In this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of Kirchhoff type. Due to the degeneration of the nonlocal term it is not possible to directly use...
We study the relationship between initial data sets with horizons and the existence of metrics of positive scalar curvature. We define a Cauchy Domain of Outer Communications (CDOC) to be an asymptotically flat initial set $(M, g, K)$ such that the b...
The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of $\mathfrak{g}$-stability...
Designing for rotational stability can dramatically affect the geometry of a space station. If improperly designed, the rotating station could end up catastrophically tumbling end-over-end. Active stabilization can address this problem; however, desi...
We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding t...
We show that the geometry of the asymptotic infinities of Minkowski spacetime (in $d+1$ dimensions) is captured by homogeneous spaces of the Poincaré group: the blow-ups of spatial (Spi) and timelike (Ti) infinities in the sense of Ashtekar--Hansen...
A convex quadrangular pyramid $ABCDE$, where $ABCD$ is the base and $E$ -- the apex, is called \emph{strongly flexible}, if it belongs to a continuous family of pairwise non-congruent quadrangular pyramids that have the same lengths of corresponding...
We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and enriched Sch...
Geometry of the rock joint is a governing factor for joint mechanical and hydraulic behavior. A new method of evaluating aperture distribution based on measurement of joint surfaces and three dimensional characteristics of each surface is developed...
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. These flat plumbing basket surface can be presented by a sequential presentation known as flat plumbing basket code first found by Furihata,...
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers $4$ or less using a special presentation of the flat plumbing basket s...
In order to achieve quantum interference of free electrons inside a solid, we have modified the geometry of the solid so that de Broglie waves interfere destructively inside the solid. Quantum interference of de Broglie waves leads to a reduction i...
In this study, the possible pairing mechanism based on attraction between electrons from adjacent CuO2 layers is proposed. Initially, each CuO2 layer was found to expand the Fermi sphere owing to ridged geometry. When the two layers are close enough...
Changes in the metal properties, caused by periodic indents in the metal surface, have been studied within the limit of quantum theory of free electrons. It was shown that due to destructive interference of de Broglie waves, some quantum states ins...
In this study, the quantum state depression (QSD) in semiconductor quantum well (QW) is investigated. The QSD emerge from the ridged geometry of the QW boundary. Ridges impose additional boundary conditions on the electron wave function and some qu...
One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spect...
Pls tell me I’m not the only one who sees this (I cannot be that cooked) ...
Context. The dipole modes are the most common geometry of oscillations in roAp stars inferred from photometric measurements and are therefore of special interest for asteroseismic purposes. Aims. We present a theoretical and analytical study of the l...