Coxeter multiarrangements with quasi-constant multiplicities

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation. As an application, we show that the characteristic polynomial of a Coxeter multiarrangement with quasi-constant multiplicity is combinatorially computable.Comment: 12 page

Totally free arrangements of hyperplanes

A central arrangement \A of hyperplanes in an $\ell$-dimensional vector space $V$ is said to be {\it totally free} if a multiarrangement (\A, m) is free for any multiplicity m : \A\to \Z_{> 0}. It has been known that \A is totally free whenever $\ell \le 2$. In this article, we will prove that there does not exist any totally free arrangement other than the obvious ones, that is, a product of one-dimensional arrangements and two-dimensional ones.Comment: 7 page

Free reflection multiarrangements and quasi-invariants

To a complex reflection arrangement with an invariant multiplicity function one can relate the space of logarithmic vector fields and the space of quasi-invariants, which are both modules over invariant polynomials. We establish a close relation between these modules. Berest-Chalykh freeness results for the module of quasi-invariants lead to new free complex reflection multiarrangements. K. Saito's primitive derivative gives a linear map between certain spaces of quasi-invariants. We also establish a close relation between non-homogeneous quasi-invariants for root systems and logarithmic vector fields for the extended Catalan arrangements. As an application, we prove the freeness of Catalan arrangements corresponding to the non-reduced root system $BC_N$.Comment: 26 pages; small change

Hydrogen-assisted fabrication of spherical gold nanoparticles through sonochemical reduction of tetrachloride gold(III) ions in water

Spherical gold nanoparticles (AuNPs) were selectively synthesized through sonochemical reduction of tetrachloride gold(III) ions ([AuCl4](-)) in an aqueous solution of hydrogen tetrachloroaurate(III) tetrahydrate (HAuCl4.H2O) with the aid of hydrogen (H-2) gas in the absence of any additional capping agents. On the other hand, various shaped-AuNPs such as spherical nanoparticles, triangular and hexagonal plates were formed from sonochemical reduction of [AuCl4](-) in argon (Ar)-, nitrogen (N-2)- or oxygen (O-2)-purged aqueous [AuCl4](-) solutions. The selective fabrication of spherical AuNPs assisted by H-2 gas is most likely attributed to the generation of hydrogen radicals (H center dot) promoted by the reaction of H-2 introduced and hydrogen oxide radicals (center dot OH) produced by sonolysis of water.ArticleULTRASONICS SONOCHEMISTRY. 21(3):946-950 (2014)journal articl

Increased LDL susceptibility to oxidation accelerates future carotid artery atherosclerosis

<p>Abstract</p> <p>Background</p> <p>We analyzed the causal relationship between LDL susceptibility to oxidation and the development of new carotid artery atherosclerosis over a period of 5 years. We previously described the determinants related to a risk of cardiovascular changes determined in a Japanese population participating in the Niigata Study, which is an ongoing epidemiological investigation of the prevention of cardiovascular diseases.</p> <p>Methods</p> <p>We selected 394 individuals (169 males and 225 females) who underwent a second carotid artery ultrasonographic examination in 2001 - 2002 for the present study. The susceptibility of LDL to oxidation was determined as the photometric absorbance and electrophoretic mobility of samples that had been collected in 1996 - 1997. The measurements were compared with ultrasonographic findings obtained in 2001 - 2002.</p> <p>Results</p> <p>The multivariate-adjusted model showed that age (odds ratio (OR), 1.034; 95% confidence interval (95%CI), 1.010 - 1.059), HbA1c (OR, 1.477; 95%CI, 0.980 - 2.225), and photometric O/N (OR, 2.012; 95%CI, 1.000 - 4.051) were significant variables that could independently predict the risk of new carotid artery atherosclerosis.</p> <p>Conclusion</p> <p>The susceptibility of LDL to oxidation was a significant parameter that could predict new carotid artery atherosclerosis over a 5-year period, and higher susceptibility was associated with a higher incidence of new carotid artery atherosclerosis.</p