Alexey Kryukov

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The formalism of local coordinates on infinite-dimensional Hilbert manifolds is introduced. Images of charts on the manifolds are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. The corresponding local coordinate form of algebra of tensor fields on Hilbert manifolds is constructed. A single tensor(More)
Dental anomalies in the Japanese mole, Mogera wogura Temminck, 1842, from northeast China and the Primorsky region of Russia were examined based on 241 specimens. The most frequent dental anomaly was oligodonty, i.e., missing P2 (18 cases) or P3 (one case). Supernumerary teeth were observed in three cases, two of which were characterized by abnormal shapes.(More)
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R n , Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of(More)
Coordinate formalism on Hilbert manifolds developed in [1] is reviewed. The results of [1] are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential(More)
Arbuscular mycorrhiza (AM) development in five non-nodulating pea (Pisum sativum L.) mutants (sym7, sym11, sym14, sym34, sym38) grown in nurse pots was analyzed at the early stages of colonization by Rhizophagus irregularis. Abundance of external mycelium attached to the root surface and parameters of internal fungal colonization, i.e. intensity of(More)
We studied the effect of delta sleep-inducing peptide (40, 120, and 360 μg/kg intraperitoneally, 1 h before the experiment) on free radical oxidation in the liver, aminotransferase activity, and total serum protein content in male Wistar rats during restraint stress. Treatment with the peptide in a dose of 40 μg/kg increased catalase and superoxide(More)
The Jungle Crow (Corvus macrorhynchos) is a widespread species in Asia that underwent remarkable postglacial recolonisations during the Pleistocene and Holocene. In order to better understand the pattern of its settling and diversification, we investigated the morphological differences among adult Jungle Crow samples obtained from locations in northern(More)
The Riemannian manifold structure of the classical (i.e. Einsteinian) spacetime is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe.(More)
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces(More)