where HJ = HJ(x, y, t) is a polynomial of x and y of which the coefficients are rational functions of t holomorphic in BJ := P−ΞJ , ΞJ 3 ∞ being the fixed singular points of the J-th Painlevé equation (Ref. 2). Here the equivalece means that the second order nonlinear differential equation in x obtained from the J-th Painlevé system by elimination of y is just the J-th Painlevé equation. The J-...

In this article we consider Wigner matrices (XN)N∈N with variance profiles which are of the form XN(i,j)=σ(i∕N,j∕N)ai,j∕ N where σ is a symmetric real positive function [0,1]2, either continuous or piecewise constant and ai,j independent, centered one above diagonal. We prove large deviation principle for largest eigenvalue those under condition that they have sharp sub-Gaussian tails some addi...

We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of...

Behavior and event-related potentials (ERP) were recorded while participants made truthful and deceptive responses about previously memorized words under three instructional conditions: consistent truthful, consistent deceptive, and random deceptive. To determine if practice affected the deception-related activity we reported previously [R. Johnson, Jr., J. Barnhardt, J. Zhu, The deceptive resp...

Structural health monitoring of cracked structures is one of beloved subject of researchers recently. Consider of crack behavior in the water and energy pipeline is important because of environmental problems. In this paper consider of crack parameters in the underwater pipe subjected to mechanical transient load is investigated. For this purpose, three- dimensional parametric model of cracked ...