Related papers: An Elementary End of the Periodic Table
Planck's constant was introduced as a fundamental scale in the early history of quantum mechanics. We find a modern approach where Planck's constant is absent: it is unobservable except as a constant of human convention. Despite long…
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
In this paper we study the finite element approximation of systems of $p(\cdot)$-Stokes type, where $p(\cdot)$ is a (non constant) given function of the space variables. We derive --in some cases optimal-- error estimates for finite element…
Present atomic theory provides accurate and reliable results for atoms with a small number of valence electrons. However, most current methods of calculations fail when the number of valence electrons exceeds four or five. This means that…
A brief review, from basic atomic constants to "Mendeleev Table" of leptons, quarks, fundamental bosons, and then to superunification of all forces and particles.
Theoretical decay half-lives of the heaviest odd-Z nuclei are calculated using the experimental Q value. The barriers in the quasimolecular shape path are determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is…
We study a two-fluid description of high and low temperature components of the electron velocity distribution of an idealized tokamak plasma. We refine previous results on the laminar steady-state solution. On the one hand, we prove global…
Finite (upper) nearlattices are essentially the same mathematical entities as finite semilattices, finite commutative idempotent semigroups, finite join-enriched meet semilattices, and chopped lattices. We prove that if an $n$-element…
The exquisite control exhibited over quantum states of individual particles has revolutionized the field of precision measurement, as exemplified by the most accurate atomic clock realized in single trapped ions. Whereas many-atom lattice…
A systematic study on the alpha decay half lives of various isotopes of superheavy element \textit{Z} = 121 within the range 290 $\leq$ A $\leq$ 339 is presented for the first time using Coulomb and proximity potential model for deformed…
$^{\rm {180m}}$Ta is the rarest naturally occurring quasi-stable isotope and the longest lived metastable state which is known. Its possible decay via the $\beta^-$ or the electron capture channel has never been observed. This article…
We present a new framework to study the time variation of fundamental constants in a model-independent way. Model independence implies more free parameters than assumed in previous studies. Using data from atomic clocks based on $^{87}$Sr,…
In this work, we propose a numerical method based on high degree continuous nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the finite element method proves to be very efficient and favorably compares with other…
Employing two state-of-the-art methods, second-order many-body perturbation theory and multiconfiguration Dirac-Fock, highly accurate calculations are performed for the lowest 318 fine-structure levels arising from the $2s^{2} 2p^{4}$, $2s…
We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the…
Mathematical formula describing the periodicity of the elements in the periodic system is presented.
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
In this paper, we study the proportion of vanishing elements of finite groups. We show that the proportion of vanishing elements of every finite non-abelian group is bounded below by $1/2$ and classify all finite groups whose proportions of…
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to…
This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials ($P_3$) and possesses $\mathcal{O}(h^2)$ convergence rate in energy norm on general shape-regular…