The Period and the Distribution of the Fibonacci-like Sequence Under Various Moduli

We reduce the Fibonacci sequence mod m for a natural number m, and denote it by F (mod m ). We are going to introduce the properties of the period and distribution of F (mod m). That is, how frequently each residue is expected to appear within a single period. These are well known themes of the research of the Fibonacci sequence, and many remarkable facts have been discovered. After that we are going to study the properties of period and distribution of a Fibonacci-like sequence that the authors introduced in article in the previous issue of Undergraduate Math Journal. This Fibonacci-like sequence also has many interesting properties, and the authors could prove an interesting theorem in this article. Some of properties are very difficult to prove, and hence we are going to present some predictions and calculations by computers

Effects of adenoviral-mediated hepatocyte growth factor on liver regeneration after massive hepatectomy in rats

Resection is the only curative treatment for liver metastasis of colorectal cancers. Despite the supreme regenerative potential of the liver, major hepatectomy sometimes leads to liver failure, and the limitation of resectable liver volumes makes advanced tumors inoperable. This study was attempted to promote liver regeneration using hepatocyte growth factor (HGF) gene transfection by venous-administered adenovirus and to improve the survival of rats after massive hepatectomy. The adenovirus that encodes HGF was administered to rats before 85%-hepatectomy. The administration of HGF gene improved the survival of rats after massive hepatectomy, while the administration of control adenovirus deteriorated their survival. Gene transfection of HGF showed up-regulation of serum HGF, stimulation of hepatocellular proliferation and rapid liver regeneration. Moreover, HGF administration reduced apoptosis of hepatocytes. The administration of HGF gene prevented liver dysfunction after major hepatectomy and may be a new assist for surgery.</p

A New Constraint on the Lyα\alpha Fraction of UV Very Bright Galaxies at Redshift 7

We study the extent to which very bright (-23.0 < MUV < -21.75) Lyman-break selected galaxies at redshifts z~7 display detectable Lya emission. To explore this issue, we have obtained follow-up optical spectroscopy of 9 z~7 galaxies from a parent sample of 24 z~7 galaxy candidates selected from the 1.65 sq.deg COSMOS-UltraVISTA and SXDS-UDS survey fields using the latest near-infrared public survey data, and new ultra-deep Subaru z'-band imaging (which we also present and describe in this paper). Our spectroscopy has yielded only one possible detection of Lya at z=7.168 with a rest-frame equivalent width EW_0 = 3.7 (+1.7/-1.1) Angstrom. The relative weakness of this line, combined with our failure to detect Lya emission from the other spectroscopic targets allows us to place a new upper limit on the prevalence of strong Lya emission at these redshifts. For conservative calculation and to facilitate comparison with previous studies at lower redshifts, we derive a 1-sigma upper limit on the fraction of UV bright galaxies at z~7 that display EW_0 > 50 Angstrom, which we estimate to be < 0.23. This result may indicate a weak trend where the fraction of strong Lya emitters ceases to rise, and possibly falls between z~6 and z~7. Our results also leave open the possibility that strong Lya may still be more prevalent in the brightest galaxies in the reionization era than their fainter counterparts. A larger spectroscopic sample of galaxies is required to derive a more reliable constraint on the neutral hydrogen fraction at z~7 based on the Lya fraction in the bright galaxies.Comment: 20 pages, 7 figures, accepted for publication in Ap

Biosynthesis and Release of Methylarsenic Compounds During the Growth of Freshwater Algae

金沢大学工学部Arsenic transformations by freshwater algae have been studied under laboratory conditions. By the use of a new analytical method, we identified methylarsenic(III) species in the growth medium of green-alga Closterium aciculare incubated under axenic conditions. The arsenate concentration in the experimental medium began to decrease just after inoculation, and the levels of arsenite and methylarsenicals increased with the growth of C. aciculare. Initially, most of the arsenate was converted into arsenite, which peaked in concentration during the exponential phase. Methylarsenicals accumulated rapidly in the stationary phase. DMAA(V) production was enhanced when the ratio of phosphate to arsenate decreased in the culture medium. The levels of DMAA(V) increased continuously toward the end of the experiment. On the other hand, methylarsenic(III) species remained relatively steady during the stationary phase. Methylarsenic(III) species accounted for 0-35% of methylarsenicals. These results suggest that arsenite and methylarsenicals (containing methylarsenic(III) species) are supplied by phytoplankton, and serve as evidence of the origin of methylarsenic(III) species in natural waters. © 2001 Elsevier Science Ltd

Application of new information entropy to source convergence diagnostics in Monte Carlo criticality calculations

In criticality safety evaluation, effective multiplication factor and its corresponding source distribution are often evaluated by the Monte Carlo method. For source convergence diagnostics a kind of information entropy (Shannon entropy) has, sometimes, been used. In the last conference (2009), we proposed new type information entropy in which the source distribution is expressed on an eigen-function space in order to evaluate the convergence not only of the effective multiplication factor but also of source distribution without increasing computing resources requirements. However, there arose questions concerning our entropy. Here, we answer some of the questions : (1) how to estimate expansion coefficients, (2) how to estimate the difference between the effective multiplication factor and the corresponding maximum eigenvalue, and (3) how to estimate the deviations of expansion coefficients due to the power iteration method using source distribution calculated by Monte Carlo methods. By applying our entropy to power iteration method, more effective source convergence diagnostics method combined with the “Sandwich Method” is attained