‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

We have derived the analytic solutions of dissipative relativistic spin hydrodynamics with Gubser expansion. Following standard strategy deriving in a flow, we take Weyl rescaling and obtain energy-momentum angular momentum conversation equations $dS_{3}\times\mathbb{R}$ space-time. then derive density, potential other thermodynamic space-time transform them back into Minkowski $\mathbb{R}^{3,1...

We study the near-flat space limit for strings on AdS5 × M5, where the internal manifold M5 is equipped with a generic metric with U(1)3 isometry. In the bosonic sector, the limiting sigma model is similar to the one found for AdS5 × S5, as the global symmetries are reduced in the most general case. When M5 is a SasakiEinstein space like T 1,1, Y p,q and Lp,q,r, whose dual CFT’s have N = 1 supe...

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in R. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α-order fractional derivatives of the velocity for some α > 0 in the space variables in L, which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the Lequicontinu...

A bstract Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin coordinate and partial-wave expansion. We explain origin space as smearing kernel in Poincare AdS, while latter three is global AdS. In we find a formula that unifies massless massive limit, which can be transformed Furthermore, also manage transform connecting all existed frameworks...

Let u be a solution to the Navier-Stokes equations in the unit disk with no-slip boundary conditions and viscosity ν > 0, and let u be a smooth solution to the Euler equations. We say that the vanishing viscosity limit holds on [0, T ] if u converges to u in L∞([0, T ];L). We show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the visco...

For a sequence of nondegenerate i.i.d. bounded random variables {Yn, n ≥ 1} defined on a probability space (Ω,F ,P) and a constant b > 1, it is shown for Wn = (b − 1) ∑n i=1 b Yi/b n+1 that S (FY1) ⊆ {c ∈ R : P ({ω ∈ Ω : c is a limit point of Wn(ω)}) = 1} = S (FV ) ⊆ [l, L] and that for almost every ω ∈ Ω, the set of limit points of Wn(ω) coincides with the set S (FV ) where S (FY1) and S (FV )...