Related papers: Champagne subregions with unavoidable bubbles
In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \begin{equation*} \left\{\aligned &(-\Delta)^su=|u|^{p-1-\varepsilon}u\ \ \mbox{in}\ \Omega &u=0\…
We study the possibility of obtaining metastable supersymmetry breaking vacua in a perturbative gauge theory without singlet fields, thus allowing for scenarios where a grand unified symmetry and supersymmetry are broken by the same sector.…
An extension is given for the standard two component model of adiabatic, Born-Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the…
We show that the Euclidean ball has the smallest volume among sublevel sets of nonnegative forms of bounded Bombieri norm as well as among sublevel sets of sum of squares forms whose Gram matrix has bounded Frobenius or nuclear (or, more…
The Brownian diffusion of micron-scale inclusions in freely suspended smectic A liquid crystal films a few nanometers thick and several millimeters in diameter depends strongly on the air surrounding the film. Near atmospheric pressure, the…
Within the MSSM framework and with purely anomaly mediated supersymmetry breaking the slepton masses turn out to be tachyonic. We resolve this problem by introducing an anomaly free U(1) gauge symmetry which provides positive $D$-term…
Let G be a connected reductive algebraic group over an algebraically closed field k. In a recent paper, Bate, Martin, R\"ohrle and Tange show that every (smooth) subgroup of G is separable provided that the characteristic of k is very good…
Let $X$ be a Banach space. We study the circumstances under which there exists an uncountable set $\mathcal A\subset X$ of unit vectors such that $\|x-y\|>1$ for distinct $x,y\in \mathcal A$. We prove that such a set exists if $X$ is…
We show that for bounded domains in $\mathbb C^n$ with $\mathcal C^{1,1}$ smooth boundary, if there is a closed set $F$ of $2n-1$-Lebesgue measure $0$ such that $\partial \Omega \setminus F$ is $\mathcal C^{2}$-smooth and locally…
In Euclidean spaces, every closed, bounded, convex set can be characterized by two equivalent notions of separation properties. This is not true in general for arbitrary Banach spaces. In this work, we present a ball separation…
Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates…
Within a class of superstring vacua which have an additional non-anomalous $U(1)'$ gauge factor, we address the scale of the $U(1)'$ symmetry breaking and constraints on the exotic particle content and their masses. We also show that an…
The general SUSY soft breaking terms for a large class of phenomenologically relevant string scenarios (symmetric orbifolds) are given. They show a certain lack of universality, but not dangerous for flavor changing neutral currents. To get…
Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal…
We present a SUSY breaking scenario based on Abelian gaugino kinetic term mixings between hidden and observable sectors. If an extra U(1) gaugino in the observable sector obtains a large mass through this mixing effect based on SUSY…
For any closed Riemannian manifold $X$ we prove that large isoperimetric regions in $X\times{\mathbb R}^n$ are of the form $X\times$(Euclidean ball). We prove that if $X$ has non-negative Ricci curvature then the only soap bubbles enclosing…
For a separable finite diffuse measure space $\mathcal{M}$ and an orthonormal basis $\{\varphi_n\}$ of $L^2(\mathcal{M})$ consisting of bounded functions $\varphi_n\in L^\infty(\mathcal{M})$, we find a measurable subset…
We prove that every open connected region of relativistic spacetime $(M,\textbf{g})$ that encloses a $b$-incomplete half-curve has an open connected subregion that encloses a $b$-incomplete half-curve and is also 'small' in the following…
A set system is called union closed if for any two sets in the set system their union is also in the set system. Gilmer recently proved that in any union closed set system some element belongs to at least a $0.01$ fraction of sets, and…
We identify $m_{12}^2$ as a spurion of non-invertible Peccei-Quinn symmetry in the type II 2HDM with gauged quark flavor. Thus a UV theory which introduces quark color-flavor monopoles can naturally realize alignment without decoupling and…