In this contribution we propose a technique to analyse arbitrary invariant subsets of chaotic dynamical systems. For this purpose we introduce the constrained Frobenius-Perron operator. We demonstrate the use of this operator by determining the geometrical multifractal spectrum of invariant chaotic subsets of one-dimensional maps which are either coexisting side by side indepen­ dently or are e...

The reaction 2-pyridone (PY) e 2-hydroxypyridine (HP) has been studied as a prototype of tautomerism of heteroaromatic compounds. Geometrical structures and relative energies of the two tautomers as welt as of the transition state (TS) for the intramolecular hydrogen transfer have been obtained using ab initio methods with different basis sets. Correlation energy is introduced through configura...

This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial resolutions, complexes of graphs, Orlik– Solomon rings, Salvetti complex, matroids, Spanier–Whitehead duality, twisted homology groups, monodromy theory and multidimensional hypergeometri...

We perform the stochastic quantization of Yang–Mills theory in configuration space and derive the Faddeev-Popov path integral density. Based on a generalization of the stochastic gauge fixing scheme and its geometrical interpretation this result is obtained as the exact equilibrium solution of the associated Fokker–Planck equation. Included in our discussion is the precise range of validity of ...

We study body-and-hinge and panel-and-hinge chains in R, with two marked points: one on the first body, the other on the last. For a general chain, the squared distance between the marked points gives a Morse-Bott function on a torus configuration space. Maximal configurations, when the distance between the two marked points reaches a global maximum, have particularly simple geometrical charact...

The title compound, C(15)H(14)N(2)O(2), an azo dye, displays a trans configuration with respect to the N=N bridge. The dihedral angle between the aromatic rings is 0.18 (14)°. There is a strong intra-molecular O-H⋯O hydrogen bond. Geometrical parameters, determined using X-ray diffraction techniques, are compared with those calculated by density functional theory (DFT), using hybrid exchange-co...

In medical image analysis, geometrical deformations are used to model intersubject variability. In orthopaedic applications, the geometrical variability is usually observable across anatomical scales. For instance, anatomical differences between mandible bones of different patients can be found on a coarse scale, between the entire left or right side, or on a fine scale, between teeth. Each lev...

Two-dimensional (2D) geometrical shape-shifting is prevalent in nature, but remains challenging in man-made "smart" materials, which are typically limited to single-direction responses. Here, we fabricate geometrical shape-shifting bovine serum albumin (BSA) microstructures to achieve circle-to-polygon and polygon-to-circle geometrical transformations. In addition, transformative two-dimensiona...

nowadays, the application of floating breakwaters in small or recreational harbors has found more popularity. these types of breakwaters are more flexible in terms of design, configuration and especially installation compared with fixed breakwaters. in the current study, the performance of floating breakwater (fbs) under regular waves was studied using the physical modeling method. for the mode...