Synthesis of pyrazine acetals by the biased reaction of symmetric 2,5-bis(chloromethyl) or 2,3,5,6-tetrakis(chloromethyl) substituents on pyrazine ring with sodium alkoxides

2,5-Bis(chloromethyl)pyrazine reacted with sodium alkoxide to give unexpected 2-dialkoxymethyl-5-methylpyrazine along with normal substitution product, 2,5-bis(alkoxymethyl)pyrazine. The reaction of 2,3,5,6-tetrakis(chloromethyl)pyrazine with sodium alkoxide afforded similar results to yield 2,6-bis(dialkoxymethyl)-3,5-dimethylpyrazine along with other alkoxymethylpyrazines. The ratio of products depended on the solvent and alkoxide used. A general discussion of the mechanism of such a pyrazine acetal synthesis in the basic conditions is given.     

Electrocatalytic Nitrite Reduction to Nitrogen Oxide by a Synthetic Analogue of the Active Site of Cu‐Containing Nitrite Reductase Incorporated in Nafion Film

The electrocatalytic reduction of nitrite to NO by [CuMe₂bpa(H₂O)(ClO₄)]⁺ ( 1 ), which is a model for the active site of copper‐containing nitrite reductase, incorporated in Nafion film was investigated. The Cu complex in the Nafion matrix exhibits an intense band at 267 nm and a broad band around 680 nm, assigned to d–d and ligand field transitions, respectively. The 77‐K EPR spectrum of 1 in the Nafion matrix reveals the typical axial signals (g_//=2.28, g =2.08, A_//=13.3 mT) of a tetragonal Cu²⁺ chromophore. The redox potential, which is related to the Cu⁺/Cu²⁺ couple, was ?146 mV (ΔE=72 mV) at pH 5.5. The redox reaction of 1 in Nafion was not dependent on pH and was a diffusion‐controlled process. The electronic structure and redox properties of 1 in the negatively charged polymer matrix were almost the same as those in aqueous solution. In the presence of nitrite, an increase in the cathodic current was observed in the cyclic voltammogram of 1 in the Nafion matrix. The current increase was dependent on the nitrite concentration and pH in solution. Upon reaching ?400 mV, a linear generation of NO was observed for the 1 /Nafion film coated electrode. The relationship between the rate of NO generation and the nitrite concentration in solution was analyzed with the Michaelis–Menten equation, where V_max=45.1 nM s^?1 and K_m=15.8 mM at pH 5.5. The Cu complex serves the function of both the catalyst and electron transport in the Nafion matrix. The sensitivity of the electrode was estimated to be 3.23 μA mM^?1 in the range of 0.1–0.4 mM nitrite.     

The second main theorem of hypersurfaces in the projective space

We deal with a holomorphic map from the complex plane ${\mathbb{C}}$ to the n-dimensional complex projective space ${\mathbb{P}^{n}(\mathbb{C})}$ and prove the Nevanlinna Second Main Theorem for some families of non-linear hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ . This Second Main Theorem implies the defect relation. If the degree of the hypersurfaces are sufficiently large, the defect of the map is smaller than one. This means that holomorphic maps which omit the irreducible hypersurface of large degree is algebraically degenerate. To prove the Second Main Theorem, we use a meromorphic partial projective connection which is totally geodesic with respect to these hypersurfaces. A meromorphic partial projective connection is a family of locally defined meromorphic connections such which work as an entirely defined meromorphic connection under the Wronskian operator. By resolving the singularity and pulling back a meromorphic partial projective connection, we also prove the Second Main Theorem for singular hypersurfaces in ${\mathbb{P}^{n}(\mathbb{C})}$ , and prove the Second Main Theorem for smooth hypersurfaces in ${\mathbb{P}^{2}(\mathbb{C})}$ which are not normal crossing.     

Error analysis for matrix eigenvalue algorithm based on the discrete hungry Toda equation

Based on the integrable discrete hungry Toda (dhToda) equation, the authors designed an algorithm for computing eigenvalues of a class of totally nonnegative matrices (Ann Mat Pura Appl, doi:10.1007/s10231-011-0231-0). This is named the dhToda algorithm, and can be regarded as an extension of the well-known qd algorithm. The shifted dhToda algorithm has been also designed by introducing the origin shift in order to accelerate the convergence. In this paper, we first propose the differential form of the shifted dhToda algorithm, by referring to that of the qds (dqds) algorithm. The number of subtractions is then reduced and the effect of cancellation in floating point arithmetic is minimized. Next, from the viewpoint of mixed error analysis, we investigate numerical stability of the proposed algorithm in floating point arithmetic. Based on this result, we give a relative perturbation bound for eigenvalues computed by the new algorithm. Thus it is verified that the eigenvalues computed by the proposed algorithm have high relative accuracy. Numerical examples agree with our error analysis for the algorithm.     

Continuous-time image reconstruction for binary tomography

Binary tomography is the process of reconstructing a binary image from a finite number of projections. We present a novel method for solving binary tomographic inverse problems using a continuous-time image reconstruction (CIR) system described by nonlinear differential equations based on the minimization of a double Kullback–Leibler divergence. We prove theoretically that the divergence measure monotonically decreases in time. Moreover, we demonstrate numerically that the quality of the reconstructed images of the nonlinear CIR system is better than those from an iterative reconstruction method.     

Equality conditions for lower bounds on the smallest singular value of a bidiagonal matrix

Several lower bounds have been proposed for the smallest singular value of a square matrix, such as Johnson’s bound, Brauer-type bound, Li’s bound and Ostrowski-type bound. In this paper, we focus on a bidiagonal matrix and investigate the equality conditions for these bounds. We show that the former three bounds give strict lower bounds if all the bidiagonal elements are non-zero. For the Ostrowski-type bound, we present an easily verifiable necessary and sufficient condition for the equality to hold.     

Extended Hypervalent 5c–6e Interactions: Linear Alignment of Five C─Z- - -O- - -Z─C (Z = S,Se) Atoms in Anthraquinone and Anthracene Systems

Abstract

Structures of 1,8-(ArZ)₂C₁₄H₆O₂ and 9-(MeO)-1,8-(ArZ)₂C₁₄H₇ (Z = S, Se) are determined by X-ray crystallographic analysis. Five C─Z- - -O- - -Z─C atoms of the compounds align linearly, which are analyzed by the extended hypervalent 5c–6e model, based on QC calculations. CT of the 5c–6e occurs as the σ^*(C─Z) ← n _p (O)→ σ*(Z─C) direction.