We derive semiclassical asymptotics for the orthogonal polynomials P n (z) on the line with respect to the exponential weight exp(−NV (z)), where V (z) is a double-well quartic polynomial, in the limit when n, N → ∞. We assume that ε ≤ (n/N) ≤ λ cr − ε for some ε > 0, where λ cr is the critical value which separates orthogonal polynomials with two cuts from the ones with one cut. Simultaneously...

In this article we study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to a pseudo-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.

We derive Painlevé–type expressions for the distribution of the m largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles in the edge scaling limit. The work of Johnstone and Soshnikov (see [7], [10]) implies the immediate relevance of our formulas for the m largest eigenvalue of the appropriate Wishart distribution.

Starting from a strong Stieltjes distribution φ, general sequences of orthogonal Laurent polynomials are introduced and some of their most relevant algebraic properties are studied. From this perspective, the connection between certain quadrature formulas associated with the distribution φ and two-point Padé approximants to the Stieltjes transform of φ is revisited. Finally, illustrative numeri...

It is shown that regularity of orthogonal wavelet matrices, i.e. vanishing of discrete moments of some of their rows, corresponds to maximizing the discrete moments of one of the rows. This leads to an algorithm for calculation of such wavelets by nding a vector which simultaneosly vanishes certain indeenite quadratic forms.

An orthogonal double cover (ODC) of the complete graph Kn by a graph G is a collection G of n spanning subgraphs of Kn, all isomorphic toG, such that any two members ofG share exactly one edge and every edge ofKn is contained in exactly two members of G. In the 1980s Hering posed the problem to decide the existence of an ODC for the case that G is an almost-Hamiltonian cycle, i.e. a cycle of le...

in this study, flow characteristics through symmetric stenosis artery are investigated. the shape of eccentricity for stenotic flows is limited by circular-cross sections and plaques are usually assumed as to be oriented concentrically. thegoverningequationsaretheusualnavier-stokesequationsandare numericallysolved by using finite volumemethod in arbitrary orthogonal curvilinear coordinates. in ad...

Motivated by the recent surge of activity on the subject, we present a brief non-technical survey of numerous classical and new results in discrepancy theory related to Roth’s orthogonal function method. Communicated by Yukio Ohkubo The goal of this paper is to survey the use of Roth’s orthogonal function method in the theory of irregularities of distribution, which, in a broad sense, means app...

Direct displacement based design (DDBD) is a conceptual framework that directly design a structure to achieve an expected performance level under specified seismic intensity. In this study, two important issues relevant to torsional response of mass eccentric 8-story RC building designed with DDBD approach are investigated. These issues are including the effects of unbalanced mass distribution ...