We examine the stochastic parabolic integral equation of convolution type U(t) +A ∫ t 0 k1(t− s)U(s) ds = ∫ t 0 k2(t− s)G(s) dWH(s), t ≥ 0, where U(t) takes values in Lq(O;R) with O a σ-finite measure space, and q ∈ [2,∞). The linear operator A maps D(A) ⊂ Lq(O;R) into Lq(O;R), is nonnegative and admits a bounded H∞-calculus on Lq(O;R). The kernels are powers of t, with k1(t) = 1 Γ(α) t α−1, k2...

The objective of this article is to introduce a novel data-driven iterative linear quadratic (LQ) control method for solving class nonlinear optimal tracking problems. Specifically, an algorithm proposed approximate the Q-factors arising from LQ stochastic This then coupled with LQ-methods determining local solutions problems in purely setting. Simulation results highlight potential field appli...

*Correspondence: [email protected] School of Mathematical and Statistics, Zaozhuang University, Zaozhuang, 277160, China Abstract Optimal asymptotic orders of the probabilistic linear (n,δ)-widths of λn,δ (Wr 2,α,β ,ν , Lq,α,β ) of the weighted Sobolev spaceW r 2,α,β equipped with a Gaussian measure ν are established, where Lq,α,β , 1≤ q≤∞, denotes the Lq space on [–1, 1] with respect to the me...

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...