The classic equation for decomposing the wavefront aberrations of axis-symmetrical optical systems has form, $$ W({h}_0,\rho,\phi )=\sum_{j=0}^{\propto } \sum_{p=0}^{\propto \sum_{m=0}^{\propto {C}_{\left(2j+m\right)\left(2p+m\right)m}({h}_0{)}^{2j+m}(\rho {)}^{2p+m}(\mathrm{cos}\phi {)}^m where j , p and m are non-negative integers, ρ ϕ polar coordinates pupil, h 0 is object height. However, o...

We study the Wasserstein metric $$W_p$$ , a notion of distance between two probability distributions, from perspective Fourier Analysis and discuss applications. In particular, we bound Earth Mover Distance $$W_1$$ distribution quadratic residues in finite field $${\mathbb {F}}_p$$ uniform by $$\lesssim p^{-1/2}$$ (the Polya–Vinogradov inequality implies p^{-1/2} \log {p}$$ ). also show that fo...

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...

We give a new definition of the derived category of constructible Q`-sheaves on a scheme, which is as simple as the geometric intuition behind them. Moreover, we define a refined fundamental group of schemes, which is large enough to see all lisse Q`-sheaves, even on non-normal schemes. To accomplish these tasks, we define and study the pro-étale topology, which is a Grothendieck topology on sc...

Background—Na/H exchange inhibition with HOE642 (cariporide) improves postischemic recovery of cardiac function, but the mechanisms of action remain speculative. Because Na/H exchange is activated on reperfusion, it was hypothesized that its inhibition delays realkalinization and decreases intracellular Na and, via Na/Ca exchange, Ca overload. Attenuated Ca overload and prolonged acidosis are k...

We prove a multiplicity result for $$\begin{aligned} {\left\{ \begin{array}{ll} -\varepsilon ^{2}\Delta _g u+\omega u+q^{2}\phi u=|u|^{p-2}u\\ -\Delta \phi +a^{2}\Delta _g^{2} + m^2 =4\pi u^{2} \end{array}\right. } \text { in }M, \end{aligned}$$where (M, g) is smooth and compact 3-dimensional Riemannian manifold without boundary, \(p\in (4,6)\), \(a,m,q\ne 0\), \(\varepsilon >0\) small enough. ...

We present improved distributed algorithms for variants of the triangle finding problem in model. show that detection, counting, and enumeration can be solved $\tilde{O}(n^{1/3})$?> rounds using expander decompositions . This matches lower bound $\tilde{\Omega }(n^{1/3})$?> by Izumi Le Gall [PODC’17] Pandurangan, Robinson, Scquizzato [SPAA’18], which holds even {CONG...

Five bacteriophages infecting only Saccharopolyspora erythraea (formerly Streptomyces erythreus) among 43 Streptomyces spp. tested were classified into two groups by phage-host relationships, restriction enzyme mapping, cohesive-end determinations, and Southern hybridizations. phi SE6, the most frequently isolated phage, produced clear plaques on all hosts tested, while phi SE45, phi SE57, phi ...