We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

A broadband continuously tunable SESAM all-fiber laser based on optical parametric generation (OPG) for coherent anti-stokes Raman scattering (CARS) imaging applications is presented in this article. This structure built all-polarization maintaining fibers yielding high environmental stability. The OPG PM photonic crystal fiber as gain pumped by a wavelength-tunable (1025 to 1055 nm) and repeti...

We introduce compactness theorems for generalized colorings and derive several particular compactness theorems from them. It is proved that the theorems and many of their consequences are equivalent in ZF set theory to BPI, the Prime Ideal Theorem for Boolean algebras. keywords: generalized graph colorings, compactness, prime ideal theorem MSC: 05C15; 03E25 .

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

Compactness in the space L(0, T ;B), B being a separable Banach space, has been deeply investigated by J.P. Aubin (1963), J.L. Lions (1961,1969), J. Simon (1987), and, more recently, by J.M. Rakotoson and R. Temam (2001), who have provided various criteria for relative compactness, which turn out to be crucial tools in the existence proof of solutions to many abstract time dependent problems re...

We consider the Fujita equation ut = ∆u+ u p on RN with N ≥ 3. We prove the existence of global, unbounded solutions for pS < p < pJL, where pS := (N + 2)/(N − 2) and pJL :=  (N − 2)2 − 4N + 8 √ N − 1 (N − 2)(N − 10) if N > 10,

A plausible formation scenario for the Galactic globular clusters 47 Tuc and Omega Cen is that they are tidally stripped remnants of dwarf galaxies, in which case likely to have retained a fraction their dark matter cores. In this study, we used ultra-wide band receiver on Parkes telescope (Murriyang) place upper limits annihilation rate exotic Light Dark Matter particles (X) via XX/$e^+e^-$ ch...