– in this paper we consider some (α ,β ) -metrics such as generalized kropina, matsumoto and f (α β )2α = + metrics, and obtain necessary and sufficient conditions for them to be einstein metrics when βis a constant killing form. then we prove with this assumption that the mentioned einstein metrics must beriemannian or ricci flat.

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...

In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and tracebased distances derived from standard Lp and Kullback-Leibler distances. Two desirable continuity properties for such distances are identified. We then establish a number of results that...

The technique of random projection is one of dimension reduction, where high dimensional vectors in RD are projected down to a smaller subspace in Rk. Certain forms of distances or distance kernels such as Euclidean distances, inner products [10], and lp distances [12] between high dimensional vectors are approximately preserved in this smaller dimensional subspace. Word vectors which are repre...

q-ary lattices are obtained from linear q-ary codes via the so-called Construction A. We study these lattices in the lp norm in R and the associated q-ary codes in the induced p-Lee metric in Zq . This induced metric extends to 1 ≤ p < ∞ the well-known Lee metric when p = 1. A previous result on lattice decoding in the Lee metric is generalized for p > 1 and the existence of perfect codes in su...

Let Ω ∈ L(logL+)2(Sn−1 × Sm−1) (n, m 2) satisfy some cancellation conditions. We prove the Lp boundedness (1 < p < ∞ ) of the singular integral T f (x1,x2) = p. v. ∫ ∫ Rn×Rm Ω(y1,y ′ 2)h(ρ1(y1),ρ2(y2)) ρα 1 (y1)ρ β 2 (y2) f (x1 − y1,x2 − y2)dy1 dy2, where ρ1 , ρ2 are some metrics which are homogeneous with respect to certain non-isotropic dilations. We also study the above singular integral alo...