Related papers: An Elementary End of the Periodic Table
Ground state energies and decay widths of particle unstable nuclei are calculated within the Hartree-Fock approximation by performing a complex scaling of the many-body Hamiltonian. Through this transformation, the wave functions of the…
We prove a nearly optimal bound on the number of stable homotopy types occurring in a k-parameter semi-algebraic family of sets in $\R^\ell$, each defined in terms of m quadratic inequalities. Our bound is exponential in k and m, but…
Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in $\ell$-algebras, preferably in $f$-algebras, and in product algebras. The additional structure of an associative multiplication leads…
We use Wegner's flow equation method to investigate the infinite-$U$ periodic Anderson model. We show that this method poses a new approach to the description of heavy fermion behaviour. Within this scheme we derive an effective Hamiltonian…
Experimental evidence over a number of recent years has shown the density parameter of the universe omega converging to the critical value of 1, which defines a flat, Euclidean universe. No such calculations have defined a critical value…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
Plutonium is the most exotic and mysterious element in the periodic table. It has 6 metallic phases and peculiar physical properties not yet understood. One of the most intriguing properties of Pu is that relatively small changes of…
In this work we prove the lower bound for the number of $T$-periodic solutions of an asymptotically linear planar Hamiltonian system. Precisely, we show that such a system, $T$-periodic in time, with $T$-Maslov indices $i_0,i_\infty$ at the…
The electronic and geometric properties of bulk fcc delta-plutonium and the quantum size effects in the surface energies and the work functions of the (001) ultra thin films (UTF) up to 7 layers have been investigated with periodic density…
The noble elements constitute the simplest group in the periodic table. At low temperatures or high pressures, the liquid phase solidifies into a face-centered cubic crystal structure (except helium). In the companion paper, we investigated…
The fundamental organizing principle resulting in the periodic table is the nuclear charge. Arranging the chemical elements in an increasing atomic number order, a symmetry pattern known as the Periodic Table is detectable. The correlation…
The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. However, the "stability of physical theories principle" seems to be the one that provides, through the tools of algebraic deformation theory,…
The feasibility of alpha and cluster decay from Pt isotopes has been investigated within the framework of Skyrme Hartree-Fock-Bogoliubov theory. Calculation has been carried out for various Skyrme forces. Harmonic oscillator and transformed…
By assuming the existence of a pseudopotential smooth enough to do Hartree-Fock variations and good enough to describe nuclear structure, we construct mass formulae that rely on general scaling arguments and on a schematic reading of shell…
We investigate finite effect algebras and their classification. We show that an effect algebra with $n$ elements has at least $n-2$ and at most $(n-1)(n-2)/2$ nontrivial defined sums. We characterize finite effect algebras with these…
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic…
Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the…
Currently, 163 isotopes of elements with Z $\ge$ 100 have been observed and the discovery of these isotopes is discussed here. For each isotope a brief synopsis of the first refereed publication, including the production and identification…
We study the local optimality of periodic point sets in $\mathbb{R}^n$ for energy minimization in the Gaussian core model, that is, for radial pair potential functions $f_c(r)=e^{-c r}$ with $c>0$. By considering suitable parameter spaces…
Let $-1<\lambda<1$ and $f:[0,1)\to\mathbb{R}$ be a piecewise $\lambda$-affine map, that is, there exist points $0=c_0<c_1<\cdots <c_{n-1}<c_n=1$ and real numbers $b_1,\ldots,b_n$ such that $f(x)=\lambda x+b_i$ for every $x\in…