相关论文: Generalized Euclidean stars with equation of state

The purpose of this Note is to unify quantum groups and star-products under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question,…

A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…

Motivated by asymptotic symmetry groups in general relativity, we consider projective unitary representations $\overline{\rho}$ of the Lie group $\mathrm{Diff}_c(M)$ of compactly supported diffeomorphisms of a smooth manifold $M$ that…

We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the…

We obtain a general sufficient condition on the geometry of possibly singular planar domains that guarantees global uniqueness for any weak solution to the Euler equations on them whose vorticity is bounded and initially constant near the…

The first detection of gravitational waves from the binary neutron star merger event GW170817 has started to provide important new constraints on the nuclear equation of state at high density. The tidal deformability bound of GW170817…

The paper provides a new framework for the description of linearized adiabatic lagrangian perturbations and stability of differentially rotating newtonian stars. In doing so it overcomes problems in a previous framework by Dyson and Schutz…

The symmetries of the L\'evy-Leblond equation are investigated beyond the standard Lie framework. It is shown that the equation has two remarkable symmetries. One is given by the super Schr\"odinger algebra and the other one by a $\ZZ$…

It is known that each symmetric stable distribution in $R^d$ is related to a norm on $R^d$ that makes $R^d$ embeddable in $L_p([0,1])$. In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to…

The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring…

We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of…

In this paper, a modified version of the hydrostatic equilibrium equation based on the mimetic gravity in the presence of perfect fluid is revisited. By using the different known equation of states, the structural properties of neutron…

After giving an overview of the history and idea of neutron stars, I shall introduce, in part one of my lectures, a representative collection of models for the equation of state of superdense neutron star matter, which account for various…

We obtain solutions of the time-dependent Einstein Field Equations which satisfy the Karmarkar condition via the method of Lie symmetries. Spherically symmetric spacetime metrics are used with metric functions set to impose conformal…

We look for ground state solutions to the Schr\"odinger-type system \[ \begin{cases} -\Delta u_j + \lambda_j u_j = \partial_jF(u)\\ \int_{\rn} u_j^2 \, dx = a_j^2\\ (\lambda_j,u_j) \in \mathbb{R} \times H^1(\mathbb{R}^N) \end{cases} j \in…

Many relevant applications of group theoretical methods to physical problems are related, in some manner, to classification schemes by means of symmetry groups. In these schemes, irreducible representations of a Lie group have to be…

We introduce the universal Euler characteristic of orbit space definable groupoids, a class of groupoids containing cocompact proper Lie groupoids as well as translation groupoids associated to proper definable group actions. We show that…

We present a rigorous framework for determining equilibrium configurations of uniformly rotating self-gravitating fluid bodies. This work addresses the longstanding challenge of modeling rotational deformation in celestial objects such as…

We consider the nonlinear Schr\"{o}dinger equation $-\Delta u + V(x) u = \Gamma(x) |u|^{p-1}u$ in $\R^n$ where the spectrum of $-\Delta+V(x)$ is positive. In the case $n\geq 3$ we use variational methods to prove that for all $p\in…

The chemotaxis system \begin{align*} u_t &= \Delta u - \nabla \cdot (u\nabla v), \\ v_t &= \Delta v - uv, \end{align*} is considered under the boundary conditions $\frac{\partial u}{\partial\nu}- u\frac{\partial v}{\partial\nu}=0$ and…