Abstract Deciding whether a given function is quasiconvex generally difficult task. Here, we discuss number of numerical approaches that can be used in the search for counterexample to quasiconvexity W . We will demonstrate these methods using planar isotropic rank-one convex $$\begin{aligned} W_\textrm{magic}^+(F)=\frac{\lambda _\textrm{max}}{\lambda _\textrm{min}}-\log \frac{\lambda _\textrm{...

We report on the spectroscopy of the 5s 1S0 (F = 9/2) → 5s5p 3P0 (F = 9/2) clock transition of Sr atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the mag...

We report on the observation and coherent excitation of atoms narrow inner-shell orbital transition, connecting erbium ground state $[\mathrm{Xe}]4{f}^{12}{(}^{3}{\text{H}}_{6})6{s}^{2}$ to excited $[\mathrm{Xe}]4{f}^{11}({{(}^{4}{\text{I}}_{15/2})}^{0})5d{(}^{5}{\text{D}}_{3/2})6{s}^{2}{(15/2,3/2)}_{7}^{0}$. This transition corresponds a wavelength 1299 nm is optically closed. perform high-res...

Model-generation based theorem provers such as SATCHMO and MGTP suffer from a combinatorial explosion of the search space caused by clauses irrelevant to the goal (negative clause) to be solved. To avoid this, two typical methods have been proposed. One is relevancy testing implemented in SATCHMORE by Loveland et al., and the other is non-Horn magic sets that are the extension of Horn magic set...

A magic square of order n is an n by n matrix with distinct nonnegative integer entries such that every row sum, column sum, and (two) diagonal sums equals to the same number m, the magic number. Adding 1 to every entry will give us a traditional magic square of positive integers. A magic square is pure if the entries are the consecutive numbers from 0 to n − 1, and hence it has magic number 3 ...

A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f(x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the ...

Carbon nanostructures with unusually large paramagnetic moments have been discovered in a theoretical study of the electronic and magnetic properties of carbon nanotubes bent into toroids. Specifically, nanotori formed from metallic nanotubes with lambda(F) = 3T, where lambda(F) is the Fermi wavelength and T the translation vector of the nanotube, exhibit giant paramagnetic moments at selected ...