Generalized Lipschitz Classes and Fourier Coefficients

Mathematical Notes -     

Optimization of the ion-pair high-performance liquid chromatographic separation of purine derivatives in erythrocytes, thymocytes and liver mitochondria

Various methods are described for the analysis of purine derivatives in biological samples by ion-pair high-performance liquid chromatography (HPLC) with both gradient and isocratic systems. A new approach is proposed that is suitable for the separation of nuclei acid constituents in different cells with a specific enzymatic activity pattern. The ion-pair HPLC methods were developed for the analysis of erythrocytes, lymphocytes and mitochondria acid-soluble fractions in clinical and experimental studies of normal and altered nucleotide metabolism. The results of studies of purine metabolite redistribution in mouse liver mitochondria during a 30-min incubation at 37 degrees C and data on purine metabolic alterations in mouse thymocytes during hepatoma growth are discussed.     

A Non-commutative Yosida–Hewitt Theorem and Convex Sets of Measurable Operators Closed Locally in Measure

We present a non-commutative extension of the classical Yosida–Hewitt decomposition of a finitely additive measure into its σ-additive and singular parts. Several applications are given to the characterisation of bounded convex sets in Banach spaces of measurable operators which are closed locally in measure.     

Electrode erosion in a pulsed plasma accelerator

There are many papers on cathode phenomena in arcs, but there is no agreed view on the processes near and at the cathode in high-current arcs, in spite of the considerable interest in these phenomena in devices for plasma acceleration [4–7]. Results are presented on cathode damage and cathode spots in plasma accelerators of rail type.     

To the theory of operator monotone and operator convex functions

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ⁺ into ℝ⁺ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra.     

Symbol algebras and cyclicity of algebras after a scalar extension

For a field F and a family of central simple F-algebras we prove that there exists a regular field extension E/F preserving indices of F-algebras such that all the algebras from the family are cyclic after scalar extension by E. Let \( \mathcal{A} \) be a central simple algebra over a field F of degree n with a primitive nth root of unity ρ _n . We construct a quasi-affine F-variety Symb(\( \mathcal{A} \)) such that for a field extension L/F Symb(\( \mathcal{A} \)) has an L-rational point if and only if \( \mathcal{A}{ \otimes_F}L \) is a symbol algebra. Let \( \mathcal{A} \) be a central simple algebra over a field F of degree n and K/F be a cyclic field extension of degree n. We construct a quasi-affine F-variety C(\( \mathcal{A} \) ,K) such that, for a field extension L/F with the property [KL : L] = [K : F], the variety C(\( \mathcal{A} \) ,K) has an L-rational point if and only if KL is a subfield of \( \mathcal{A}{ \otimes_F}L \).