223 research outputs found
Geometric overconvergence of rational functions in unbounded domains
The basic aim of this paper is to study the phenomenon of overconvergence for rational functions converging geometrically on [0, + ∞)
The support of the logarithmic equilibrium measure on sets of revolution in
For surfaces of revolution in , we investigate the limit
distribution of minimum energy point masses on that interact according to
the logarithmic potential , where is the Euclidean distance
between points. We show that such limit distributions are supported only on the
``out-most'' portion of the surface (e.g., for a torus, only on that portion of
the surface with positive curvature). Our analysis proceeds by reducing the
problem to the complex plane where a non-singular potential kernel arises whose
level lines are ellipses
Structural risk assessment and aircraft fleet maintenance
In the present analysis, deterministic flaw growth analysis is used to project the failure distributions from inspection data. Inspection data is reported for each critical point in the aircraft. The data will indicate either a crack of a specific size or no crack. The crack length may be either less than, equal to, or greater than critical size for that location. Non-critical length cracks are projected to failure using the crack growth characteristics for that location to find the life when it will be at critical length. Greater-than-critical length cracks are projected back to determine the life at failure, that is, when it was at critical length. The same process is used as in the case of a non-critical crack except that the projection goes the other direction. These points, along with the critical length cracks are used to determine the failure distribution. To be able to use data from different aircraft to build a common failure distribution, a consistent life variable must be used. Aircraft life varies with the severity of the usage; therefore the number of flight hours for a particular aircraft must be modified by its usage factor to obtain a normalized life which can be compared with that from other aircraft
Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle
Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form where for and can be extended as a holomorphic and non-vanishing function to an annulus containing the unit circle. The formulas obtained are valid uniformly in the whole complex plane. As a consequence, we obtain some results about the distribution of zeros of these polynomials, the behavior of their leading and Verblunsky coefficients, as well as give an alternative proof of the Fisher-Hartwig conjecture about the asymptotics of Toeplitz determinants for such type of weights. The main technique is the steepest descent analysis of Deift and Zhou, based on the matrix Riemann-Hilbert characterization proposed by Fokas, Its and Kitaev
Out of plane analysis for composite structures
Simple two dimensional analysis techniques were developed to aid in the design of strong joints for integrally stiffened/bonded composite structures subjected to out of plane loads. It was found that most out of plane failures were due to induced stresses arising from rapid changes in load path direction or geometry, induced stresses due to changes in geometry caused by buckling, or direct stresses produced by fuel pressure or bearing loads. While the analysis techniques were developed to address a great variety of out of plane loading conditions, they were primarily derived to address the conditions described above. The methods were developed and verified using existing element test data. The methods were demonstrated using the data from a test failure of a high strain wingbox that was designed, built, and tested under a previous program. Subsequently, a set of design guidelines were assembled to assist in the design of safe, strong integral composite structures using the analysis techniques developed
Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
We apply the nonlinear steepest descent method to a class of 3x3
Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix
random model. The general case of two equilibrium measures supported on an
arbitrary number of intervals is considered. In this case, we solve the
Riemann-Hilbert problem for the outer parametrix in terms of sections of a
spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and
establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference
Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary
We investigate the zero temperature structure of a crystalline monolayer
constrained to lie on a two-dimensional Riemannian manifold with variable
Gaussian curvature and boundary. A full analytical treatment is presented for
the case of a paraboloid of revolution. Using the geometrical theory of
topological defects in a continuum elastic background we find that the presence
of a variable Gaussian curvature, combined with the additional constraint of a
boundary, gives rise to a rich variety of phenomena beyond that known for
spherical crystals. We also provide a numerical analysis of a system of
classical particles interacting via a Coulomb potential on the surface of a
paraboloid.Comment: 12 pages, 8 figure
Uniform approximation by incomplete polynomials
For any θ with 0<θ<1, it is known that, for the set of all incomplete polynomials of type θ, i.e, {p(x)=∑k=snakxk:s≥θ⋅n}, to have the Weierstrass property on [aθ,1], it is necessary that θ2≤aθ≤1. In this paper, we show that the above inequalities are essentially sufficient as well
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