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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)

- Masakazu Asahara, Alexey Kryukov, Masaharu Motokawa
- Acta Theriologica
- 2011

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)

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)

- Alexey Kryukov
- Int. J. Math. Mathematical Sciences
- 2005

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 form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observ-ables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear… (More)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The… (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)

- Alexey Kryukov, Vladislav Dorosh
- 2006

1. Title: Proposal to add old Cyrillic titlo-letters to the UCS 2. Requester's name: On behalf of the Slavonic Typography Community: Alexey Kryukov <akrioukov@newmail.ru>, Vladislav Dorosh <irmologion@narod.ru> 3. Requester type (Member body/Liaison/Individual contribution): Individual contribution 4. Submission date: 01/30/2006 5. Requester's reference (if… (More)

- Oksana Y. Shtark, Anton S. Sulima, +7 authors Vladimir A. Zhukov
- Symbiosis
- 2016

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)