The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for...

The noise in daily infection counts of an epidemic should be super-Poissonian due to intrinsic epidemiological and administrative clustering. Here, we use this clustering classify the official national SARS-CoV-2 check for that are unusually anti-clustered. We adopt a one-parameter model $\phi _i^{\prime}$ infections per cluster, dividing any count n i into $n_i/ ‘clusters’, ‘country’ . assume ...

The commutation principle of Ramírez et al. (SIAM J Optim 23:687–694, 2013) proved in the setting Euclidean Jordan algebras says that when sum a real valued function h and spectral $$\Phi $$ is minimized/maximized over set E, any local optimizer at which Fréchet differentiable operator commutes with derivative $$h^{\prime }(a)$$ . In this note, we describe some analogs above result by assuming ...

Let $G$ be a tamely ramified reductive $p$-adic‎ ‎group‎. ‎We study distinction of a class of irreducible admissible representations‎ ‎of $G$ by the group of fixed points $H$ of an involution‎ ‎of $G$‎. ‎The representations correspond to $G$-conjugacy classes of‎ ‎pairs $(T,phi)$‎, ‎where $T$ is a‎ ‎tamely ramified maximal torus of $G$ and $phi$ is a quasicharacter‎ ‎of $T$ whose restriction t...

For a given pseudo-Brewster angle phi(pB) of minimum reflectance |r(p)| of p-polarized light at a dielectric-conductor interface, the second-Brewster angle phi(2B) of minimum reflectance ratio |rho|=|r(p)|/|r(s)| of the p and s polarizations is determined for all possible values of the complex relative dielectric function epsilon that lead to the same phi(pB). The difference phi(2B)-phi(pB) is ...

The Honor Society of Phi Kappa Phi is the nation's oldest, largest, and most highly selective all-discipline honor society, with more than three hundred chapters on campuses across the country. The structure and continuity of the organization depend on volunteer faculty and student leaders at each college or university, both for selection and induction of honorees and for our increasing service...