Avian beak diversity is a classic example of morphological evolution. Recently, we showed that localized cell proliferation mediated by bone morphogenetic protein 4 (BMP4) can explain the different shapes of chicken and duck beaks (Wu et al. [2004] Science 305:1465). Here, we compare further growth activities among chicken (conical and slightly curved), duck (straight and long), and cockatiel (...

Abstract For the quintic quasitopological action which has no well-defined variational principle, we introduced a surface term that for spacetime with flat boundaries make well-defined. Moreover, investigated numerical solutions of above-mentioned gravity coupled to nonlinear logarithmic and exponential electrodynamics. It horizon curvature except one conical singularity at $$r=0$$ <mml:math xm...

We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7). The relies on the study adiabatic limit metrics Spin(7) principal Seifert circle bundles over asymptotically conical G2 orbifolds. we produce have asymptotic geometry, so-called ALC that generalises to higher dimensions geometry 4-dimensional ALF hyperk\"ahler metrics. apply our...

We present and prove Polyakov-Alvarez type comparison formulas for the determinants of Friederichs extensions Laplacians corresponding to conformally equivalent metrics on a compact Riemann surface with conical singularities. In particular, we find how depend orders also illustrate these general results several examples: based our recover known obtain new explicit singular surfaces without boun...

A variety of approaches have been pursued to obtain a notion of discrete constant mean curvature (cmc) surfaces. Two different starting points arise from the interpretation of cmc surfaces as critical points of an area functional [9, 16], and on the other hand from an integrable systems point of view [4, 10]. One principal difference of the two approaches is that, in the first approach, the und...

Abstract We study the spectrum of Laplace operators on a one-parameter family gravitational instantons bi-axial Bianchi IX type coupled to an abelian connection with self-dual curvature. The geometries includes Taub-NUT (TN), Taub-bolt and Euclidean Schwarzschild interpolates between them. interpolating have conical singularities along submanifold co-dimension two, but we prove that associated ...

We construct the first smooth bubbling geometries using Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. classify charged this framework. Smooth consist of chain Kaluza-Klein bubbles that can be neutral or wrapped by electromagnetic fluxes, and free curvature conical singularities. discuss how such t...

This paper presents finite element analysis of the strength of roadheaher conical picks. Failure forms of conical picks are investigated, and the FE model of conical pick is established based on ANSYS. The static analysis is carried out according to the load calculated by empirical formula and the deformation map and stress distribution are obtained. The results show that the maximum stress of ...