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.

     

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.     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Time-Dependent Resonant Tunneling in a Double-Barrier Diode Structure

The elastic moduli of bilayer graphene nanomeshes, i.e., nanomeshes of bilayer graphene, where layers at the edges of “closed” holes are coupled to each other by a continuous network of sp²-hybridized atoms, have been calculated by ab initio methods. Structures with different configurations of holes in layers with AA, AB, and 30° stackings have been studied. It has been shown that the ultimate tensile strength of the nanomeshes under consideration is higher than that of graphene nanostructures and is comparable with the ultimate tensile strength of bilayer graphene and single-layer carbon nanotubes. A possible application of such strong nanomeshes as nanocontainers for hydrogen storage and other compressed gases has been also discussed.

     

Optical Properties of Single-Crystal Germanium in the THz Range

Optics and Spectroscopy - The transmission of intrinsic, antimony-doped, and gallium-doped Ge single crystals in the THz spectral range have been experimentally investigated. It is shown that the...     

Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.