Related papers: Duane -- Hunt relation improved
We present a unified approach to improved $L^p$ Hardy inequalities in $\R^N$. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
The Dunnett procedure compares several treatment or dose groups with a control group, while controlling the familywise error rate. When deviations from the normal distribution and heterogeneous variances occur, the nominal $\alpha$ level…
We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…
In the present work we suggest a non-local generalization of quantum theory which include quantum theory as a particular case. On the basis of the idea, that Planck constant is an adiabatic invariant of the free/coupled electromagnetic…
We improve constants in the Rademacher-Menchov inequality.
The accelerating expansion of the Universe points to a small positive value for the cosmological constant or vacuum energy density. We discuss recent ideas that the cosmological constant plus LHC results might hint at critical phenomena…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
We present improved Coulomb correction formulae for Bose-Einstein correlations including also exchange term and use them to calculate appropriate correction factors for several source functions. It is found that Coulomb correction to the…
X-ray and gamma-ray observations of astrophysical objects at cosmological distances can be used to probe the energy dependence of the speed of light with high accuracy and to search for violations of Lorentz invariance and CPT symmetry at…
We show that promoting the trace part of the Einstein equations to a trivial identity results in the Newton constant being an integration constant. Thus, in this formulation the Newton constant is a global dynamical degree of freedom which…
We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed : 1) improvement of observational means (ground-based radio and optical…
We extend the Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)] of the exchange potential to two dimensions. We prove and demonstrate that a direct extension of the underlying formalism may lead to divergent behavior of the…
The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble-Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative…
The aim of this review article is to assess the descriptive capabilities of the Hubbard-rooted LDA+U method and to clarify the conditions under which it can be expected to be most predictive. The paper illustrates the theoretical foundation…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact"…
We consider several transitions between narrow lines that have an enhanced sensitivity to a possible variation of the fine structure constant, alpha. This enhancement may allow a search to be performed with an effective suppression of the…
The shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections…
We discuss two different approximation schemes for the self-consistent solution of the {\it relativistic} Brueckner-Hartree-Fock equation for finite nuclei. In the first scheme, the Dirac effects are deduced from corresponding nuclear…
We propose the use of two point Pade approximants to find expressions valid uniformly in coupling constant for theories with both weak and strong coupling expansions. In particular, one can use these approximants in models with a…