We investigate positive solutions (x, y) of the Diophantine equation x2 − (k2 + 1)y2 = k2 that satisfy y < k − 1, where k ≥ 2. It has been conjectured that there is at most one such solution for a given k.

An abelian group may be defined by the property that, in an automorphism of the group, more than three fourths its operators may be placed in a one to one correspondence with their inverses.f It may be of interest to know the groups possessing the property that five eighths or more of the operators may be made to correspond to their inverses. The principal object of this paper, however, is to e...

Rate coefficients are reported for the gas-phase reaction of the hydroxyl radical (OH) with C2HCl3 (k(1)) and C2Cl4 (k2) over an extended temperature range at 740+/-10 Torr in a He bath gas. These absolute rate measurements were accomplished using a laser photolysis/laser-induced fluorescence (LP/LIF) technique under slow flow conditions. The simple Arrhenius equation adequately describes the l...

The Kneser graph K(n, k) is the graph whose vertices are the k-elements subsets of an n-element set, with two vertices adjacent if the sets are disjoint. The square G2 of a graph G is the graph defined on V (G) such that two vertices u and v are adjacent in G2 if the distance between u and v in G is at most 2. Determining the chromatic number of the square of the Kneser graph K(2k + 1, k) is an...

K2, a synthetic cannabinoid (SC), is an emerging drug of abuse touted as "legal marijuana" and marketed to young teens and first-time drug users. Symptoms associated with K2 use include extreme agitation, syncope, tachycardia, and visual and auditory hallucinations. One major challenge to clinicians is the lack of clinical, pharmacological, and metabolic information for the detection and charac...

The NP-hard Star Editing problem has as input a graph G = (V, E) with edges colored red and black and two positive integers k1 and k2, and determines whether one can recolor at most k1 black edges to red and at most k2 red edges to black, such that the resulting graph has an induced subgraph whose edge set is exactly the set of black edges. A generalization of Star Editing is Union Editing, whi...

UbiA prenyltransferase domain containing 1 (UBIAD1) is a novel vitamin K2 biosynthetic enzyme screened and identified from the human genome database. UBIAD1 has recently been shown to catalyse the biosynthesis of Coenzyme Q10 (CoQ10) in zebrafish and human cells. To investigate the function of UBIAD1 in vivo, we attempted to generate mice lacking Ubiad1, a homolog of human UBIAD1, by gene targe...

Initial results on particle yields obtained by the HARP experiment are presented. The measurements correspond to proton–nucleus collisions at beam energies of 12.9 GeV /c and for a thin Al target of 5% interacion legth. The angular range considered is between 10 and 250 mrad. This results are the first step in the upcoming measurement of the forward production cross-section for the same target ...

1. Joint binomial moments (bivariate case) The last two decades have seen major developments in the theory of order statistics and its applications to practical problems. Under the impetus of advances in the probabilistic theory, new statistical methods have been developed for both univariate and multivariate problems. The books by [6,1,5] are considered among the most popular books on this top...