Related papers: Resurgence and Mould Calculus
Based on the mathematically well defined Pad\'e Theory, a theoretically safe new procedure for the extraction of the pole mass and width of a resonance is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to…
We estimate the abundance of the coherent oscillation of moduli, which linearly couple to matter fields through higher dimensional operators. During the (p)reheating after inflation, matter particles are efficiently produced and it can…
In this work, we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation $$u \mapsto…
This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's $J_2$ and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane,…
Developing a bottom-up (molecular) theory for the electromechanical response of aperiodic materials is a prerequisite for understanding the piezoelectric properties of systems such as nanoparticles, (non-crystalline) polymers, or…
We explore the ideas of resurgence and Pad\'{e}-Borel resummation in the Euler-Heisenberg Lagrangian of scalar quantum electrodynamics, which has remained largely unexamined in these contexts. We thereby extend the related seminal works in…
We propose an extremely simple mathematical model that is shown to be able to account for more than 99 per cent of all the variation in economic and demographic macrodynamics of the world for almost two millennia of its history. This…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
Rook theory has been investigated by many people since its introduction by Kaplansky and Riordan in 1946. Goldman, Joichi and White in 1975 showed that the sum over $k$ of the product of the $(n-k)$-th rook numbers multiplied by the $k$-th…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
The original article of Rudolf Kohlrausch (1854) on stretched exponentials and their application to describe relaxation phenomena has been often misquoted in the literature after its rediscovery around 1984. We discuss here this fact and…
In this paper, we develop a multivariate regression model and a neural network model to predict the Reynolds number (Re) and Nusselt number in turbulent thermal convection. We compare their predictions with those of earlier models of…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
A novel mechanism of reaction-induced active molecular motion, not involving any kind of self-propulsion, is proposed and analyzed. Because of the momentum exchange with the surrounding solvent, conformational transitions in…
The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel'fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field…
In this reverse archeological find, we see how mathematics will be written in fifty years.
We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce…
Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations. However, it is a significant challenge for the system with long-range interactions. We employ symbolic regression to regress…
The $\lambda$$\Pi$-calculus modulo theory is an extension of simply typed $\lambda$-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the…
A mechanism of inflation from higher dimensions compactification is studied. An Early Universe capable of providing exponential growth for some dimensions and exponential contraction for others, giving therefore an explanation for the big…