A lattice diagram is a finite list L = of lattice cells. The corresponding lattice diagram determinant is ∆ L (X; Y) = det x pj i y qj i. The space M L is the space spanned by all partial derivatives of ∆ L (X; Y). We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.

A 17-year-old Hispanic female presented to our hospital with complaints of right upper quadrant abdominal pain, vomiting, and fever. Physical exam was positive for hepatomegaly. Abdominal computed tomography showed multiple hypoechoic liver masses. Liver biopsy was done, which was diagnostic for hepatic epithelioid hemangioendothelioma.

The main purpose of this study was to assess the differences in the peripapillary retinal nerve fiber layer (pRNFL) and ganglion cell-inner plexiform layer (GCIPL) thicknesses between subjects with megalopapilla (MP) and those with large (physiological) cup discs (LCD) measured by spectral-domain optical coherence tomography. The secondary purpose was to determine whether pRNFL and GCIPL thickn...

We prove that any pair of bivariate trinomials has at most 16 roots in the positive quadrant, assuming there are only finitely many roots there. The best previous upper bound independent of the polynomial degrees (following from a general result of Khovanski with stronger non-degeneracy hypotheses) was 248,832. Our proof allows real exponents and extends to certain systems of n-variate fewnomials.

The scale-invariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant.

MATERIALS AND METHODS: All patients undergoing reconstruction following primary BCC excision of the nasal alae were recruited through a single institution. Patient demographics, details of resection and reconstruction were recorded. Positive margins were scored using a quadrant-based directionality system. Defect size was classified as large or small stratified by median defect area. Fisher’s e...