相关论文: An Exact Solution with $f^2 = 1$ and $\Lambda \ne …

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…

Recently it has been noted by Di Valentino, Melchiorri and Silk (2019) that the enhanced lensing signal relative to that expected in the spatially flat $\Lambda$CDM model poses a possible crisis for the…

We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a…

We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…

The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…

The dispersion measure-redshift relation of fast radio bursts (FRBs) provides a valuable cosmological probe for constraining the Hubble constant, offering an independent measurement that could help resolve the ongoing Hubble tension. In…

We show that the prescribed Gaussian curvature equation in $\mathbb{R}^2$ $$-\Delta u= (1-|x|^p) e^{2u},$$ has solutions with prescribed total curvature equal to $\Lambda:=\int_{\mathbb{R}^2}(1-|x|^p)e^{2u}dx\in \mathbb{R}$, if and only if…

Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently…

We give a direct proof of the local $Tb$ Theorem, in the Euclidean setting, and under the assumption of dual exponents. This Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator, supposing the…

The Hubble tension is shown to be solvable, without any free parameter, conceptually and quantitatively, within the approach of modified weak-field General Relativity involving the cosmological constant $\Lambda$. That approach enables one…

An auto-B\"acklund transformation for the quad equation $\mathrm{Q1}_1$ is considered as a discrete equation, called $\mathrm{H2}^a$, which is a so called torqued version of $\mathrm{H2}$. The equations $\mathrm{H2}^a$ and $\mathrm{Q1}_1$…

A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to…

This paper provides some statistics for the coefficients of Russell- Type modular equations for the modular function, {\lambda}({\tau}). The results hold uniformly for all odd primes. They do not rely on any numerical evaluations of…

An explicit and complete set of constants of the motion are constructed algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models consisting of an arbitrary number of non-interacting species. The inheritance of constants of…

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to…

The closed form solution is found for the fully nonlinear dynamics of the gyroscope with a fixed point at the tip. The solution is found by using Cardano's formulae to factor a cubic, in the case where all roots are known to be real. From…

We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis,…

A novel explicit method to model Lorentz linear dispersive media with finite difference method are presented. The method shows an explicit method without any modification to the Leap-Frogging scheme. The polarizations of the Lorentz media…

A new class of solutions of Einstein's equations is derived providing a physically plausible hydrodynamic description of cosmological matter in the radiation era of the Universe expansion. The solutions are characterized by the LTB metric…

We derive an exact $f(T)$ gravity in the absence of ordinary matter in Friedmann-Robertson-Walker (FRW) universe, where $T$ is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor $\mathcal{T}^{\mu \nu}$ of…