In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and submanifolds, assuming such smooth cancellation is possible. This technique applied to show existence h-principle embeddings with prescribed structure.

PURPOSE Investigations in the field of the learning competence that investigate the impact of the acquisition of new individual competence of those responsible for ophthalmologic clinics, by means of a MBA Administration in Health course, on the organizational modernity of ophthalmologic clinics. METHODS Survey using questionnaires applied to students and former students of the course and to ...

AIM To evaluate the influence of food habits, specifically adherence to the Mediterranean diet, on carotid intima-media thickness (CIMT) and the presence of plaques in HIV-infected patients taking antiretroviral therapy (ART) and non-HIV-infected participants and to determine if HIV infection contributes independently to subclinical atherosclerosis. METHODS We conducted a cross-sectional stud...

A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs $G$ and $H$ are 2-isomorphic, or equivalently, their cycle matroids isomorphic if only can be transformed into by a series operations called switches. In this paper we consider the quantitative question arising Whitney's theorem: Given two 2-isomorphic graphs, transform one another applying at most $k$ switches? This pro...

We consider a two-group randomized clinical trial, where mortality affects the assessment of a follow-up continuous outcome. Using the worst-rank composite endpoint, we develop a weighted Wilcoxon-Mann-Whitney test statistic to analyze the data. We determine the optimal weights for the Wilcoxon-Mann-Whitney test statistic that maximize its power. We derive a formula for its power and demonstrat...

These introductory notes on Whitney towers in 4-manifolds, as developed collaboration with Jim Conant and Peter Teichner, are an expansion of three expository lectures given at the Winter Braids X conference February 2020 Pisa, Italy. Topics presented include local manipulations surfaces 4–space, fundamental definitions related to their associated trees, geometric Jacobi identities, classificat...

We introduce a natural partial order ≤ in structurally natural finite subsets the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers' triangular array-are then calculated and the explicit formula for them is provided. Next-in the second construction-we endow the set sums of prefa...

For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.