Spectral estimates for unreduced symmetric KKT systems arising from Interior Point methods

We consider symmetrized Karush–Kuhn–Tucker systems arising in the solution of convex quadratic programming problems in standard form by Interior Point methods. Their coefficient matrices usually have 3 × 3 block structure, and under suitable conditions on both the quadratic programming problem and the solution, they are nonsingular in the limit. We present new spectral estimates for these matrices: the new bounds are established for the unpreconditioned matrices and for the matrices preconditioned by symmetric positive definite augmented preconditioners. Some of the obtained results complete the analysis recently given by Greif, Moulding, and Orban in [SIAM J. Optim., 24 (2014), pp. 49‐83]. The sharpness of the new estimates is illustrated by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhanced fluorescence detection of metal ions using light-harvesting mesoporous organosilica

Enhanced fluorescence detection of metal ions was realized in a system consisting of a fluorescent 2,2′‐bipyridine (BPy) receptor and light‐harvesting periodic mesoporous organosilica (PMO). The fluorescent BPy receptor with two silyl groups was synthesized and covalently attached to the pore walls of biphenyl (Bp)‐bridged PMO powder. The fluorescence intensity from the BPy receptor was significantly enhanced by the light‐harvesting property of Bp‐PMO, that is, the energy funneling into the BPy receptor from a large number of Bp groups in the PMO framework which absorbed UV light effectively. The enhanced emission of the BPy receptor was quenched upon the addition of a low concentration of Cu²⁺ (0.15–1.2×10^?6 M ), resulting in the sensitive detection of Cu²⁺. Upon titration of Zn²⁺ (0.3–6.0×10^?6 M ), the fluorescence excitation spectrum was systematically changed with an isosbestic point at 375 nm through 1:1 complexation of BPy and Zn²⁺ similar to that observed in BPy‐based solutions, indicating almost complete preservation of the binding property of the BPy receptor despite covalent fixing on the solid surface. These results demonstrate that light‐harvesting PMOs have great potential as supporting materials for enhanced fluorescence chemosensors.     

First-principles materials design of CuInSe2-based high-efficiency photovoltaic solar cells

Based on ab initio   electronic structure calculations by self-interaction-corrected local-density-approximation (SIC-LDA) with the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA), we propose a materials design for high efficiency photovoltaic solar cells (PVSCs). It is shown that (i) the concentration dependence of the mixing energy of CuIn_1−xGa_xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Ga}}_x{\mathrm{Se}}_2$ shows upward convexity, thus this system favors phase separation. Due to the type II band alignment between CuInSe₂${\mathrm{CuInSe}}_2$ and CuGaSe₂${\mathrm{CuGaSe}}_2$, efficient electron–hole separation is realized in decomposed phase of this system. (ii) CuIn_1−xZn_0.5xSn_0.5xSe₂${\mathrm{CuIn}}_{1-x}{\mathrm{Zn}}_{0.5x}{\mathrm{Sn}}_{0.5x}{\mathrm{Se}}_2$ has a direct band gap and no impurity state appears in the gap. Therefore, cost reduction is possible by using Zn and Sn instead of In. (iii) n-type CuAl_1−xSn_xS₂${\mathrm{CuAl}}_{1-x}{\mathrm{Sn}}_x{\mathrm{S}}_2$ and p-type Cu_1−xV_CuxAlS₂${\mathrm{Cu}}_{1-x}{\mathrm{V}}_{\mathrm{Cu}x}{\mathrm{AlS}}_2$ have negative activation energy for doped impurities and are expected to be low-resistive transparent conducting sulfides, which should be useful for CuInSe₂${\mathrm{CuInSe}}_2$-based PVSCs.