O polynomických řešeních homogenní lineární diferenciální rovnice druhého řádu
On a new set of orthogonal polynomials
An orthogonal system of polynomials, arising from a second-order ordinary differential equation, is presented.
On algebraic solutions of algebraic Pfaff equations
We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
On complexity and motion planning for co-rank one sub-riemannian metrics
In this paper, we study the motion planning problem for generic sub-riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [10, 11]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic case, we study some non-generic generalizations in the analytic case.
On complexity and motion planning for co-rank one sub-Riemannian metrics
In this paper, we study the motion planning problem for generic sub-Riemannian metrics of co-rank one. We give explicit expressions for the metric complexity (in the sense of Jean [CITE]), in terms of the elementary invariants of the problem. We construct asymptotic optimal syntheses. It turns out that among the results we show, the most complicated case is the 3-dimensional. Besides the generic C∞ case, we study some non-generic generalizations in the analytic case.
On first integrals for polynomial differential equations on the line
We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.
On formal theory of differential equations. II.
On holomorphic foliations without algebraic solutions.
On -quasi-derivatives for solutions of perturbed general quasi-differential equations
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of th order with complex coefficients , provided that all th quasi-derivatives of solutions of and all solutions of its normal adjoint are in and under suitable conditions on the function .
On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary
On Some Classes Of Linear Equations
On some classes of linear equations.
On some classes of linear equations, II.
On Some Classes Of Linear Equations III
On some classes of linear equations. IV.
On Sumudu transform and system of differential equations.
On the applications of a new technique to solve linear differential equations, with and without source.
On the approximation of real continuous functions by series of solutions of a single system of partial differential equations
We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function can be approximated with arbitrary accuracy by an infinite sum of analytic functions , each solving the same system of universal partial differential equations, namely (σ = 1,..., s).
On the closed-form solution of the improved labor augmented Solow-Swan model.
On the existence of solutions of certain nonlinear equations occurring in the transformation theory of a linear second order differential equation with complex valued coefficients