Now showing items 1-10 of 55
On the number of zeros of iterated operators on analytic Legendre expansions
Let L=(1−z2)D2−2zD, D=d/dz and f(z)=∑n=0∞cnpn(z), with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=L(Lk−1), k≥2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk).
Riesz bases and positive operators on Hilbert space
It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product onH in which it is an orthonormal ...
Radial oscillations of encapsulated microbubbles in viscoelastic liquids
(American Institute of Physics, 2002-10)
The small-amplitude radial oscillations of a gas microbubble encapsulated by a viscoelastic solid shell and surrounded by a slightly compressible viscoelastic liquid are studied theoretically. The Kelvin-Voigt and 4-constant ...
Sound-ultrasound interaction in bubbly fluids: Theory and possible applications
(American Institute of Physics, 2001-12)
The interaction between sound and ultrasound waves in a weakly compressible viscous liquid with gas bubbles is considered. Using the method of multiple scales one- and two-dimensional nonlinear interaction equations are ...
Scalings for fragments produced from drop breakup in shear flow with inertia
(American Institute of Physics, 2001-08)
When a drop is sheared in a matrix liquid, the largest daughter drops are produced by elongative end pinching. The daughter drop size is found to scale with the critical drop size that would occur under the same flow ...
Dynamics of self-driven microcantilevers
(American Institute of Physics, 2002-04-01)
The small amplitude thermal vibrations of the microcantilever of an atomic force microscope can be enhanced via a delayed feedback system. This is verified experimentally for a triangular cantilever, and modeled theoretically ...
The effect of insoluble surfactant at dilute concentration on drop breakup under shear with inertia
(American Institute of Physics, 2004-01)
Direct numerical simulations are conducted with a volume-of-fluid continuous surface stress algorithm. The linear equation of state is used to characterize the effects of an insoluble surfactant at low concentration on a ...
Effect of inertia on drop breakup under shear
(American Institute of Physics, 2001-01)
A spherical drop, placed in a second liquid of the same density and viscosity, is subjected to shear between parallel walls. The subsequent flow is investigated numerically with a volume-of-fluid continuous-surface-force ...
Growth of functions in cercles de remplissage
(Cambridge University Press, 2002-02)
Suppose that f is meromorphic in the plane, and that there is a sequence z(n) --> infinity and a sequence of positive numbers epsilon(n) --> 0, such that epsilon(n)\z(n)f(#)(z(n))/log\z(n)\ --> infinity. It is shown that ...
Convergence theorems for intermediate problems. II
(Cambridge University Press, 2002)
Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundary-value problems and atomic problems. ...