Related papers: Reconsidering Power Functional Theory
The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
Power transforms, such as the Box-Cox transform and Tukey's ladder of powers, are a fundamental tool in mathematics and statistics. These transforms are primarily used for normalizing and standardizing datasets, effectively by raising…
We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum…
This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by…
This is an elementary introduction to Wilson renormalization group and continuum effective field theories. We first review the idea of Wilsonian effective theory and derive the flow equation in a form that allows multiple insertion of…
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
First and second order corrections for the scattering of different types of particles by a weak gravitational field, treated as an external field, are calculated. These computations indicate a violation of the Equivalence Principle: to…
Research on power values of power sums has gained much attention of late, partially due to the explosion of refinements in multiple advanced tools in (computational) Number Theory in recent years. In this survey, we present the key tools…
This paper presents a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
We study properties of an attractive-repulsive energy functional based on power-kernels, which can be used for halftoning of images. In the first part of this work, using a variational framework for probability measures, we examine…
This paper provides, from one side, a review of the theory of the cosmological mass function from a theoretical point of view, starting from the seminal paper of Press & Shechter (1974) to the last developments (Del Popolo & Gambera (1998,…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
We have derived a rigorous theoretical proof of the Strutinsky energy theorem. This proof not only provides a proper interpretation of the shell-correction decomposition, resolving decades of confusion, but also lays a foundation for…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
We comment on a recent paper by Yuen-Zhou et al. [ Phys. Chem. Chem. Phys. 2009, 11, 4509 ] which extends some of the results of Time-Dependent Current Density Functional Theory applied to open quantum systems. Besides pointing out some…
For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.
We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…