5,6,7,7a,9,10,14b,14c-Octahydro-4-[2,3-O-(1-methylethylidene )-beta-D- ribofuranosyl]cyclopenta-[4,5]pyrimido[5',4':3,4]pyrrolo[2,1- a]isoquinoline-1,3(2H,4H)-dione, C25H31N3O6, M(r) = 469.54, tetragonal, P4(3)2(1)2, a = 12.577 (2), b = 12.577 (2), c = 29.893 (4) A, V = 4729 (1) A3, Z = 8, Dx = 1.319 g cm-3, lambda (Cu K alpha) = 1.5418 A, mu = 7.9 cm-1, F(000) = 2000, T = 298 K, final R = 0.03...

We prove the existence of a set of two-scale magnetic Wannier orbitals, wmn(r), in the infinite plane. The quantum numbers of these states are the positions (m,n) of their centers which form a von Neumann lattice. Function w00(r) localized at the origin has a nearly Gaussian shape of exp(−r2/4l2)/ √ 2π for r ∼ √ 2πl, where l is the magnetic length. This region makes a dominating contribution to...

We study the bifurcation of local critical periods in the differential system { ẋ = −y +Bxn−1y, ẏ = x+Dx + Fxn−2y2, where B,D,F ∈ R and n > 3 is a fixed natural number. Here by “local” we mean in a neighbourhood of the center at the origin. For n even we show that at most two local critical periods bifurcate from a weak center of finite order or from the linear isochrone, and at most one local ...

Certain non-linear relations between the generators of the (qdeformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and q-deformation. ⋆ Invited talk at International Conference on Complex and Hypercomplex Analysis, Mexico-city, Mexico (1994); to be published in Proceedings † On leave of absence from the Institute for Theoretical and Experimental Physic...

For a complete connected Riemannian manifold M let V∈C2(M) be such that μ(dx)=e−V(x)vol(dx) is probability measure on M. Taking μ as reference measure, we derive inequalities for measures linking relative entropy, Fisher information, Stein discrepancy and Wasserstein distance. These strengthen in particular the famous log-Sobolev transportation-cost inequality extend so-called Entropy/Stein-dis...

In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M(Q) = i ( d dx Im −Q −Q − d dx Im ) , where Q represents a symmetric m × m matrix (i.e., Q(x) = Q(x) a.e.) with entries in L loc (R), is J -self-adjoint, where J is the antilinear conjugation defined by J = σ1C, σ1 = ( 0 Im Im 0 ) and C(a1, . . . , am, b1, . . . , bm) = (a1, . . . ,...

In this paper, we prove a Stolarsky type inequality for pseudo-integrals. More precisely, we show that: ∫ sup [0,1] f(x 1 a+b )dx ≥ ( ∫ sup [0,1] f(x 1 a )dx ) ̄ ( ∫ sup [0,1] f(x 1 b )dx ) , where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly decreasing function ( strictly increasing function ) and μ is the sup-measure the same as Theorem 2.4. Also ̄ is represented by an increasing...

We determine the best constant K and extremals of the Opial-type inequality ∫ b a |yy ′| dx ≤ K(b − a) ∫ b a |y ′|2 dx where y is required to satisfy the boundary condition ∫ b a y dx = 0. The techniques employed differ from either those used recently by Denzler to solve this problem or originally to prove the classical inequality; but they also yield a new proof of that inequality.

In this article we give different sufficient conditions for inequality (∫ b a f(x)dx )β ≥ ∫ b a f(x)dx to hold.

The atomic geometries and transition levels of point defects and substitutional dopants in few-layer and bulk black phosphorus are calculated. The vacancy is found to reconstruct in monolayer P to leave a single dangling bond, giving a negative U defect with a +/- transition level at 0.24 eV above the valence band edge. The V(-) state forms an unusual 4-fold coordinated site. In few-layer and b...