For two graphs G and H , let the mixed anti-Ramsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edge-coloring of a complete graph with n vertices having no monochromatic subgraph isomorphic to G and no totally multicolored (rainbow) subgraph isomorphic to H . These two numbers generalize the classical anti-Ramsey and Ramsey numbers, respectively. ...

Facility of bulk aqueous humor outflow via conventional channels, true facility, and pressure sensitive suppression of aqueous humor inflow, pseudofacility, were measured by constant pressure perfusion in 24 eyes of 12 rhesus monkeys. True facility was found to have a mean value of 0.55 ,uL minr mm. Hg~ and pseudofacility was found to have a mean value of 0.12 p.L minr mm. Hg-. This figure is i...

This paper investigates the class of rings in which every nn-absorbing ideal is a prime ideal, called nn-AB ring, where nn positive integer. We give characterization an ring. Next, for ring RR, we study concept Ω(R)={ωR(I);I proper R},Ω(R)={ωR(I);I R}, ωR(I)=min{n;I n-absorbing R}ωR(I)=min{n;I R}. show that if RR Artinian or Prüfer domain, then Ω(R)∩NΩ(R)∩N does not have any gaps (i.e., wheneve...

We also saw that λ2 = minR(y). The issue is that we may have vol(St) > vol(V −St). To fix this, we will modify y so that vol(supp(y)) ≤ m (recall that vol(V ) = 2m). The idea is to pick c such that the two sets {i : y(i) < c} and {i : y(i) > c} both have volume at most m, then find St for both of them and take the best one. This lecture is derived from Lau’s 2012 notes, Week 2, http://appsrv.cs...

The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidskĭı inequalities. We give an elementary proof of the latter for hyperbolic polynomials. This proof is free from representation theory and Schubert calculus arguments, as well as fr...

Typically association rule mining only considers positive frequent itemsets in rule generation, where rules involving only the presence of items are generated. In this paper we consider the complementary problem of negative association rule mining, which generates rules describing the absence of itemsets from transactions. We describe a new approach called MINR (Mining Interesting Negative Rule...

We study the discrete spectrum of the Hamiltonian H = −∆ + V (r) for the Coulomb plus power-law potential V (r) = −1/r + β sgn(q)r, where β > 0, q > −2 and q 6= 0 . We show by envelope theory that the discrete eigenvalues Enl of H may be approximated by the semiclassical expression Enl(q) ≈ minr>0{1/r − 1/(μr) + sgn(q)β(νr)q}. Values of μ and ν are prescribed which yield upper and lower bounds....

BACKGROUND Digital mammography systems, thanks to a physical performance better than conventional screen-film units, have the potential of reducing the dose to patients, without decreasing the diagnostic accuracy. PURPOSE To achieve a physical and clinical comparison between two systems: a screen-film plate and a dual-side computed radiography system (CRM; FUJIFILM FCR 5000 MA). MATERIAL AN...

Text mining (TM) in the field of biology is fast becoming a routine analysis for the extraction and curation of biological entities (e.g., genes, proteins, simple chemicals) as well as their relationships. Due to the wide applicability of TM in situations involving complex relationships, it is valuable to apply TM to the extraction of metabolic interactions (i.e., enzyme and metabolite interact...