Block Sensitivity of Minterm-Transitive Functions

Boolean functions with symmetry properties are interesting from a complexity theory perspective; extensive research has shown that these functions, if nonconstant, must have high `complexity' according to various measures. In recent work of this type, Sun gave bounds on the block sensitivity of nonconstant Boolean functions invariant under a transitive permutation group. Sun showed that all such functions satisfy bs(f) = Omega(N^{1/3}), and that there exists such a function for which bs(f) = O(N^{3/7}ln N). His example function belongs to a subclass of transitively invariant functions called the minterm-transitive functions (defined in earlier work by Chakraborty). We extend these results in two ways. First, we show that nonconstant minterm-transitive functions satisfy bs(f) = Omega(N^{3/7}). Thus Sun's example function has nearly minimal block sensitivity for this subclass. Second, we give an improved example: a minterm-transitive function for which bs(f) = O(N^{3/7}ln^{1/7}N).Comment: 10 page

F-mode sensitivity kernels for flows

We compute f-mode sensitivity kernels for flows. Using a two-dimensional model, the scattered wavefield is calculated in the first Born approximation. We test the correctness of the kernels by comparing an exact solution (constant flow), a solution linearized in the flow, and the total integral of the kernel. In practice, the linear approximation is acceptable for flows as large as about 400 m/s.Comment: 4 pages, 3 figures. Proceedings of SOHO18/GONG 2006/HELAS I. Beyond the Spherical Sun: A new era of helio- and asteroseismology. Sheffield, England. August, 200

Sun shield

A shading device which is capable of compactly storing a flexible shade on a biased, window shade type spring roller is disclosed. It is controlled to deliver the shade selectively to either its operative shading or compact storage orientation

Pseudoscalar Conversion and X-rays from the Sun

We investigate the detection of a pseudoscalar $\phi$ that couples electromagnetically via an interaction ${1\over4}g \phi F {\tilde F}$. In particular, we focus on the conversion of pseudoscalars produced in the sun's interior in the presence of the sun's external magnetic dipole field and sunspot-related magnetic fields. We find that the sunspot approach is superior. Measurements by the SXT on the Yohkoh satellite can measure the coupling constant down to $g=0.5$--$1 \times 10^{-10}\,\rm GeV^{-1}$, provided the pseudoscalar mass $m < 7{\times} 10^{-6}\,$eV, which makes it competitive with other astrophysical approaches.Comment: 15 pages, RevTex file. Figures available upon request to [email protected]. (please include full mailing address in request). Submitted to Physics Letters

Measures of Intermediate Entropies for Skew Product Diffeomorphisms

In this paper we study a skew product map $F$ with a measure $\mu$ of positive entropy. We show that if on the fibers the map are $C^{1+\alpha}$ diffeomorphisms with nonzero Lyapunov exponents, then $F$ has ergodic measures of intermediate entropies. To construct these measures we find a set on which the return map is a skew product with horseshoes along fibers. We can control the average return time and show the maximum entropy of these measures can be arbitrarily close to $h_\mu(F)$.Comment: 12 pages, a few mistakes corrected, some sections seriously rewritte