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1.

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.

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The combinatorial integral approximation decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and computing a discrete-valued approximation of the relaxed control. Different algorithms exist for the second step to construct piecewise constant discrete-valued approximants that are defined on given decompositions of the domain. It is known that the resulting discrete controls can be constructed such that they converge to a relaxed control in the \(\hbox {weak}^*\) topology of \(L^\infty \) if the grid constant of this decomposition is driven to zero. We exploit this insight to formulate a general approximation result for optimization problems, which feature discrete and distributed optimization variables, and which are governed by a compact control-to-state operator. We analyze the topology induced by the grid refinements and prove convergence rates of the control vectors for two problem classes. We use a reconstruction problem from signal processing to demonstrate both the applicability of the method outside the scope of differential equations, the predominant case in the literature, and the effectiveness of the approach.

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The structure, chemical composition, and magnetic properties of electrochemically deposited nanocrystalline Co-Ni-Fe films were investigated using a number of techniques. A high saturation magnetic induction up to B s = 21 kG was attained. An enhancement of the saturation magnetization compared to the ideal anticipated one was revealed, which correlated with the nonlinear behavior of the structural phase composition and lattice parameters with the change of the composition. The text was submitted by the authors in English.  相似文献   
8.
Methods for phase stabilization of ammonium nitrate were sought for in order to considerably expand the application area of this oxidizing agent in various-purpose self-combustible formulations, including that in a new generation of gas-generating formulations for automobile air bags. New methods for stabilization of ammonium nitrate were studied and, in particular, a search was made for organic compounds that can stabilize ammonium nitrate even at their low content. The mechanism of phase state stabilization of ammonium nitrate by compounds of this kind was examined.  相似文献   
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Kinetic, sorption and selectivity properties of commercial adsorbents are improved by adding petroleum residues (tar asphaltene concentrates) 13% of whole mass. Obtained adsorbents can be used for selective extraction of nobel metals from multicomponent polymetallic solutions of heavy metals and fro sewages purification for removing arsenic.  相似文献   
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The lidar equation for the vibrational backscattering of neodymium laser radiation and its harmonics by hydrogen molecules is solved numerically. Inclined paths in the atmosphere are investigated with the aim of selecting the transmitter wavelength for detecting the lowest concentrations of hydrogen. Zh. Tekh. Fiz. 68, 20–22 (January 1998)  相似文献   
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