With the rising prevalence of antimicrobial resistance, the treatment success of standard triple therapy has recently declined to unacceptable levels (ie, 80% or less). Following the failure of conventional triple therapy, novel eradication regimens have been developed including sequential therapy, concomitant quadruple therapy, hybrid (dual-concomitant) therapy, bismuth-containing quadruple th...

A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct elements increased by 1 is a perfect square. Diophantus found a set of four positive rationals with the above property. The first Diophantine quadruple was found by Fermat (the set {1, 3, 8, 120}). Baker and Davenport proved that this particular quadruple cannot be extended to a Diophantine quint...

Let Θ = (α, β) be a point in R, with 1, α, β linearly independent over Q. We attach to Θ a quadruple Ω(Θ) of exponents which measure the quality of approximation to Θ both by rational points and by rational lines. The two “uniform” components of Ω(Θ) are related by an equation, due to Jarńık, and the four exponents satisfy two inequalities which refine Khintchine’s transference principle. Conve...

DNA complexes, like the double crossover, are used as building blocks for the assembly of higher-order structures. Currently, the number of experimentally proven reliable complexes is small. We have begun work on expanding the collection of such complexes. Here we report on our design concepts and initial experiments. In particular, we present experimental evidence of two new complexes: quadrup...

A complex diophantine quadruple with the property D (z), where z ∈ Z[√−2], is a subset of Z[√−2] of four elements such that the product of its any two distinct elements increased by z is a perfect square in Z[ √−2]. In the present paper we prove that if b is an odd integer, then there does not exist a diophantine quadruple with the property D(a + b √−2). For z = a + b√−2, where b is even, we pr...

Maps between manifolds M → N (` > 0) have multiple points, and more generally, multisingularities. The closure of the set of points where the map has a particular multisingularity is called the multisingularity locus. There are universal relations among the cohomology classes represented by multisingularity loci, and the characteristic classes of the manifolds. These relations include the celeb...

We report the discovery of a compact, coplanar, quadruple-lined, eclipsing quadruple star system from Transiting Exoplanet Survey Satellite data, TIC 454140642, also known as TYC 0074-01254-1. The target was first detected in Sector 5 with 30-minute cadence full-frame images and then observed 32 2-minute cadence. light curve exhibits two sets primary secondary eclipses periods PA = 13.624 days ...

In this paper we obtain existence and uniqueness results for quadruple fixed points of operators F : X → X. We also give some examples to support our results.

Here we report the observation of quadruple Weyl point charge 4 in phononic crystals, highest topological a twofold degenerate node can carry. Besides point, semimetal also hosts conventional, quadratic, and spin-1 points, which stands as system with yet richest types points. The quadruple-helicoid surface states, specific to are demonstrated. finding high-charge enriches knowledge semimetals m...