Hahn's Symmetric Quantum Variational Calculus

We introduce and develop the Hahn symmetric quantum calculus with applications to the calculus of variations. Namely, we obtain a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for variational problems within the context of Hahn's symmetric calculus. Moreover, we show the effectiveness of Leitmann's direct method when applied to Hahn's symmetric variational calculus. Illustrative examples are provided.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 06-Sept-201

On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

Measurement and comparison of individual external doses of high-school students living in Japan, France, Poland and Belarus -- the "D-shuttle" project --

Twelve high schools in Japan (of which six are in Fukushima Prefecture), four in France, eight in Poland and two in Belarus cooperated in the measurement and comparison of individual external doses in 2014. In total 216 high-school students and teachers participated in the study. Each participant wore an electronic personal dosimeter "D-shuttle" for two weeks, and kept a journal of his/her whereabouts and activities. The distributions of annual external doses estimated for each region overlap with each other, demonstrating that the personal external individual doses in locations where residence is currently allowed in Fukushima Prefecture and in Belarus are well within the range of estimated annual doses due to the background radiation level of other regions/countries

On consensus in the Cucker--Smale type model on isolated time scales

This article addresses a consensus phenomenon in a Cucker-Smale model where the magnitude of the step size is not necessarily a constant but it is a function of time. In the considered model the weights of mutual influences in the group of agents do not change. A sufficient condition under which the proposed model tends to a consensus is obtained. This condition strikingly demonstrates the importance of the graininess function in a consensus phenomenon. The results are illustrated by numerical simulations.publishe

Angiomyolipoma Have Common Mutations in TSC2 but No Other Common Genetic Events

Renal angiomyolipoma are part of the PEComa family of neoplasms, and occur both in association with Tuberous Sclerosis Complex (TSC) and independent of that disorder. Previous studies on the molecular genetic alterations that occur in angiomyolipoma are very limited. We evaluated 9 angiomyolipoma for which frozen tissue was available from a consecutive surgical series. Seven of 8 samples subjected to RT-PCR-cDNA sequencing showed mutations in TSC2; none showed mutations in TSC1 or RHEB. Six of the seven mutations were deletions. We searched for 983 activating and inactivating mutations in 115 genes, and found none in these tumors. Similarly analysis for genomic regions of loss or gain, assessed by Affymetrix SNP6.0 analysis, showed no abnormalities. Loss of heterozygosity in the TSC2 region was commonly seen, except in patients with low frequency TSC2 mutations. We conclude that sporadic renal angiomyolipoma usually have mutations in TSC2, but not TSC1 or RHEB, and have no other common genomic events, among those we searched for. However, chromosomal translocations and gene fusion events were not assessed here. TSC2 inactivation by mutation is a consistent and likely necessary genetic event in the pathogenesis of most angiomyolipoma

Targeted Deletion of Kcne2 Causes Gastritis Cystica Profunda and Gastric Neoplasia

Gastric cancer is the second leading cause of cancer death worldwide. Predisposing factors include achlorhydria, Helicobacter pylori infection, oxyntic atrophy and TFF2-expressing metaplasia. In parietal cells, apical potassium channels comprising the KCNQ1 α subunit and the KCNE2 β subunit provide a K+ efflux current to facilitate gastric acid secretion by the apical H+K+ATPase. Accordingly, genetic deletion of murine Kcnq1 or Kcne2 impairs gastric acid secretion. Other evidence has suggested a role for KCNE2 in human gastric cancer cell proliferation, independent of its role in gastric acidification. Here, we demonstrate that 1-year-old Kcne2−/− mice in a pathogen-free environment all exhibit a severe gastric preneoplastic phenotype comprising gastritis cystica profunda, 6-fold increased stomach mass, increased Ki67 and nuclear Cyclin D1 expression, and TFF2- and cytokeratin 7-expressing metaplasia. Some Kcne2−/−mice also exhibited pyloric polypoid adenomas extending into the duodenum, and neoplastic invasion of thin walled vessels in the sub-mucosa. Finally, analysis of human gastric cancer tissue indicated reduced parietal cell KCNE2 expression. Together with previous findings, the results suggest KCNE2 disruption as a possible risk factor for gastric neoplasia

Fractional variational problems depending on indefinite integrals and with delay

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example, where we nd analytically the minimizer