Related papers: The Simplest Exact Solutions in the LTB Model

We derive a direct general map from the luminosity distance D(z) to the inhomogeneous matter distribution M(r) in the Lemaitre-Tolman-Bondi (LTB) cosmology and compute several examples. One of our examples explicitly demonstrates that it is…

We continue the study of local $Tb$ theorems for square functions defined in the upper half-space $(\mathbb{R}^{n+1}_+, \mu \times dt/t)$. Here $\mu$ is allowed to be a non-homogeneous measure in $\mathbb{R}^n$. In this paper we prove a…

This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the…

We give distance--redshift relations in terms of elliptic integrals for three different mass distributions of the Friedmann-Lema\^\i tre-Robertson-Walker (FLRW) cosmology. These models are dynamically pressure free FLRW on large scales but,…

This short paper proposes to learn models of satisfiability modulo theories (SMT) formulas during solving. Specifically, we focus on infinite models for problems in the logic of linear arithmetic with uninterpreted functions (UFLIA). The…

Previous work has shown that reasoning with real-time temporal logics is often simpler when restricted to models with bounded variability---where no more than v events may occur every V time units, for given v, V. When reasoning about…

We analyze some exact and approximate solutions to nonlinear equations for heat transfer models. We prove that recent results derived from a method based on Lie algebras are either trivial or wrong. We test a simple analytical expression…

The Hubble constant ($H_0$) is one of the most important parameters in the standard $\rm \Lambda CDM$ model. The measurements given by the main two methods show a gap larger than $4\sigma$, which is known as Hubble tension. Fast radio…

Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a…

Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…

This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently…

The algebraic properties of drift-flux two-phase fluids models without gravitational and wall friction forces are studied. More precisely, for the two fluids we consider equation of states of polytropic gases. We perform a classification…

A numerical approach is considered for spherically symmetric spacetimes that generalize Lemaitre-Tolman-Bondi dust solutions to nonzero pressure ("LTB spacetimes"). We introduce quasi-local (QL) variables that are covariant LTB objects…

Recently hints of lepton flavor non-universality emerged when the BaBar Collaboration observed deviations from the standard model predictions in $R(D^{(*)}) \equiv {\cal B}({\bar B} \to D^{(*)+} \tau^- {\bar\nu}_\tau) / {\cal B}({\bar B}…

The infinite U Hubbard model, with exclusion of double occupancy of sites, can be considered as a free orthofermion Hamiltonian which is exactly soluble. It is found that the orthofermion distribution function is similar to the mean number…

We probe the validity of Crooks' fluctuation relation on the fluctuating lattice-Boltzmann model (FLBM), a highly simplified lattice model for a thermal ideal gas. We drive the system between two thermodynamic equilibrium states and compute…

A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition at the face $x=0$ is studied with the aim of finding explicit…

In this work we prove the existence of solution for a class of perturbed fractional Hamiltonian systems given by \begin{eqnarray}\label{eq00} -{_{t}}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) - L(t)u(t) + \nabla W(t,u(t)) = f(t),…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

In this work we calculate the equation of state of nuclear matter for different proton fractions at zero and finite temperature within the Thomas Fermi approach considering three different parameter sets: the well-known NL3 and TM1 and a…