Let S0 (p) denote the sphere spectrum localized at an odd prime p. Then we have the first beta element β1 ∈ π2p2−2p−2(S (p)), whose cofiber we denote by W . We also consider a generalized Smith-Toda spectrum Vr characterized by BP∗(Vr) = BP∗/(p, vr 1). In this note, we show that an element of π∗(Vr ∧W ) gives rise to a beta element of homotopy groups of spheres. As an application, we show the e...

Abstract. We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave equation. We instead rely upon a class of Keel-Smith-Sogge estimates for the perturbed wave equation. Using this, a notable simplification is made ...

We study the critical thresholds for the compressible pressureless Euler equations with pairwise attractive or repulsive interaction forces and non-local alignment forces in velocity in one dimension. We provide a complete description for the critical threshold to the system without interaction forces leading to a sharp dichotomy condition between global in time existence or finite-time blow-up...

Explicit receiver structures for the optimum detection of M-ary orthogonal signals in impulsive noise environments typical of ELF are determined. The resulting optimum structures, while shown to bear some resemblance to that which would have been obtained in the presence of Gaussian noise alone, exhibit an interesting nonlinear behavior. The difficulties in the actual implementation of this rec...

We investigate the variance of the optimal alignment score of two independent iid binary, with parameter 1/2, sequences of length n. The scoring function is such that one letter has a somewhat larger score than the other letter. In this setting, we prove that the variance is of order n, and this confirms Waterman’s conjecture in this case.

Since B (s) and d(s) are coprime, the proof is complete. From the lemma, the blocking zeros are seen to coincide with the roots, counting multiplicities, of q(s) = 0. For the sake of comparison, we remark that Rosenbrock [3] defines the zeros of G(s) to be the roots of cl(s)cz(s). . c,(s)=O. Desoer and Schulman [ I ] and Wolovich [2], without specifying multiplicities, identify the roots of c,...