Let Pn be a set of n points on the plane in general position, n ≥ 4. A convex quadrangulation of Pn is a partitioning of the convex hull Conv(Pn) of Pn into a set of quadrilaterals such that their vertices are elements of Pn, and no element of Pn lies in the interior of any quadrilateral. It is straightforward to see that if P admits a quadrilaterization, its convex hull must have an even numbe...

Peanut (PN) and tree nut (TN) allergies are among the leading causes of fatal food-induced anaphylaxis and are increasing in prevalence, especially in children. Their cosensitization and concurrent clinical allergy have been understudied. This retrospective study investigated the correlation between PN and TN allergy, both in terms of in vitro sensitization (IVS) and clinical allergic manifesta...

Closure of the nostril by electrocauterization on postnatal day (PN) 1 or 2 was used to study effects of olfactory deprivation on developing olfactory epithelium (OE) and bulb (OB) in CD-1 mice. No damage was observed in OE sections 1 or 3 days after closure, and at PN 30 no difference was found in the number of OE receptors between closed and open sides. Odor deprivation and a decrease in func...

Axonal regeneration of retinal ganglion cells (RGCs) into a normal or pre-degenerated peripheral nerve graft after an optic nerve pre-lesion was investigated. A pre-lesion performed 1-2 weeks before a second lesion has been shown to enhance axonal regeneration in peripheral nerves (PN) but not in optic nerves (ON) in mammals. The lack of such a beneficial pre-lesion effect may be due to the lon...

In this paper, we construct the reduced genus-two Gromov-Witten invariants of degree d ≥ 3 for the standard projective space Pn of dimension n ≤ 7. This invariant counts the number of simple genus-two holomorphic curves in Pn of degree d that satisfy appropriate number of constraints.

Let C ⊂ Pn be a rational normal curve and let `O : Pn+1 99K Pn be any tangential projection form a point O ∈ TAC where A ∈ C. In this paper we relate the minimum number r of addenda that are needed to write a binary form p of degree (n + 1) and defined over an algebraically closed field of characteristic zero as linear combination of (n+1)-th powers of linear binary forms L1, . . . , Lr, with t...

Let Pn and Qn be the polynomials obtained by repeated differentiation of the tangent and secant functions respectively. From the exponential generating functions of these polynomials we develop relations among their values, which are then applied to various numerical sequences which occur as values of the Pn and Qn. For example, Pn(0) and Qn(0) are respectively the nth tangent and secant number...

Background Periostin (PN) epithelial and stromal overexpression in tumor pathology has been studied according to tumor growth, angiogenesis, invasiveness, and metastasis, but a limited number of studies address PN in thyroid tumors. Aim Our study aimed to analyze PN expression in different histological variants of PTC and to correlate its expression with the clinicopathological prognostic fac...