相关论文: Optimal Synthesis in a Radially Symmetric Grushin …

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…

We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…

In this work, we study the rigidity problem for the logarithmic Sobolev inequality on a complete metric measure space $(M^n,g,f)$ with Bakry-\'Emery Ricci curvature satisfying $Ric_f\geq \frac{a}{2}g$, for some $a>0$. We prove that if…

A family of exact solutions is presented which represents a rigidly rotating cylinder of dust in a background with a negative cosmological constant. The interior of the infinite cylinder is described by the Godel solution. An exact solution…

We construct a $\mathcal{PT}$-symmetric Richardson--Gaudin models for spin-$\tfrac{1}{2}$ systems by deforming the closed integrable Hamiltonian through complex-valued transverse magnetic fields and coupling constants. By defining parity as…

In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas…

Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the…

The classical construction of the symplectic structure on the space of geodesic trajectories via Hamiltonian reduction fails in the pseudo-Riemannian setting due to a dimensional mismatch created by the null geodesics. This paper proposes a…

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of the solution at time $t\in\R$. The initial measure $\mu_0$ has a translation-invariant…

We investigate complete minimal hypersurfaces in the Euclidean space $% \ {R}^{4}$, with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^{3}\to {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker curvature…

We match the vacuum, stationary, cylindrically symmetric solution of Einstein's field equations with $\Lambda$, in a form recently given by Santos, as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe. There are…

Instead of conformal to flat spacetime, we take the metric conformal to a spacetime which can be thought of as ``minimally'' curved in the sense that free particles experience no gravitational force yet it has non-zero curvature. The base…

Consider a Urysohn integral equation $x - \mathcal{K} (x) = f$, where $f$ and the integral operator $\mathcal{K}$ with kernel of the type of Green's function are given. In the computation of approximate solutions of the given integral…

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic…

After a brief historical comment on the study of BRS(or BRST) symmetry , we discuss the quantization of gauge theories with Gribov copies. A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very…

Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and…

We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schr\"odinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete…

Ratner's theorem implies topological rigidity of immersed totally geodesic subspaces of noncompact type in finite-volume locally symmetric spaces. In higher rank and infinite volume, however, counter-examples to this rigidity have remained…

In this paper, we investigate spherically symmetric perfect fluid gravitational collapse in metric $f(R)$ gravity. We take non-static spherically symmetric metric in the interior region and static spherically symmetric metric in the…

We analyze the problem of gravitational collapse considering the matching of an exterior region described by the Vaidya's metric and an interior region described by a spherically symmetric shear-free inhomogeneous geometry sourced by a…