相关论文: Extrapolation of Hubble Curves

Fractional differential equations model processes with memory effects, providing a realistic perspective on complex systems. We examine time-delayed differential equations, discussing first-order and fractional Caputo time-delayed…

We present results for two-loop diagrams with massive quarks in the eikonal approximation. Explicit expressions are given for the UV poles in dimensional regularization of several of the required integrals.

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced…

We focus on numerical techniques for expanding 3-loop Feynman integrals with respect to the dimensional regularization parameter $\varepsilon,$ which is related to the space-time dimension as $\nu = 4-2\varepsilon,$ and describes underlying…

We study the convergence of bound-state quadrupole moments in finite harmonic oscillator spaces. We derive an expression for the infrared extrapolation for the quadrupole moment of a nucleus and benchmark our results using different model…

We present a novel function fitting method for approximating the propagation of the time-dependent electric dipole moment from real-time electronic structure calculations. Real-time calculations of the electronic absorption spectrum require…

Examples of scalar conserved currents are presented for trigonometric, hyperbolic and elliptic versions of the Hubbard model with non-nearest neighbour variable range hopping. They support for the first time the hypothesis about the…

We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighbourhood of the logarithmic…

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…

The Helmholtz equation is notoriously difficult to solve with standard numerical methods, increasingly so, in fact, at higher frequencies. Controllability methods instead transform the problem back to the time-domain, where they seek the…

Solutions of the Friedmann-Lemaitre cosmological equations of general relativity have been found with finite-time singularities that are everywhere regular, have regular Hubble expansion rate, and obey the strong-energy conditions but…

We present a collection of integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, $u(\x) - \alpha^2 \Delta u(\x) = 0$, in bounded or unbounded multiply-connected domains. We consider both Dirichlet…

Feynman diagrams are calculated by means of their Taylor series expansion in terms of external momenta squared. It is demonstrated in various examples that by the application of conformal mapping and Pad\'{e} approximants, it is possible to…

In this article, we construct algebraic equations for a curve C and a map f to an elliptic curve E, with pre-specified branching data. We do this by determining certain relations that the periods of C and E must satisfy and use these…

We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…

The mathematical model representing the equation of motion of a pendulum is nonlinear. Solutions that satisfy the equation cannot be represented by elementary functions, such as trigonometric functions. To solve such problems, it is common…

We study the most general cosmological model with real scalar field which is minimally coupled to gravity. Our calculations are based on Friedmann-Lemaitre-Robertson-Walker (FLRW) background metric. Field equations consist of three…

In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…

We propose a model-independent formalism to numerically solve the modified Friedmann equations in the framework of $f(T)$ teleparallel cosmology. Our strategy is to expand the Hubble parameter around the redshift $z=0$ up to a given order…

The Hubbard model is exactly solved for two particles with opposite spins on d-dimensional hypercubes. It is shown that the spectrum can be separated into two parts: a trivial (U-independent) part resulting from symmetries of hypercubes and…