Erratum to: The Software System LingvoDoc and the Possibilities It Offers for Documentation and Analysis of Ob-Ugric Languages

Doklady Mathematics - An Erratum to this paper has been published: https://doi.org/10.1134/S1064562422340038     

Binuclear complexes of copper(II) with 1′-phthalazinylhydrazones of substituted salicylic aldehydes: Physico-chemical study and quantum-chemical simulation

Binuclear complexes of copper(II) with 1′-phthalazinylhydrazones of substituted salicylic aldehydes have been prepared and studied. Antiferromagnetic exchange interaction between copper(II) ions has been revealed in all the complexes. Taking advantage of quantum-chemical simulation, we have investigated the influence of the complexes structural isomerism on the character of the exchange interaction between the paramagnetic centers. X-ray absorbance spectroscopy afforded the structural parameters of coordination spheres of copper(II) ions; it has been demonstrated that dimerization occurred via the nitrogen atoms of phthalazine fragments.     

Copper(II) and nickel(II) complexes with bis(azomethine)—a condensation product of 1-phenyl-3-methyl-4-formyl-5-mercaptopyrazole with 1,3-diaminopropan-2-ol

The copper(II) and nickel(II) complexes based on bis(azomethine), which is the condensation product of 1-phenyl-3-methyl-4-formyl-5-mercaptopyrazole with 1,3-diaminopropan-2-ol, are synthesized. Bis-azomethines can form both binuclear and mononuclear complexes in which the hydroxy group is not involved in coordination. The binuclear copper(II) complexes with the acetate and pyrazolate bridges exhibit an antiferromagnetic exchange, which strength is determined by the nature of the bridge (2J = ?154 and ?424 cm^?1, respectively). The structure parameters of the coordination spheres of the complexes are determined by X-ray absorption spectroscopy. The structure of the CHCl₃ solvate of the binuclear copper(II) complex with the pyrazolate bridge is solved by X-ray diffraction analysis (CIF file CCDC 964655).     

Transport properties of granular metals at low temperatures

We investigate transport in a granular metallic system at large tunneling conductance between the grains, g(T)>1. We show that at low temperatures, Tg(T)delta) behavior where conductivity is controlled by the scales of the order of the grain size. In three dimensions we predict the metal-insulator transition at the bare tunneling conductance g(C)(T)=(1/6pi)ln((E(C)/delta), where E(C) is the charging energy of a single grain. Corrections to the density of states of granular metals due to the electron-electron interaction are calculated. Our results compare favorably with the logarithmic dependence of resistivity in the high-T(c) cuprate superconductors indicating that these materials may have a granular structure.     

Measurement of the relative probability of the decay φ → η′γ in the channel η′ → ηπ0π0, η → γγ

The process e ⁺ e ^? → η′γ, η′ → η π⁰π⁰, η → γγ is investigated by an SND detector in experiment on a VEPP-2M equipment with colliding electron-positron beams. The analysis of experimental data yields a value of B(? → η′γ)=(6.7 _?4.2 ^+5.0 ±1.5)×10^?5 for the decay probability. Taking into account a previous measurement of this quantity by an SND detector in the decay channel η′ → π⁺π^?η, one finally obtains B(?→η ′γ)=(6.7 _?2.4 ^+2.8 ±0.8)×10^?5.     

Study of the Process $${e}^{{+}}{e}^{{-}}{\to}{\eta\pi}^{{0}}{\gamma}$$ in the Cossision-Energy Range of $$\sqrt{{s}}{=}{1.05{-}2.00}$$ GeV

Physics of Atomic Nuclei - The process $$e^{+}e^{-}\to\eta\pi^{0}\gamma$$ is studied in the range of center-of-mass (c.m.) collision energies between 1.05 and 2.00 GeV on the basis of data...     

Measurement of the Cross Section for the Process $${e^{+}e^{-}}{\to}{K}^{{+}}{K}^{{-}}{\pi}^{{0}}$$ with the SND Detector at Collision Energies of $$\sqrt{{s}}{=}{1.3{-}2.0}$$ GeV in the Center-of-Mass Frame

Physics of Atomic Nuclei - In an experiment with the SND detector at the VEPP-2000 $$e^{+}e^{-}$$ collider, the cross sections for the processes $$e^{+}e^{-}\to K^{+}K^{-}\pi^{0}$$ and...     

Searching for the process e+e- → K+K-π0 in experiments with the spherical neutral detector at VEPP-2M

We have searched for the process e⁺e^- → K⁺K^-π⁰ at energies up to 1.38 GeVin an experiment with the spherical neutral detector at the VEPP-2M e⁺e^- collider. The upper limits of the cross sections for the processes σ(e⁺e →; φπ: → K⁺K^-π⁰) < 0.023 nb and σ(e⁺e^- → KK*(892) → K⁺K^-π⁰) < 0.059 nb have been established at a 95% confidence level.     

The Software System LingvoDoc and the Possibilities It Offers for Documentation and Analysis of Ob-Ugric Languages

Doklady Mathematics - The LingvoDoc system ( http://lingvodoc.ispras.ru ) provides a service for collaborative language documentation and computations on the collected data. This software system...     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.