Let I = [a, b] ⊂ R, let 1 < p ≤ q <∞, let u and v be positive functions with u ∈ Lp′ (I), v ∈ Lq(I) and let T : Lp(I)→ Lq(I) be the Hardy-type operator given by

Let I = [a, b] ⊂ R, let 1 < q ≤ p <∞, let u and v be positive functions with u ∈ Lp′(I), v ∈ Lq(I) and let T : Lp(I) → Lq(I) be the Hardy-type operator given by

BACKGROUND Tibial eminence fractures occur most commonly in skeletally immature children. Several techniques using physeal-sparing fracture fixation have been described, but their structural properties have not been evaluated. PURPOSE To determine the strength and resistance to displacement of physeal-sparing techniques used to fix tibial eminence fractures. STUDY DESIGN Controlled laborato...

Let Lq(s) be the product of Dirichlet L-functions modulo q. Then Lq(s) has at most one zero in the region Rs ≥ 1− 1 6.3970 logmax(q, q|Is|) .

BACKGROUND High-risk (hr)HPV testing plays an important role in primary cervical cancer screening. Subsequent hrHPV genotyping might contribute to better risk stratification. The majority of hrHPV tests do not include identification of individual hrHPV genotypes. OBJECTIVES The digene HPV Genotyping RH Test (strip-based) and LQ Test (xMAP-based) allow genotyping of GP5+/6+ amplimers, but thei...

Proof of Lemma 1: This retailer would see (y/L) of the total demand, hence the cumulative distribution function of its demand is H(s) = F(sL/y) where F() gives the cumulative distribution function for total market demand, x. Differentiating H(s) gives the required result. () parts) by on (integrati) () () () () () () () () () () () 0 , max(0 0 0 0 0 0 ds s F L y ds s f s y Lq L y ds s f s y Lq ...

One of the fundamental tools in radiation biology is a formalism describing time-dose relationships. For example, there is a need for reliable predictions of radiotherapeutic isoeffect doses when the temporal exposure pattern is changed. The most commonly used tool is now the linear-quadratic (LQ) formalism, which describes fractionation and dose-protraction effects through a particular functio...

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Major objective of the web-based learning is to design customized courseware taking into account of the input knowledge level and the specific objective of each individual learner. In order to improve the design of adaptive dynamic courseware to meet the requirement of individual learner we have already presented concept of Learner Quanta (LQ) & Learner Quanta Cloud (LQC) [9]. In this paper, co...

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space L(R). We obtain that if u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 1 with 3 < p ≤ ∞; or ∇u ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or the pressure P ∈ Lq(0, T ;L(R)) for 2 q + 3 p ≤ 2 with 3 2 < p ≤ ∞; or ∇P ...