Electronic structure and the hydrogen-shift isomerization of hydrogen nitryl HNO2

Summary Electronic structure of hydrogen nitryl HNO₂, a yet not identified entity, and the path of its possible isomerization totrans-HONO have been investigated byab initio SCF and MRD-CI computations using the 6-31G** basis set. HNO₂ isC _2v -symmetric and its ground state (¹ A ₁) is less stable thantrans-HONO by 66 kJ/mol (with the SCF vibrational zero-point energy correction). The lowest two excited singlet states (¹ A ₂ and¹ B ₁) are nearly degenerate, their vertical excitation energies being predicted to be 4.8 eV. The isomerization path is traced by the CASSCF procedure and the activation barrier height is evaluated by the CI treatment. HNO₂ in its ground state isomerizes totrans-HONO by maintaining the planar (C _s-symmetric) structure. The activation energy is calculated to be 171 kJ/mol, which is clearly lower than the calculated H-N bond energy (253 kJ/mol). The transition state seems to be more adequately described as an interacting system of proton and the nitrite anion rather than as a pair of two fragment radicals.     

On two expressions of the MLE for a special case of the extended growth curve models

An algebraic proof is given on the equivalence between two solutions of MLEs for a special case of the extended growth curve models called the Banken model. One solution given by Verbyla and Venables is an iterative solution in the general case but reduces to a non-iterative one in the case of the Banken model. The other solution given by von Rosen is a closed-form solution specifically targeted at the Banken model. The proof has turned out to be quite challenging yet intriguing as it touches on many aspects of intricate matrix theory involving projection matrices.     

On the necessary and sufficient condition for the extended Wedderburn–Guttman theorem

Let A be a u by v matrix, and let M and N be u by p and v by q matrices, where p may not be equal to q or rank(M^′AN)<min(p,q). Recently, Galantai [A. Galantai, A note on the generalized rank reduction, Acta Math. Hungarica 116 (2007) 239–246] presented what he claimed to be the necessary and sufficient condition for rank(A-AN(M^′AN)^-M^′A)=rank(A)-rank(AN(M^′AN)^-M^′A) to hold. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn–Guttman theorem. In this paper, we show that some of Galantai’s assertions are incorrect.     

Synthesis of novel phenylazomethine dendrimers having a cyclam core and their zinc complex

[structure: see text] Novel phenylazomethine dendrimers having a cyclam core were synthesized by the convergent method. The dendrimers showed selective coordination with zinc chloride on the cyclam ring and with tin chloride on the imine groups. The metal cyclam exhibits a metal-assembling function to provide a multinuclear hetero metal complex.     

Generalized canonical correlation analysis with missing values

Generalized canonical correlation analysis is a versatile technique that allows the joint analysis of several sets of data matrices. The generalized canonical correlation analysis solution can be obtained through an eigenequation and distributional assumptions are not required. When dealing with multiple set data, the situation frequently occurs that some values are missing. In this paper, two new methods for dealing with missing values in generalized canonical correlation analysis are introduced. The first approach, which does not require iterations, is a generalization of the Test Equating method available for principal component analysis. In the second approach, missing values are imputed in such a way that the generalized canonical correlation analysis objective function does not increase in subsequent steps. Convergence is achieved when the value of the objective function remains constant. By means of a simulation study, we assess the performance of the new methods. We compare the results with those of two available methods; the missing-data passive method, introduced in Gifi’s homogeneity analysis framework, and the GENCOM algorithm developed by Green and Carroll. An application using world bank data is used to illustrate the proposed methods.     

Perfectly conducting channel and universality crossover in disordered graphene nanoribbons

The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e., for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through intervalley scattering display ordinary localization behavior. The two regimes belong to different universality classes: unitary for long-range impurities and orthogonal for short-range impurities.     

Electrochemical reduction of carbon dioxide catalyzed by cofacial dinuclear metalloporphyrin

Cofacial dinuclear metalloporphyrins exhibited a catalytic activity for the electrochemical reduction of carbon dioxide. The cofacial dinuclear porphyrin was automatically generated by mixing a cationic cobalt porphyrin (CoTMPyP) and an anionic metalloporphyrin (MTPPS) in solution. The redox system of this complex was examined by electrochemical methods. According to the cyclic voltammogram, the catalytic active species was generated at −1.8V vs. Ag/Ag⁺, which was considered to be a monovalent cobalt porphyrin, Co(I)TMPyP. The catalytic activity of the dinuclear complex was two times greater than that of the mononuclear one because the anionic porphyrin acted as an electron mediator.     

On V-orthogonal projectors associated with a semi-norm

For any n ×  p matrix X and n ×  n nonnegative definite matrix V, the matrix X(X′V X)⁺ X′V is called a V-orthogonal projector with respect to the semi-norm , where (·)⁺ denotes the Moore-Penrose inverse of a matrix. Various new properties of the V-orthogonal projector were derived under the condition that rank(V X) =  rank(X), including its rank, complement, equivalent expressions, conditions for additive decomposability, equivalence conditions between two (V-)orthogonal projectors, etc.