Classical density

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  • Classical physics breaks down to the level of atoms and molecules. This was made possible by the invention of a new apparatus that enabled the introduction of measurements in microscopic area of physics. There were two revolutions in the way we viewed the physical world in the twentieth century: relativity and quantum mechanics. Quantum mechanics was born in 1924, through the work of Einstein, Rutherford and Bohr, Schrödinger and Heisenberg, Born, Dirac, and many others. The principles of quantum mechanics that were discovered then are the same as we know them today....

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  • Room temperature ionic liquids (RTILs) are an interesting and valuable family of compounds. Although they are all salts, their components can vary considerably, including imidazolium, pyridinium, ammonium, phosphonium, thiazolium, and triazolium cations. In general, these cations have been combined with weakly coordinating anions. Common examples include tetrafluoroborate, hexafluorophosphate, triflate, triflimide, and dicyanimide.

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  • Steiner symmetrization, one of the simplest and most powerful symmetrization processes ever introduced in analysis, is a classical and very well-known device, which has seen a number of remarkable applications to problems of geometric and functional nature. Its importance stems from the fact that, besides preserving Lebesgue measure, it acts monotonically on several geometric and analytic quantities associated with subsets of Rn. Among these, perimeter certainly holds a prominent position.

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  • Let X be a smooth quasiprojective subscheme of Pn of dimension m ≥ 0 over Fq . Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX (m + 1)−1 , where ζX (s) = ZX (q −s ) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming the abc conjecture and another conjecture. 1. Introduction The classical Bertini theorems say that if a subscheme...

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  • Chemical reactions take place due to the redistribution of electron density among the reacting partners. Focusing on changes in electron density, which accompany the breaking and forming of chemical bonds, instead of the changes in the wave function accompanying them, allows us to use the ‘‘classical’’ three-dimensional language. Conceptual density functional theory (DFT) quantifies the possible responses of the system to various changes in density.

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  • P-glycoprotein (Pgp), a member of the ATP-binding cassette (ABC) super-family responsible for the ATP-driven extrusion of diverse hydrophobic molecules from cells, is a cause of multidrug resistance in human tumours. Pgp can also operate as a phospholipid and glycosphingolipid flippase, and has been functionally linked to cholesterol, suggesting that it might be associated with sphingolipid–cholesterol microdomains in cell membranes.

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