We find that the fundamental quadratic form of classical string propagation in 2 + 1 dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the 2 + 1 black hole anti de Sitter spacetime), all three equations must be included to cover the generic str...

It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...

where ω = vk and k± = k x̂ ± kΓ ŷ. Slepian also noted that if v < c, then cos(kΓy) = cosh(kΓ′y) where Γ′ = iΓ = √ 1− v2/c2, and the waveform (1) again propagates with speed v. The vector potential (1), together with scalar potential V = 0, satisfy the conditions for the Coulomb, Gibbs, Lorenz and velocity gauges. See, for example, [2]. For completeness, the electric field is E = iωA ≡ E+ + E− wh...

Baryon stopping at the SPS and RHIC energies is calculated by introducing a new baryon junction mechanism into HIJING. The exchange of a baryon junction, according to Regge phenomenology, leads to a cosh[(y− yCM)/2] rapidity dependence and an 1/ 4 √ s energy dependence of the inclusive baryon cross section. This baryon junction dynamics also leads naturally to enhanced pT broadening in pA and A...

References 1. Cosh C. Science-reporting smell test of the week [Internet]. Toronto (ON): Maclean’s; May 4, 2010 [cited 2010 May 21]. Available from: http://www2.macleans.ca/tag/natalie-mota/. 2. Kessler RC, Berglund P, Chiu WT, et al. The US National Comorbidity Survey Replication (NCS-R): design and fi eld procedures. Int J Methods Psychiatr Res. 2004;13:69–92. 3. Mota NP, Burnett M, Sareen J....

The Fourier transform truncated on $$[-c,c]$$ has for a long time been analyzed as acting $$L^2(-1/b,1/b)$$ into $$L^2(-1,1)$$ and its right-singular vectors are the prolate spheroidal wave functions. This paper considers operator defined larger space $$L^2(\cosh (b|\cdot |))$$ which it remains injective. main purpose is (1) to provide nonasymptotic upper lower bounds singular values with simil...

The propagation properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) in atmospheric turbulence are investigated based on the extended Huygens–Fresnel diffraction integral and Rytov method. analytical formula for average intensity vHChGB propagating turbulent atmosphere is derived detail. influence strength distribution under change parameters conditions illustrated numerically discussed. ...

Abstract We prove two conjectural identities of Z.-W. Sun concerning Apéry-like series. One the series is alternating, whereas other one not. Our main strategy to convert and alternating log-sine-cosine log-sinh-cosh integrals, respectively. Then we express all these integrals using single-valued Bloch–Wigner–Ramakrishnan–Wojtkowiak–Zagier polylogarithms. The conjectures then follow from a few ...