamma neutronaktivációs analízissel mintegy 30 gamma spektrumot vettünk fel az egyes burkolatokon, 5 mm-es lépésekben. A CODEX-LOCA-200 és CODEX-LOCA-E4 kísérletekben a H/Zr profilok mindkét típusú burkolatnál három csoportra oszthatók. Az elsőben csak kisebb deformáció vagy repedés látható néhány száz ppm körüli tömegarány értékekkel. A második csoportban közepes mértékű volt a felhasadás, és az értékek széles skálán (200-1800 ppm) mozognak. A legmagasabb értékeket (6000-7000 ppm) a nagy repedéssel vagy teljes töréssel rendelkező harmadik csoportban tapasztaltuk

Use of 3D mesh geometries and additive manufacturing in neutron beam experiments

PGAI-NT, a neutron-based element composition and structure analysis method, is well applicable to the non-destructive characterization of valuable artefacts, paleontological, bulk geological samples or to industrial reverse engineering. To set up the measurement geometry and scanning positions for items with unconstrained shapes, sizes, and matrices, accurate knowledge of the object’s geometry is a must. We applied portable structured-light 3D optical scanning or segmented neutron/X-ray tomography data to produce 3D meshes of the complex samples. Subsequently, 3D printing was used to fabricate detailed replicas of museum objects, as well as their gentle ad hoc sample holders, or produce custom parts of the Budapest PGAA instrument