This study was designed to identify independent predictors of all osteoporosis-related fractures (ORFs) among healthy Saudi postmenopausal women. We prospectively followed a cohort of 707 healthy postmenopausal women (mean age, 61.3±7.2 years) for 5.2±1.3 years. Data were collected on demographic characteristics, medical history, personal and family history of fractures, lifestyle factors, dail...

The law of multiplicative error is presented for independent observations and correlated observations represented by the q-product, respectively. We obtain the standard log-normal distribution in the former case and the log-q-normal distribution in the latter case. Queirós’ q-log normal distribution is also reconsidered in the framework of the law of error. These results are presented with math...

We prove that PSL2(Z[ 1 p ]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL2(Z[ 1 p ]) and PSL2(Z[ 1 q ]) are not quasi-isometric unless p = q, and, independent of p, the quasi-isometry group of PSL2(Z[ 1 p ]) is PSL2(Q). In addition, we characterize PSL2(Z[ 1 p ]) uniquely among all finitely generated groups by ...

Let hom(H,G) denote the number of homomorphisms from a graph H to a graph G. Sidorenko’s conjecture asserts that for any bipartite graph H, and a graph G we have hom(H,G) > v(G) ( hom(K2, G) v(G)2 )e(H) , where v(H), v(G) and e(H), e(G) denote the number of vertices and edges of the graph H and G, respectively. In this paper we prove Sidorenko’s conjecture for certain special graphs G: for the ...

The Bethe-Salpeter wave function X( q v + P v, q •) for two spin-l/2 quarks bound by the exchange of a scalar meson is examined in the ladder model. We seek the behavior <if X as the squared momentum, (q + P)2, on one leg becomes infinite while the squared momentum, q 2, on the other leg remains fixed. This behavior is investigated by making a Wick rotation, expanding x in partial-wave amplitud...

Pinsker’s widely used inequality upper-bounds the total variation distance ‖P−Q‖1 in terms of the Kullback-Leibler divergence D(P‖Q). Although in general a bound in the reverse direction is impossible, in many applications the quantity of interest is actually D∗(v,Q) — defined, for an arbitrary fixed Q, as the infimum of D(P‖Q) over all distributions P that are at least vfar away from Q in tota...

We consider a linear algebraic system A(p)x = b(q), where the elements of the matrix and the right-hand side vector are linear functions of uncertain parameters varying within given intervals. The linear tolerance problem for the so-called parametric tolerable solution set Σtol(A(p), b(q), [p], [q]) = {x ∈ Rn | (∀p ∈ [p])(∃q ∈ [q])(A(p)x = b(q))} requires an inner estimation of this solution se...