Superconductors with non-trivial band topology are emerging as one of the best avenues to study quantum anomalies and experimental realization Majorana Fermions. This article reports successful crystal growth superconducting SnAs, which can have topologically states, evidenced in DFT (Density Functional Theory) calculations, Z2 invariants, surface state. Here, we followed a two-step method grow...

We show that the unit ball of lp(Γ) in its weak topology is a continuous image of σ1(Γ) and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when Γ is uncountable. For a set Γ and a real number 1 < p < ∞, the Banach space lp(Γ) is a reflexive space, hence its unit ball is compact in the weak topology and in fact, it ...

It is known that for a sequence of independent and identically distributed random variables (Xn) the regular variation condition is equivalent to weak convergence of partial maximaMn = max{X1, . . . , Xn}, appropriately scaled. A functional version of this is known to be true as well, the limit process being an extremal process, and the convergence takes place in the space of càdlàg functions e...

Suppose F is a field with a nontrivial valuation v and valuation ring Ov, E is a finite field extension and w is a quasi-valuation on E extending v. We study the topology induced by w. We prove that the quasi-valuation ring determines the topology, independent of the choice of its quasi-valuation. Moreover, we prove the weak approximation theorem for quasi-valuations.

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...

Let T : K → H be a nonlinear mapping from a nonempty closed invex subset K of an infinite-dimensional Hilbert space H into H . Let f : K → R be proper, invex, and lower semicontinuous on K and let h : K → R be continuously Fréchet-differentiable on K with h′, the gradient of h, (η,α)-strongly monotone, and (η,β)-Lipschitz continuous on K . Suppose that there exist an x∗ ∈ K , and numbers a > 0,...

Assuming that the underlying probability space is non-atomic we prove that products of random matrices (linear cocycles) with simple Lyapunov spectrum form an L p-dense set (1 p < 1) in the space of all cocy-cles satisfying the integrability conditions of the multiplicative ergodic theorem. However, the linear cocycles with one-point spectrum are also L p-dense. Further, in any L 1-neighborhood...

GP studied preferences over menus (sets) of alternatives. This implicitly means that the decision maker chooses a menu and then selects an alternative from the menu. Consider a compact metric space Z of prizes. Let ∆ be the set of all Borel probability measures over Z. An element in ∆ represents an alternative for (implicit) choice. Assume that ∆ is endowed with the topology of weak convergence...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional on the space of Lipschitz maps into the domain of non-empty, convex and weak*-compact valued functions ordered by reverse inclusion, is continuous. For finite dime...