A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

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.

     

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

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Theory of chemical bonds in metalloenzymes XXII: a concerted bond-switching mechanism for the oxygen–oxygen bond formation coupled with one electron transfer for water oxidation in the oxygen-evolving complex of photosystem II

ABSTRACT

QM(UB3LYP)/MM(AMBER) calculations were performed for the locations of the transition structure (TS) of the oxygen–oxygen (O–O) bond formation in the S₄ state of the oxygen-evolving complex (OEC) of photosystem II (PSII). The natural orbital (NO) analysis of the broken-symmetry (BS) solutions was also performed to elucidate the nature of the chemical bonds at TS on the basis of several chemical indices defined by the occupation numbers of NO. The computational results revealed a concerted bond switching (CBS) mechanism for the oxygen–oxygen bond formation coupled with the one-electron transfer (OET) for water oxidation in OEC of PSII. The orbital interaction between the σ-HOMO of the Mn(IV)₄–O₍₅₎ bond and the π*-LUMO of the Mn(V)₁=O₍₆₎ bond plays an important role for the concerted O–O bond formation for water oxidation in the CaMn₄O₆ cluster of OEC of PSII. One electron transfer (OET) from the π-HOMO of the Mn(V)₁=O₍₆₎ bond to the σ*-LUMO of the Mn(IV)₄–O₍₅₎ bond occurs for the formation of electron transfer diradical, where the generated anion radical [Mn(IV)₄–O₍₅₎]^-? part is relaxed to the ?Mn(III)₄?…?O₍₅₎^- structure and the cation radical [O₍₆₎=Mn(V)₁]⁺ ? part is relaxed to the ⁺O₍₆₎–Mn(IV)₁? structure because of the charge-spin separation for the electron-and hole-doped Mn–oxo bonds. Therefore, the local spins are responsible for the one-electron reductions of Mn(IV)₄->Mn(III)₄ and Mn(V)₁->Mn(IV)₁. On the other hand, the O₍₅₎^- and O₍₆₎⁺ sites generated undergo the O–O bond formation in the CaMn₄O₆ cluster. The Ca(II) ion in the cubane- skeleton of the CaMn₄O₆ cluster assists the above orbital interactions by the lowering of the orbital energy levels of π*-LUMO of Mn(V)₁=O₍₆₎ and σ*-LUMO of Mn(IV)₄–O₍₅₎, indicating an important role of its Lewis acidity. Present CBS mechanism for the O–O bond formation coupled with one electron reductions of the high-valent Mn ions is different from the conventional radical coupling (RC) and acid-base (AB) mechanisms for water oxidation in artificial and native photosynthesis systems. The proton-coupled electron transfer (PC-OET) mechanism for the O–O bond formation is also touched in relation to the CBS-OET mechanism.     

Eye-safe compact scanning LIDAR technology

A 1.5-μm eye-safe, 3-D scanning, and compact Mie LIght Detection and Ranging (LIDAR) is presented. The transmitter of the LIDAR is based on a KTA optical parameter oscillator (OPO) resonator. For detecting return signals, an InGaAs APD is used. The all solid-state OPO laser transmitter has the feature of small volume and lightweight, which allows a 165-lb compact eye-safe scanning LIDAR to be constructed. A system simulation using our own model was conducted to direct the system development. A method to solve the problem with small active area APD detectors was developed and described. The preliminary field-test measurement results indicated that the LIDAR has the capability to detect aerosols and clouds in lower atmospheres up to three dimensions.     

<Emphasis Type="Italic">FCC/BCC</Emphasis> competition and enhancement of saturation magnetization in nanocrystalline Co-Ni-Fe films

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.     

1,3-dihalo-5,5-dimethylhydantoin/NaNO2 as an efficient heterogeneous system for the N-nitrosation of N,N-dialkylamines under mild conditions

A combination of 1,3-dihalo-5,5-dimethylhydantoin (X = Br, Cl) and sodium nitrite in the presence of wet SiO₂ was used as an effective nitrosating agent for the nitrosation of N,N-dialkyl amines to their corresponding nitroso derivatives under mild and heterogeneous conditions in good to excellent yields.