where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...

When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inve...

Are there some implementations of technology in the language classroom which lead to measurable advantages over others? Sturm and Golato (in press) found considerable variance on dictée tests within groups of students who practiced a list of accent-bearing target words by handwriting, typing using preprogrammed function keys, or typing using ALT+ numeric codes. These results contradict the resu...

The indefinite Sturm-Liouville operator A = (sgn x)(−d2/dx2 + q(x)) is studied. It is proved that similarity of A to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components Aess and Adisc of A corresponding to essential and discrete spectrums, respe...

We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t, λ of the mapping problem. The parameter λ is designed in such a way that for fixed t, it plays the r...

This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of nonselfadjoint Sturm-Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can nd the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the compound matrix method (using the Magnus e...

Astract: The estimation of the projective structure of a scene from image correspondences can be formulated as the minimization of the mean-squared distance between predicted and observed image points with respect to the projection matrices, the scene point positions, and their depths. Since these unknowns are not independent, constraints must be chosen to ensure that the optimization process i...

In this paper we analyze the convergence of a centered finite-difference approximation to the nonselfadjoint Sturm-Liouville eigenvalue problem 2[u\ = [a(x) u'Y b{x)u' + c(x)u = \u, 0 < x < 1, ( } «(0) = u(l) = 0 where S has smooth coefficients and a(x) ï a« > 0 on [0, 1]. We show that the rate of convergence is 0(Az2) as in the selfadjoint case for a scheme of the same accuracy. We also establ...

Here I show compatibility of two definition of generalized curvature bounds — the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott–Villani– Sturm. Introduction Let me denote by CD[m, κ] the class of metric-measure spaces which satisfy a weak curvature-dimension condition for dimension m and curvature κ (see preliminaries). B...

Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...