This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by prescribed data. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler’s equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrödinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow...

The aim of this paper is to derive spectral and condition number estimates of the single-layer operator for low-frequency multiple scattering problems. This work extends to dense media the analysis initiated in [7]. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary eleme...

Distributed sensing of structural states is essential to vibration control, health monitoring and shape control of precision structronic systems. Paraboloidal shells of revolution are widely used in aerospace, telecommunication, etc. structures. However, distributed sensing of paraboloidal shell structures is rarely investigated over the years. Micro-sensing characteristics, sensor segmentation...

Thin-walled structures like crash boxes may be used as energy absorption members in automotive chassis. There have been many studies addressing the behaviors of energy absorption members on frontal crash. These researches have attempted to predict the energy absorption and maximum impact load in shell structures. The energy absorption and maximum impact load depend on many parameters including ...

We consider stability properties of discrete-time bilinear lters. Simple su cient conditions are given for bounded-input bounded-output stability (with not necessarily zero initial conditions), lp stability, and three other important types of stability. In particular, conditions are given under which asymptotically periodic inputs produce asymptotically periodic outputs with the same period. Re...

Radial blow-up, including inhomogeneous versions, of boundary faces of a manifold (always with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be particular cases of generalized boundary blow-up in which a new manifold and blow-down map are constructed from, and conversely determine, combinatorial dat...

This paper investigates the buckling of finite isotropic rectangular plates with circular cutout under uniaxial and biaxial loading. The complex potential method is used to calculate the pre-buckling stress distribution around the cutout in the plate with finite dimensions. To satisfy the in-plane boundary conditions, the generalized complex-potential functions are introduced and a new method b...

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These t...

in this paper, nonlinear dynamic behaviours of carbon nanotube conveying fluidwith slip boundary conditions is studied using variation iteration method. the developed solutions are used to investigate the effects of various parameters on the nonlinear vibration of the nanotube. from the result, it is observed that increase in the slip parameter leads to decrease in the frequency of vibration an...