Optimality of generalized Bernstein operators

AbstractWe show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems

A stability version of H\"older's inequality

We present a stability version of H\"older's inequality, incorporating an extra term that measures the deviation from equality. Applications are given.Comment: Journal of Mathematical Analysis and Applications, Volume 343, Issue 2, Pages 842-852. This version differs from the published one in that it contains a new reference, and a trivial improvement of Corollary 3.2. fo

A pharmacometrics model to define docetaxel target in early breast cancer

Aims: We aimed to study the relation between pharmacokinetics (PK) and pharmacodynamics (PD) of docetaxel in early breast cancer and recommend a target exposure. Methods: A PK/PD study was performed in 27 early breast cancer patients treated with doxorubicin and cyclophosphamide for 4 cycles followed by 4 cycles of docetaxel 75-100 mg/m2 infused every 21 days. Individual Bayesian estimates of docetaxel PK parameters were obtained using a nonparametric population PK model developed with data from patients with metastatic breast cancer who received dose-intensified docetaxel (300-350 mg/m2 ). Docetaxel area under the curve (AUC) and maximum concentration (Cmax) in each cycle and total cumulative AUC (AUCcum) were calculated and related to the incidence of adverse effects and tumour recurrence. Results: Docetaxel clearance showed no change over the 4 treatment cycles, but a gradual increase in the volume of distribution was observed. One third of the patients had at least 1 dose reduction of docetaxel due to toxicity. The mean AUC, AUCcum and Cmax in patients showing docetaxel-associated adverse events were significantly higher than in patients free of toxicity (P 4.5 mg*h/L and 3.5 mg/L, respectively, were risk factors for docetaxel toxicity, while an AUC <4.5 mg*h/L was associated with tumour recurrence. Conclusion: We report for the first time a relation between docetaxel exposure and toxicity and recommend specific targets of drug exposure with implications for the clinical management of early breast cancer patients

Boundedness and unboundedness results for some maximal operators on functions of bounded variation

We characterize the space $BV(I)$ of functions of bounded variation on an arbitrary interval $I\subset \mathbb{R}$, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator $M_R$ from $BV(I)$ into the Sobolev space $W^{1,1}(I)$. By restriction, the corresponding characterization holds for $W^{1,1}(I)$. We also show that if $U$ is open in $\mathbb{R}^d, d >1$, then boundedness from $BV(U)$ into $W^{1,1}(U)$ fails for the local directional maximal operator $M_T^{v}$, the local strong maximal operator $M_T^S$, and the iterated local directional maximal operator $M_T^{d}\circ ...\circ M_T^{1}$. Nevertheless, if $U$ satisfies a cone condition, then $M_T^S:BV(U)\to L^1(U)$ boundedly, and the same happens with $M_T^{v}$, $M_T^{d} \circ ...\circ M_T^{1}$, and $M_R$.Comment: 15 page

Effects of dexmedetomidine on subthalamic local field potentials in parkinson's disease

Background: Dexmedetomidine is frequently used for sedation during deep brain stimulator implantation in patients with Parkinson's disease, but its effect on subthalamic nucleus activity is not well known. The aim of this study was to quantify the effect of increasing doses of dexmedetomidine in this population. Methods: Controlled clinical trial assessing changes in subthalamic activity with increasing doses of dexmedetomidine (from 0.2 to 0.6 μg kg-1 h-1) in a non-operating theatre setting. We recorded local field potentials in 12 patients with Parkinson's disease with bilateral deep brain stimulators (24 nuclei) and compared basal activity in the nuclei of each patient and activity recorded with different doses. Plasma levels of dexmedetomidine were obtained and correlated with the dose administered. Results: With dexmedetomidine infusion, patients became clinically sedated, and at higher doses (0.5-0.6 μg kg-1 h-1) a significant decrease in the characteristic Parkinsonian subthalamic activity was observed (P<0.05 in beta activity). All subjects awoke to external stimulus over a median of 1 (range: 0-9) min, showing full restoration of subthalamic activity. Dexmedetomidine dose administered and plasma levels showed a positive correlation (repeated measures correlation coefficient=0.504; P<0.001). Conclusions: Patients needing some degree of sedation throughout subthalamic deep brain stimulator implantation for Parkinson's disease can probably receive dexmedetomidine up to 0.6 μg kg-1 h-1 without significant alteration of their characteristic subthalamic activity. If patients achieve a 'sedated' state, subthalamic activity decreases, but they can be easily awakened with a non-pharmacological external stimulus and recover baseline subthalamic activity patterns in less than 10 min

Dimension dependency of the weak type (1, 1) bounds for maximal functions associated to finite radial measures

We show that the smallest constants appearing in the weak type (1, 1) inequalities satisfied by the centred Hardy-Littlewood maximal function associated to some finite radial measures, such as the standard gaussian measure, grow exponentially fast with the dimension

Differentiation of integrals in Rω

We show that the Lebesgue differentiation theorem does not hold in R with the "product" Lebesgue measure. © 2001 Akadémiai Kiadó

A stability version of Hölder's inequality for 0 < p < 1

We use a refinement of Holder's inequality for 1 < p < to obtain the corresponding refinement when r (0,1). This in turn allows us to sharpen the reverse triangle inequality on the nonnegative functions in Lr, for r (0, 1). © 2007 Victoria University. All rights reserved

A product of doubling measures on the real line

A product of doubling measures on the real line can be defined in such a way that another doubling measure on the line is obtained. It follows that doubling measures on the line form a semiring

On high dimensional maximal operators

In this note we describe some recent advances in the area of maximal function inequalities. We also study the behaviour of the centered Hardy-Littlewood maximal operator associated to certain families of doubling, radial decreasing measures, and acting on radial functions. In fact, we precisely determine when the weak type (1, 1) bounds are uniform in the dimension