Lamb waves propagation in elastic plane layers with a joint strip

The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.     

Microcavity confinement based on an anomalous zero group-velocity waveguide mode

We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately pi/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.     

Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air

A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal.     

On the rate of convergence of sequential quadratic programming with nondifferentiable exact penalty function in the presence of constraint degeneracy

We analyze the convergence of a sequential quadratic programming (SQP) method for nonlinear programming for the case in which the Jacobian of the active constraints is rank deficient at the solution and/or strict complementarity does not hold for some or any feasible Lagrange multipliers. We use a nondifferentiable exact penalty function, and we prove that the sequence generated by an SQP using a line search is locally R-linearly convergent if the matrix of the quadratic program is positive definite and constant over iterations, provided that the Mangasarian-Fromovitz constraint qualification and some second-order sufficiency conditions hold. Received: April 28, 1998 / Accepted: June 28, 2001?Published online April 12, 2002     

Vanishing cycles of pencils of hypersurfaces

We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of certain variation maps.     

A remark on sets having the Steinhaus property

A point set satisfies the Steinhaus property if no matter how it is placed on a plane, it covers exactly one integer lattice point. Whether or not such a set exists, is an open problem. Beck has proved [1] that any bounded set satisfying the Steinhaus property is not Lebesgue measurable. We show that any such set (bounded or not) must have empty interior. As a corollary, we deduce that closed sets do not have the Steinhaus property, fact noted by Sierpinski [3] under the additional assumption of boundedness.     

Classical and statistical analysis of40Ar(300 MeV)+197Au deep inelastic interaction

We examine the way in which local field effects in the neutron refractive index affect the values of coherent scattering lengths determined by various kinds of neutron optical measurements. We find that under typical experimental conditions these effects are negligible for interferometry measurements but that they are significant for gravity refractometry measurements, producing changes in the effective scattering length of as much as two or three standard deviations in some cases. Refined values of the scattering lengths are obtained for the thirteen elements for which data are presently available. The special role of local field effects in neutron transmission is also discussed.     

Irreducible representations of infinite-dimensional Lie algebras

Some results concerning the operatorially irreducible, topologically irreducible, operatorially and topologically irreducible representations of a class of infinite-dimensional Lie algebras by bounded operators in a complex Banach space are obtained.