$L^{p}$ Estimates for Joint Quasimodes of Semiclassical Pseudodifferential Operators Whose Characteristic Sets Have $k$th Order Contact

In this paper we develop $L^{p}$ estimates for functions $u$, which are joint quasimodes of semiclassical pseudodifferential operators $p_{1}(x,hD)$ and $p_{2}(x,hD)$ whose characteristic sets meet with $k$th order contact, $k\geq{}1$. As part of the technical development we use Fourier integral operators to adapt a flat wavelet analysis to the curved level sets of $p_{1}(x,\xi )$.

A Note on Infinite Type Germs of a Real Hypersurface in

The purpose of this article is to show that there exists a smooth real hypersurface germ of D'Angelo infinite type in such that it does not admit any (singular) holomorphic curve that has infinite order contact with at . 2010 Mathematics Subject Classification. Primary 32T25; Secondary 32C25. Key words and phrases: Holomorphic vector field, automorphism group, real hypersurface, infinite type point.

Second-Order Contact Kinematics Between Three-Dimensional Rigid Bodies

In this discussion, we provide corrections to the second-order kinematic equations describing contact between three-dimensional rigid bodies, originally published in Sarkar et al. (1996) [“Velocity and Acceleration Analysis of Contact Between Three-Dimensional Rigid Bodies,” ASME J. Appl. Mech., 63(4), pp. 974–984].

Contigious hyperquadrics of coequipped hyperbands sHm

We consider hyperquadrics that are internally connected to coequipped hyperbands in the projective space. Specifically, a hyperquadric Qn1 tangent to a hyperplane at the point is called a contiguous hyper quadric of a hyperband if it has a second-order contact with the base surface of the hyperband. In a the third order differential neighborhood of the forming element of the hyperband, two two-parameter bundles of fields of adjoining hyperquadrics are internally invariantly joined, their equations are given in a dot frame. The set of hyperquadrics such that the plane and the plane of Cartan are conjugate with respect to hyperquadric Qn1 is considered. The condition is shown under which the normal of the 2nd kind and the Cartan plane are conjugate with respect to the hyperquadric Qn1 . In addition, the following theorem is proved: normalization of a coequipped regular hyperband has a semi-internal equipment if and only if its normals of the first and second kind are polarly conjugate with respect to the hyperquadric.

PION PHOTOPRODUCTION IN A GAUGE-INVARIANT CHIRAL UNITARY FRAMEWORK

We investigate pion photoproduction off the proton in a manifestly gauge-invariant chiral unitary extension of chiral perturbation theory. In a first step, we consider meson-baryon scattering taking into account all next-to-leading order contact interactions. The resulting low-energy constants are determined by a fit to s-wave pion-nucleon scattering and the low-energy data for the reaction π-p → ηn. Having determined the low-energy constants, we then analyse the data on the s-wave multipole amplitudes E0+ of pion and eta photoproduction. These are parameter-free predictions, as the two new low-energy constants are determined by the neutron and proton magnetic moments.