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In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
These maps are quasisymmetric, although they are a much narrower subclass of quasisymmetric maps. For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ...
Each chemical element has a unique atomic number (Z— for "Zahl", German for "number") representing the number of protons in its nucleus. [4] Each distinct atomic number therefore corresponds to a class of atom: these classes are called the chemical elements. [5] The chemical elements are what the periodic table classifies and organizes.
Chemical imaging (as quantitative – chemical mapping) is the analytical capability to create a visual image of components distribution from simultaneous measurement of spectra and spatial, time information. [1] [2] Hyperspectral imaging measures contiguous spectral bands, as opposed to multispectral imaging which measures spaced spectral ...
Kneading theory provides an effective calculus for describing the qualitative behavior of the iterates of a piecewise monotone mapping f of a closed interval I of the real line into itself. Some quantitative invariants of this discrete dynamical system , such as the lap numbers of the iterates and the Artin–Mazur zeta function of f are ...
1965 — Alexander arrangement of elements: Designed to complement the point at which education on the arrangement of atoms into a chart begins, much as the world globe establishes the reality, and to emphasise the vital and convenient nature of flat printed projections or maps [81] 1999 — Moran's spiral periodic table: In hexagonal form [82]
Hence the identity map is always 1-quasiconformal. If f : D → D′ is K-quasiconformal and g : D′ → D′′ is K′-quasiconformal, then g o f is KK′-quasiconformal. The inverse of a K-quasiconformal homeomorphism is K-quasiconformal. The set of 1-quasiconformal maps forms a group under composition.
Hence, in many cases the elements of a particular group have the same valency. However, this periodic trend is not always followed for heavier elements, especially for the f-block and the transition metals. These elements show variable valency as these elements have a d-orbital as the penultimate orbital and an s-orbital as the outermost orbital.