Related papers: On logarithmic solutions of A-hypergeometric syste…
We consider the Lane-Emden system-$\Delta$u = |v| p-1 v,-$\Delta$v = |u| q-1 u in R d. When p $\ge$ q $\ge$ 1, it is known that there exists a positive radial stable solution (u, v) $\in$ C 2 (R d) if and only if d $\ge$ 11 and (p, q) lies…
For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a non-trivial minuscule representation and a connected marked surface $\Sigma$ with at least two marked points and no punctures, we prove that the cluster algebra…
We obtain the second-order asymptotics for the radiation field of spherically symmetric solutions to the wave equation on spherically symmetric and asymptotically flat backgrounds including the Schwarzschild and sub-extremal…
We find static charged black hole solutions in nonlinear massive gravity. In the parameter space of two gravitational potential parameters $(\alpha, \beta)$ we show that below the Compton wavelength the black hole solutions reduce to that…
We give necessary conditions for when a subset of $\mathbb{T}^n$ can contain the support of some non-zero RP-measure. Among other things we show that the support of a positive RP-measure cannot be contained in reflections of inverse images…
This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear…
In Hilbert space setting we prove local lipchitzness of projections onto parametric polyhedral sets represented as solutions to systems of inequalities and equations with parameters appearing both in left-hand-sides and right-hand-sides of…
In this paper, we present two new families of spatially homogeneous black hole solution for $z=4$ Ho\v{r}ava-Lifshitz Gravity equations in $(4+1)$ dimensions with general coupling constant $\lambda$ and the especial case $\lambda=1$,…
We show that if v is an axially symmetric suitable weak solution to the Navier Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg) such that the radial component of v has a higher regularity (i.e. satisfies weighted…
Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mirror pairs, the number of rational points over a finite…
An integer linear system is a set of inequalities with integer constraints. The solution graph of an integer linear system is an undirected graph defined on the set of feasible solutions to the integer linear system. In this graph, a pair…
We consider a generalization of the Cheeger problem in a bounded, open set $\Omega$ by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable powers of a weighted volume. We show that any…
Take a holomorphic Lie algebroid $(V,\, \phi)$ on a compact connected Riemann surface $X$ such that the anchor map $\phi$ is not surjective. Let $P$ be a parabolic subgroup of a complex reductive affine algebraic group $G$ and $E_P\,…
We describe the $(\alpha,\beta)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(\alpha,\beta)$-metrics that satisfy the $\sigma T$-condition $\sigma_hT^h_{ijk}=0$, where $\sigma_h=\frac{\partial \sigma}{\partial x^h}$ and…
In this paper, we primarily focus on analyzing the stability property of phase retrieval by examining the bi-Lipschitz property of the map $\Phi_{\boldsymbol{A}}(\boldsymbol{x})=|\boldsymbol{A}\boldsymbol{x}|\in \mathbb{R}_+^m$, where…
Let a sequence $\Lambda\subset\mathbb{C}$ be such that the corresponding system of exponential functions $\mathcal{E}(\Lambda):=\{e^{i\lambda t}\}_{\lambda\in\Lambda}$ is complete and minimal in $L^2(-\pi,\pi)$ and thus each function $f\in…
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…
For the general class of pseudo-Finsler spaces with $(\alpha,\beta)$-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian…
Consider the following Lane-Emden system with Dirichlet boundary conditions: \[ -\Delta U = |V|^{\beta-1}V,\ -\Delta V = |U|^{\alpha-1}U \text{ in }\Omega,\qquad U=V= 0 \text{ on }\partial \Omega, \] in a bounded domain $\Omega$, for…
We prove one direction of homological mirror symmetry for complete intersections in algebraic tori, in all dimensions. The mirror geometry is not a space but a LG model, i.e. a pair given by a space and a regular function. We show that the…