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‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

in this paper, we investigate the canonical property of solutions of a system of differentialequations having a singularity and turning point of even order. first, by a replacement, we transform thesystem to the sturm-liouville equation with a turning point. using the asymptotic estimates for a specialfundamental system of solutions of sturm-liouville equation, we study the infinite product rep...

Abstract The method of blowing up points indeterminacy certain systems two ordinary differential equations is applied to obtain information about the singularity structure solutions corresponding non-linear equations. We first deal with so-called Painlevé example, which passes test, but have more complicated singularities. Resolving base in equivalent system we can explain singularities origina...

A special instance of the algebraic Riccati equation XCX−XE−AX+B = 0 where the n × n matrix coefficients A,B,C,E are rank structured matrices is considered. Relying on the structural properties of Cauchy-like matrices, an algorithm is designed for performing the customary Newton iteration in O(n2) arithmetic operations (ops). The same technique is used to reduce the cost of the algorithm propos...

Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equal footing without constraint, the state of ‘equipartition’ may bear no specific structure. Fluid turbulence is a typical example—while turbulent mixing seems to increase entropy, a variety of sustained vortical struct...

The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum. In the Hamiltonian formalism, topological invariants restrict the orbits to submanifolds of the phase space. While the coadjoint orbits have a natural symplectic structure, the global geometry of the degenerate (constrained) Poisson manifold can be very complex. Som...

The objective of this paper is to study the theoretical analysis of linear differential-algebraic equations (DAEs) of higher order as well as the regularity and singularity of matrix polynomials. Some invariants and condensed forms under appropriate equivalent transformations are established for systems of linear higher-order DAEs with constant and variable coefficients. Inductively, based on c...

In this article, we consider the Poisson equation on a polygonal domain with the domain singularity raised from the changed boundary conditions with the inner angle ω > π 2 . The solution of the Poisson equation with such singularity has a singular decomposition: regular part plus singular part. The singular part is a linear combination of one or two singular functions. The coefficients of the ...

An open question contributed by Yu. Orlov to a recently published volume ”Unsolved Problems in Mathematical Systems and Control Theory”, V.D. Blondel & A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal control-affine problems. These noncoercive problems in general admit ’cheap (generalized) controls’ as minimizers; it has been questioned whether and under what ...