We propose accurate computable error bounds for quantities of interest in plane-wave electronic structure calculations, particular ground-state density matrices and energies, interatomic forces. These are based on an estimation the terms residual solved equations, which is then efficiently approximated with terms. After providing coarse analysis inverse Jacobian, we improve these by solving a l...

In this letter, the wavelet transform is used to decompose classical linearly polarized plane light wave into a series of discrete Morlet wavelets. It found that energy can be discrete, associated with its structure.It also changeable basic packet or train vector $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}\over k} $ and structure form ${H_{0k}} = n{p_{0k}}\omega$ $(...

In this article we will discuss combinatorial structure of the parameter plane family $ \mathcal F = \{ \lambda \tan z^2: \in \mathbb C^*, \ z C\}.$ The space contains components where dynamics are conjugate on their Julia sets. complement these is bifurcation locus. These hyperbolic post-singular set disjoint from set. We prove that all bounded except four period one and they simply connected.

In the title compound, C(11)H(8)N(6)O(4)S, the plane of the coumarin aromatic ring is twisted by 17.2 (2)° with respect to the plane of the azide group bound to the methyl-ene substituent, whereas it is twisted by 83.2 (2)° to the plane of the azide attached to the sulfonyl group. The crystal structure is stabilized by weak C-H⋯O inter-actions, leading to the formation of dimers with R(2) (2)(1...

We investigate coherent phonon propagation in a thin film of ferroelectric PbZr(0.2)Ti(0.8)O(3) (PZT) by ultrafast x-ray diffraction experiments, which are analyzed as time-resolved reciprocal space mapping in order to observe the in- and out-of-plane structural dynamics, simultaneously. The mosaic structure of the PZT leads to a coupling of the excited out-of-plane expansion to in-plane lattic...