*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...

Indirect methods recombine the elements of triangular meshes to produce quadrilaterals. The resulting quadrilaterals are usually randomly oriented, which is not desirable. However, by aligning the vertices of the initial triangular mesh, precisely oriented quads can be produced. Levy’s algorithm is a non-linear optimization procedure that can align points according to a locally defined metric. ...

In this article we investigate the metric signature as a non-differentiable degree of freedom. The specific model is a vacuum 7D Universe on the principal bundle with an SU(2) structural group. An analytical solution is found which to a 4D observer appears as a flat Universe with a fluctuating metric signature, and frozen extra dimensions with an SU(2) instanton gauge field. A piece of this sol...

Let (X, d), (Y, ρ) be metric spaces and f : X → Y an injective mapping. We put ‖f‖Lip = sup{ρ(f(x), f(y))/d(x, y); x, y ∈ X, x 6= y}, and dist(f) = ‖f‖Lip.‖f ‖Lip (the distortion of the mapping f). We investigate the minimum dimension N such that every n-point metric space can be embedded into the space lN ∞ with a prescribed distortion D. We obtain that this is possible for N ≥ C(logn)2n3/D, w...

Abstract. Let M be a closed linear subspace of a normed linear space X. For a given f ∈ X denote by PM f the set of best approximations to f from M . The operator PM is termed the metric projection onto M . In this paper we are interested in the stability of the metric projection PM relative to perturbations of the subspace M . We mainly consider the case where X = Lp, p ∈ [1,∞]. We consider a ...

0

Background: Lumbar puncture (LP) is a worth procedure in diagnosis of oncological diseases and intrathecal administration of antineoplastic drugs. The effort should be to minimize pain of LP in children with cancers. This clinical trial was done to compare success rates in performing LP and reducing anxiety and pain of LP in sitting and lateral decubitus positions in 1 to 5-year-old children. ...

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, th...