Related papers: Remling's Theorem on canonical systems

We present Bernstein lethargy theorem and examine the relationship between Bernstein lethargy theorem and reflexivity.

We show global existence and uniqueness of strong solutions for the Schrodinger-Poisson system in the repulsive Coulomb case with relativistic kinetic energy.

Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a…

In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651--672, 2013], we prove its…

We introduce Verblunsky-type coefficients of Toeplitz and Hankel matrices, which correspond to the discrete Dirac and canonical systems generated by Toeplitz and Hankel matrices, respectively. We prove one to one correspondences between…

The proof of the Jacobi property of the guiding-center Vlasov-Maxwell bracket underlying the Hamiltonian structure of the guiding-center Vlasov-Maxwell equations is presented.

We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…

The paper contains a new proof of the theorem by Krieger which establishes the canonicity of the future cover of a sofic shift. In addition the paper describes a method to produce new canonical covers from a given one, resulting in…

In the first part of the paper Beilinson's theorem on the bounded derived category of coherent sheaves on P^n is extended to weighted projective spaces in a rather explicit form. To this purpose the usual category of coherent sheaves is…

We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.

We obtain a correct generalization of Shokurov's non-vanishing theorem for log canonical pairs. It implies the base point free theorem for log canonical pairs. We also prove the rationality theorem for log canonical pairs. As a corollary,…

We show that Jacobi's bound for the order of a system of ordinary differential equations stands in the case of a diffiety defined by a quasi-regular system. We extend the result when there are less equations than variables and characterize…

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

In this paper, we introduce and develop the concept of \emph{ramification} in a given modulus. We study some properties in relation to this concept and it's connection to some important problems in mathematics, particularly the Goldbach…

In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi…

The Landsberg-Schaar relation is a classical identity between quadratic Gauss sums, normally used as a stepping stone to prove quadratic reciprocity. The Landsberg-Schaar relation itself is usually proved by carefully taking a limit in the…

We compute the characteristic cycle of a rank one sheaf on a smooth surface over a perfect field of positive characteristic. We construct a canonical lifting on the cotangent bundle of Kato's logarithmic characteristic cycle using…

The Hamiltonian treatment of constrained systems in $G\ddot{u}ler's$ formalism leads us to the total differential equations in many variables. These equations are integrable if the corresponding system of partial differential equations is a…

The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection between these two concepts and prove a formula which expresses…