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We generalize Atsuyama's result on the geometry of symmetric spaces of type EVI to the case of fields of characteristic zero. We relate the possible mutual positions of two points with the classification of balanced symplectic ternary algebras (also known as Freudenthal triple systems). [ABSTRACT FROM AUTHOR]

In this paper we study commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such structures on A K 2 and A K 3 and describe some generalizations on A K n for any dimension n. [ABSTRACT FROM AUTHOR]

We prove that frame set F g for imaginary shift of sinc-function g (t) = sin ⁡ π b (t − i w) t − i w , b , w ∈ R ∖ { 0 } can be described as F g = { (α , β) : α β ⩽ 1 , β ⩽ | b | }. In addition, we prove that F g = { (α , β) : α β ⩽ 1 } for window functions g of the form 1 t − i w (1 − ∑ k = 1 ∞ a k e 2 π i b k t) , such that ∑ k ⩾ 1 | a k | e 2 π | w b k | < 1 , w b k < 0. [ABSTRACT FROM AUTHOR]

We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms; in particular, we reproduce quadratic equations by Lichtenstein defining them. [ABSTRACT FROM AUTHOR]

The recently proposed interface equilibria‐triggered dynamic diffusion model of the boundary potential has proven its high predictive efficiency for quantification of the ion exchange and co‐extraction effects at the interface, as well as of the trans‐membrane transfer effect, on the electrode response. It is applicable for both ion exchanger‐based and neutral carrier‐based electrodes. In this communication, the adaptability of this model to more complex cases, when non‐ion‐exchange extraction processes at the interface (partition of organic acids' and bases' molecular forms and extraction of ionic associates) are coupled with protolytic equilibria in the aqueous phase and with self‐solvation process in the membrane phase, is demonstrated. By the example of electrodes reversible to ions of highly lipophilic physiologically active bases and acids (amiodarone, verapamil, vinpocetine, salicylic acid), it is shown that the peculiarities of their functioning, such as a very strong pH effect on the potential of cation‐selective electrodes, non‐monotonic pH dependence of the potential and super‐Nernstian response slope in certain pH region for a salicylate‐selective electrode, are well described within the model. [ABSTRACT FROM AUTHOR]