Extenders density

Mira variables form an important subgroup of the red giant stars which are typical representatives of stars showing burnt material at their surfaces. Since the photospheres of Miras are not in hydrostatic equilibrium but are characterized by spherically very extended density stratifications, their properties and emitted spectra differ substantially from those of non-Miras, and any attempts to analyse Mira spectra by means of conventional techniques must fail. Non-hydrostatic models are needed for analysis work. 

Spencer and Danner s modification to the Racket equation1 is a reliable way to predict and extend density data... 

J. Cerny, P. Hobza, The X3LYP extended density functional accurately describes H-bonding but fails completely for stacking. Phys. Chem. Chem. Phys. 7, 1624—1626 (2005)... 

Xu, X., and Goddard, W.A. III., The X3LYP extended density functional for accmate descriptions of nonbond interactions, spin states, and thermochemical properties., Proc. Natl. Acad. Sci. U.S.A., 101, 2673-2677 (2004). 

For an isolated cell the pressure is given by the particle density at the outer cell boundary. As a corollary, it must then also be positive. This is a rigorous statement, true for the spherical, cylindrical, and planar cell model [27], It is a merit of the PB equation that it retains the validity of this exact relation. For the extended density functional theories this no longer holds, and additional terms appear [5]. 

Density Functions play a fundamental role in the definition of Quantum Theory, due to this they are the basic materials used in order to define Quantum Objects and from this intermediate step, they constitute the support of Quantum Similarity Measures. Here, the connection of Wavefunctions with Extended Density Functions is analysed. Various products of this preliminary discussion are described, among others the concept of Kinetic Energy Distributions. Another discussed set of concepts, directly related with the present paper, is constituted by the Extended Hilbert Space definition, where their vectors are defined as column structures or diagonal matrices, containing both wavefunctions and their gradients. The shapes of new density distributions are described and analysed. All the steps above summarised are completed and illustrated, when possible, with practical application examples and visualisation pictures. 

The present work pretends to follow the path of these approaches, hopefully adding new ways and insights to study molecular shape and to analyse generally extended Density Function (DF) concepts. This paper do not tries to substitute in any way this previous brilliant work. On the contrary, pretends to... 

Figure 23.- Comparative analysis of extended density functions over the Ribulose molecule (front view) for several isodensity values.

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