Related papers: Differential spaces in integrable Hamiltonian syst…
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
The hyperinvariant subspace problem is solved in the setting of Hilbert and right Hamilton space, motivated by my earlier works in the invariant subspace problem.
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.
This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.
We present an example of an integrable Hamiltonian system with scalar potential in the three-dimensional Euclidean space whose integrals of motion are quadratic polynomials in the momenta, yet its Hamilton-Jacobi / Schrodinger equation…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…
In the paper we construct an hierarchy of integrable Hamiltonian systems which describe the variation of n-wave envelopes in nonlinear dielectric medium. The exact solutions for some special Hamiltonians are given in terms of elliptic…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…
We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function.
This paper is an overview of our works which are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous velocity independent forces. The two types of…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
The Neumann system on the 2-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian point of view on separation of variables. It is shown that, from this standpoint, its separation coordinates and its integrals of…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…