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Half-linear dynamic equations on time scales: IVP and oscillatory properties.
The basic results of oscillation theory of the Sturm-Liouville linear differential equation are extended to the half-linear dynamic equation on an arbitrarytime scale. The questions concerning the existence and uniqueness o...
BA - Obecná matematika
- 2002 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Linear Hamiltonian dynamic systems on time scales: Sturmian property of principal solution
Basic results of the oscillation and transformation theories of linear Hamiltonian dynamic systems on time scales are presented. In particular, a Sturmian-type property for the principal solutions is established....
BA - Obecná matematika
- 2001 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Hardy inequality on time scales and its application to half-linear dynamic equations
A time scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equati...
BA - Obecná matematika
- 2005 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Comparison theorems for linear dynamic equations on time scales
We obtain several comparison theorems for second order linear dynamic equations on a time scale. These result extend comparison theorems for the continuous case and provide some new results in the discrete case, as well as other mor...
BA - Obecná matematika
- 2002 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
An eigenvalue problem for linear Hamiltonian dynamic systems
In this paper we consider eigenvalue problems on time scales involving linear Hamiltonian dynamic systems. We give conditions that ensure that the eigenvalues of the problem are isolated and bounded below. The presented results are ...
BA - Obecná matematika
- 2005 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Embedding of Linear Hamiltonian Systems on Small Time Scales
If a time scale $/T$ is in a sense small, then for any linear Hamiltonian dynamic system $x^{/Delta}=S(t)x$ on $/T$ its translation operator $e_{S(/cdot)(t,s)}$ is a restriction of a translation operator generated by a linear
BA - Obecná matematika
- 2006 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Set of experimental methods for scale-linearity verification in laser interferometers with nanometer resolution.
We present three methods of scale-linearity verification for high-resolution laser interferometers. Methods are scoped to Michelson type interferometer where detection technique with signals in quadrature supported by a single-frequ...
BH - Optika, masery a lasery
- 2002 •
- D
Rok uplatnění
D - Stať ve sborníku
Linear Hamiltonian systems on time scales: transformations
In this work we develop a transformation theory for linear Hamiltonian systems on an arbitrary time scale T. We prove that, under suitable assumptions, a linear Hamiltonian system is transformed into a system of the same fo...
BA - Obecná matematika
- 1999 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Derivation of Formulas for Variational Type of Conformal Projections
The contribution deals with the derivation of linear scale and formulas for projections for a considered area on a spherical surface (ellipsoid).We want to derive formulas for variational type of projections for a given area so that...
BA - Obecná matematika
- 2003 •
- D
Rok uplatnění
D - Stať ve sborníku
Integral comparison theorems for second order linear dynamic equations
Some integral comparison theorems for scalar second order linear differential equations are extended to dynamic equations on time scales. Several examples and applications to difference equations are given....
BA - Obecná matematika
- 2007 •
- D
Rok uplatnění
D - Stať ve sborníku
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