On Neyman–Pearson minimax detection of Poisson process intensity

The problem of the minimax testing of the Poisson process intensity \({\mathbf{s}}\) is considered. For a given intensity \({\mathbf{p}}\) and a set \(\mathcal{Q}\), the minimax testing of the simple hypothesis \(H_{0}: {\mathbf{s}} = {\mathbf{p}}\) against the composite alternative \(H_{1}: {\mathbf{s}} = {\mathbf{q}},\,{\mathbf{q}} \in \mathcal{Q}\) is investigated. The case, when the 1-st kind error probability \(\alpha \) is fixed and we are interested in the minimal possible 2-nd kind error probability \(\beta ({\mathbf{p}},\mathcal{Q})\), is considered. What is the maximal set \(\mathcal{Q}\), which can be replaced by an intensity \({\mathbf{q}} \in \mathcal{Q}\) without any loss of testing performance? In the asymptotic case (\(T\rightarrow \infty \)) that maximal set \(\mathcal{Q}\) is described.

     

Experimental investigation for stability and surface properties of TiO2 and Al2O3 water-based nanofluids

Journal of Thermal Analysis and Calorimetry - Nanofluids have gained recent attention because of their potential applications in diverse engineering fields like enhancing thermal transport,...     

Kinetics and Mechanism of the Reaction of Triphenylphosphine with Methyl Vinyl Ketone

Russian Journal of General Chemistry - Kinetics of the reaction of triphenylphosphine with methyl vinyl ketone has been studied using the stopped flow technique. The experimental data have...     

Unique Solvability of a Linear Parabolic Problem with Nonlocal Time Data

Siberian Mathematical Journal - We consider a problem for a first-order differential equation in a Hilbert space. We replace the initial data with some condition that...     

Synthesis and Anticancer Activity of Certain Selenophene Derivatives

Russian Journal of Organic Chemistry - Selenopheno[2,3-d]pyrimidine- and selenopheno[2,3-d][1,2,3]triazine-containing compounds were synthesized starting from...     

Optimized spacer layer thickness for plasmonic-induced enhancement of photocurrent in a-Si:H

Journal of Nanoparticle Research - Plasmonic interfaces consisting of silver nanoparticles of different sizes (50–100&;nbsp;nm) have been processed by the self-assembled dewetting...     

Formation and pharmacological activity of silicon—chitosan-containing glycerohydrogels obtained by biomimetic mineralization

The biomimetic sol—gel synthesis of silicon—chitosan-containing glycerohydrogels was carried out using silicon tetraglycerolate as a precursor. It was found that chitosan accelerates gel formation in weakly acidic media. In more acidic media, the kinetics of the process changes according to the curve with a maximum, which can be attributed to different mechanisms of silanol condensation before and after the isoelectric point. The investigated silicon—chitosan-containing glycerohydrogels exhibit antibacterial, anti-inflammatory, and wound healing activity. The synthesized hybrid glycerohydrogels are promising materials for biomedical applications.     

Investigation of Plasma Oscillations in Glasslike Dielectrics by Means of Total External Reflection of X Rays

Technical Physics - Glasslike dielectrics are investigated by methods of plasmon dispersion and asymmetry of the number of localized electrons in the region in which total external reflection of...