971 research outputs found
Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization
In this article, we study an analog of the Bj\"orling problem for isothermic
surfaces (that are more general than minimal surfaces): given a real analytic
curve in , and two analytic non-vanishing orthogonal
vector fields and along , find an isothermic surface that is
tangent to and that has and as principal directions of
curvature. We prove that solutions to that problem can be obtained by
constructing a family of discrete isothermic surfaces (in the sense of Bobenko
and Pinkall) from data that is sampled along , and passing to the limit
of vanishing mesh size. The proof relies on a rephrasing of the
Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its
discretization which is induced from the geometry of discrete isothermic
surfaces. The discrete-to-continuous limit is carried out for the Christoffel
and the Darboux transformations as well.Comment: 29 pages, some figure
Generalized -harmonic Equation and The Inverse Mean Curvature Flow
We introduce and study generalized -harmonic equations (1.1). Using some
ideas and techniques in studying -harmonic functions from [W1] (2007), and
in studying nonhomogeneous -harmonic functions on a cocompact set from [W2,
(9.1)] (2008), we find an analytic quantity in the generalized -harmonic
equations (1.1) on a domain in a Riemannian -manifold that affects the
behavior of weak solutions of (1.1), and establish its link with the geometry
of the domain. We obtain, as applications, some gradient bounds and
nonexistence results for the inverse mean curvature flow, Liouville theorems
for -subharmonic functions of constant -tension field, , and
nonexistence results for solutions of the initial value problem of inverse mean
curvature flow.Comment: 14 pages, to appear in Journal of Geometry and Physic
Highly oscillatory solutions of a Neumann problem for a -laplacian equation
We deal with a boundary value problem of the form where for and , and is a
double-well potential. We study the limit profile of solutions when and, conversely, we prove the existence of nodal solutions associated
with any admissible limit profile when is small enough
Historic buildings and the creation of experiencescapes: looking to the past for future success
Purpose: The purpose of this paper is to identify the role that the creative re-use of historic buildings can play in the future development of the experiences economy. The aesthetic attributes and the imbued historic connotation associated with the building help create unique and extraordinary âexperiencescapesâ within the contemporary tourism and hospitality industries. Design/methodology/approach: This paper provides a conceptual insight into the creative re-use of historic buildings in the tourism and hospitality sectors, the work draws on two examples of re-use in the UK. Findings: This work demonstrates how the creative re-use of historic buildings can help create experiences that are differentiated from the mainstream hospitality experiences. It also identifies that it adds an addition unquantifiable element that enables the shift to take place from servicescape to experiencescape. Originality/value: There has been an ongoing debate as to the significance of heritage in hospitality and tourism. However, this paper provides an insight into how the practical re-use of buildings can help companies both benefit from and contribute to the experiences economy
Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization
We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller
Differential modulation of cisplatin accumulation in leukocytes and tumor cells by the paclitaxel vehicle Cremophor EL
Log Odds and the Interpretation of Logit Models
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142912/1/hesr12712.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142912/2/hesr12712_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142912/3/hesr12712-sup-0001-AppendixSA1.pd
Linear approaches to intramolecular Förster Resonance Energy Transfer probe measurements for quantitative modeling
Numerous unimolecular, genetically-encoded Forster Resonance Energy Transfer (FRET) probes for monitoring biochemical activities in live cells have been developed over the past decade. As these probes allow for collection of high frequency, spatially resolved data on signaling events in live cells and tissues, they are an attractive technology for obtaining data to develop quantitative, mathematical models of spatiotemporal signaling dynamics. However, to be useful for such purposes the observed FRET from such probes should be related to a biological quantity of interest through a defined mathematical relationship, which is straightforward when this relationship is linear, and can be difficult otherwise. First, we show that only in rare circumstances is the observed FRET linearly proportional to a biochemical activity. Therefore in most cases FRET measurements should only be compared either to explicitly modeled probes or to concentrations of products of the biochemical activity, but not to activities themselves. Importantly, we find that FRET measured by standard intensity-based, ratiometric methods is inherently non-linear with respect to the fraction of probes undergoing FRET. Alternatively, we find that quantifying FRET either via (1) fluorescence lifetime imaging (FLIM) or (2) ratiometric methods where the donor emission intensity is divided by the directly-excited acceptor emission intensity (denoted R<sub>alt</sub>) is linear with respect to the fraction of probes undergoing FRET. This linearity property allows one to calculate the fraction of active probes based on the FRET measurement. Thus, our results suggest that either FLIM or ratiometric methods based on R<sub>alt</sub> are the preferred techniques for obtaining quantitative data from FRET probe experiments for mathematical modeling purpose
DATA AND INITIAL MODEL SET-UP FOR THE 2022 STOCK SYNTHESIS STOCK ASSESSMENT OF THE EASTERN ATLANTIC AND MEDITERRANEAN BLUEFIN TUNA
This document describes the data used for Stock Synthesis assessment for the Eastern Atlantic
and Mediterranean bluefin tuna. The initial model configuration, fleet definitions, selectivity
modeling and main parameterization are also outlined. The model runs from 1950 to 2020 and
is fit to length composition data and pair age-length data treated as conditional age-at-length.En prens
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