We demonstrate spontaneous spatial order in stripe and super-lattice solitons a Rashba spin-orbit (SO) coupled spin-1 uniform quasi-two-dimensional (quasi-2D) ferromagnetic Bose-Einstein condensate (BEC). For weak SO coupling, the are of (−1,0,+1) or (0,+1,+2) type with intrinsic vorticity, where numbers parentheses denote angular momentum spin components Fz=+1,0,−1, respectively. intermediate ...

We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f : {0, 1} → {0, 1} that is mildly hard on average, i.e. every circuit of size 2 fails to compute f on at least a 1/poly(l) fraction of inputs, we can build a PRG : {0, 1} n) → {0, 1} computable in ATIME (O(1), log n) = alternating time O(lo...

PURPOSE To investigate the morphology of corneal caps in femtosecond laser small incision lenticule extraction (SMILE) and its relation to the refractive outcomes. METHODS A prospective study of fifty-four corneal caps created with VisuMax femtosecond laser were examined using an Fourier-domain optical coherence tomography at 1 day, 1 week, 1 month and 6 months after SMILE. The cap thickness ...

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary Σ. We prove that (M, g) is isometric to a spacelike slice (R \ Bm 2 (0), (1 + m 2|x| ) 4δij) of a Schwarzschild spacetime under the mere assumption that Σ has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that Σ has constant positive mean curv...

We consider order and type properties of Marcinkiewicz and Lorentz function spaces.We show that if 0 < p < 1, a p-normable quasi-Banach space is natural (i.e. embeds into a q-convex quasi-Banach lattice for some q > 0) if and only if it is finitely representable in the space Lp,∞. We also show in particular that the weak Lorentz space L1,∞ do not have type 1, while a non-normable Lorentz space ...

The infinite (in both directions) sequence of the distributions μ of the stochastic integrals ∫∞− 0 c−N (k) t− dL (k) t for integers k is investigated. Here c > 1 and (N (k) t , L (k) t ), t ≥ 0, is a bivariate compound Poisson process with Lévy measure concentrated on three points (1, 0), (0, 1), (1, c−k). The amounts of the normalized Lévy measure at these points are denoted by p, q, r. For k...

A new method to construct aggregation functions is introduced. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction method is based on linear interpolation on segments connecting the diagonal (resp. opposite diagonal) of the unit square and the points (0, 1) and (1, 0) (resp. (0, 0) and (1, 1)). Speci...