Search

This paper develops two novel and fast Riemannian second-order approaches for solving a class of matrix trace minimization problems with orthogonality constraints, which is widely applied in multivariate statistical analysis. The existing majorization method is guaranteed to converge but its convergence rate is at best linear. A hybrid Riemannian Newton-type algorithm with both global and quadratic convergence is proposed firstly. A Riemannian trust-region method based on the proposed Newton method is further provided. Some numerical tests and application to the least squares fitting of the DEDICOM model and the orthonormal INDSCAL model are given to demonstrate the efficiency of the proposed methods. Comparisons with some latest Riemannian gradient-type methods and some existing Riemannian second-order algorithms in the MATLAB toolbox Manopt are also presented.

Presented in this article are the anion-tuning formation, crystal structures and luminescent properties of four coordination polymers of N,N′-di(3-pyridine) oxamide (DPOM), including two one-dimensional (1D) chain/ladder polymers, [Ni(DPOM)(H2O)4]SO4·2H2O (1) and [Cd4(DPOM)6(NO3)8] (2), as well as two 3D coordination polymers, [Zn2(DPOM)(H2O)4(SO4)2] (3) and [Cd2(DPOM)(H2O)4(SO4)2] (4). The results of single crystal X–ray diffraction analyses indicate that in these coordination polymers, DPOM ligand serves as a bridge, connecting metal ions by both terminal pyridine N atoms. 1 is a 1D chain structure formed by the bridge of DPOM. 2 is a 1D ladder-like structure featuring Cd(NO3)2 structural units bridged by DPOM ligands. Both 3 and 4 are 3D pillar-layer structures with the 2D inorganic layer ZnSO4/CdSO4 pillared by DPOM ligands. The results of photoluminescent measurements illustrate that upon excitation, 2–4 can emit fluorescence in 408, 416, and 422 nm in the solid state, respectively.

Supramolecular isomerism for coordination networks refers to the existence of different architectures having the same building blocks and identical stoichiometries. For a given building block, different arrangements can lead to the formation of a series of supramolecular isomers. Two one-dimensional CoIIcoordination polymers based onN,N′-bis(pyridin-3-yl)oxalamide (BPO), bothcatena-poly[[[dichloridocobalt(II)]-bis[μ-N,N′-bis(pyridin-3-yl)oxalamide-κ2N:N′]] dimethylformamide disolvate], {[CoCl2(C12H10N4O2)2]·2C3H7NO}n, have been assembled by the solvothermal method. Single-crystal X-ray diffraction analyses reveal that the two compounds are supramolecular isomers, the isomerism being induced by the orientation of the dimethylformamide (DMF) molecules in the crystal lattice.