About the Defectivity of Certain Segre–Veronese Varieties

We study the regularity of the higher secant varieties of ℙ1 × ℙn, embedded with divisors of type (d, 2) and (d, 3). We produce, for the highest defective cases, a “determinantal” equation of the secant variety. As a corollary, we prove that the Veronese triple embedding of ℙn is not Grassmann defective.

Elastic-Plastic Wrinkling of Sandwich Panels With Layered Cores

Elastic-plastic wrinkling of compression loaded sandwich panels made with layered cores was studied analytically and experimentally. A core with a stiff layer near the sandwich skins can improve various properties, including wrinkling and impact strengths, with only a minor weight penalty. The 2D plane stress and plane strain bifurcation problems were solved analytically, save for a determinantal equation which was solved numerically. Experiments were performed on aluminum skin/foam core sandwich panels with different combinations of stiff and soft core materials. Good correlation between experiments and theory was obtained.

Multivariate Linear Rational Expectations Models

This paper considers the solution of multivariate linear rational expectations models. It is described how all possible classes of solutions (namely, the unique stable solution, multiple stable solutions, and the case where no stable solution exists) of such models can be characterized using the quadratic determinantal equation (QDE) method of Binder and Pesaran (1995, in M.H. Pesaran & M. Wickens [eds.], Handbook of Applied Econometrics: Macroeconomics, pp. 139–187. Oxford: Basil Blackwell). To this end, some further theoretical results regarding the QDE method expanding on previous work are presented. In addition, numerical techniques are discussed allowing reasonably fast determination of the dimension of the solution set of the model under consideration using the QDE method. The paper also proposes a new, fully recursive solution method for models involving lagged dependent variables and current and future expectations. This new method is entirely straightforward to implement, fast, and applicable also to high-dimensional problems possibly involving coefficient matrices with a high degree of singularity.

The dynamic analysis of mechanical systems and structures with large parameter variations

A general approach to the analysis of mechanical systems and structures where large parameter variations occur is outlined. Aircraft and missile problems where there are acknowledged changes in the system model coefficients are identified. Performance variations associated with operational conditions are investigated. Simple solutions to the determinantal equation are proposed.

Nonreciprocal Propagation of Guided Waves in Sliding Laminae of Isotropic Dielectrics

The well-known relation of Fresnel and Lorentz for the effect of material motion on the propagation of light is extended to guided waves propagating in a system of dielectric layers differing in refractive index as well as in the magnitude of their velocities. The analysis is based only on the existence of a transverse dispersion (determinantal equation) which is invariant with respect to sliding motion at least to first order in β. A one-to-one correspondence ("transmodification") of wave vectors in the moving and in the quiescent state is used to demonstrate that nonuniform motion can lead to (convectively) unstable modes. The theory is applied to a moving parallel-plate waveguide and to the model of a glow discharge enclosed in a circular waveguide.