Correlative Sparsity in Primal-Dual Interior-Point Methods for LP,SDP, and SOCP

Exploiting sparsity has been a key issue in solving large-scale optimization problems. The most time-consuming part of primal-dual interior-point methods for linear programs, second-order cone programs, and semidefinite programs is solving the Schur complement equation at each iteration, usually by the Cholesky factorization. The computational efficiency is greatly affected by the sparsity of the coefficient matrix of the equation which is determined by the sparsity of an optimization problem (linear program, semidefinite program or second-order cone program). We show if an optimization problem is correlatively sparse, then the coefficient matrix of the Schur complement equation inherits the sparsity, and a sparse Cholesky factorization applied to the matrix results in no fill-in. S. Kim’s research was supported by Kosef R01-2005-000-10271-0 and KRF-2006-312-C00062.     

Bonding structure of phenylacetylene on hydrogen-terminated Si(111) and Si(100): surface photoelectron spectroscopy analysis and ab initio calculations

Interfaces between phenylacetylene (PA) monolayers and two silicon surfaces, Si(111) and Si(100), are probed by X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy, and the results are analyzed using ab initio molecular orbital calculations. The monolayer systems are prepared via the surface hydrosilylation reaction between PA and hydrogen-terminated silicon surfaces. The following spectral features are obtained for both of the PA-Si(111) and PA-Si(100) systems: a broad π-π* shakeup peak at 292 eV (XPS), a broad first ionization peak at 3.8 eV (UPS), and a low-energy C 1s → π* resonance peak at 284.3 eV (NEXAFS). These findings are ascribed to a styrene-like π-conjugated molecular structure at the PA-Si interface by comparing the experimental data with theoretical analysis results. A conclusion is drawn that the vinyl group can keep its π-conjugation character on the hydrogen-terminated Si(100) [H:Si(100)] surface composed of the dihydride (SiH(2)) groups as well as on hydrogen-terminated Si(111) having the monohydride (SiH) group. The formation mechanism of the PA-Si(100) interface is investigated within cluster ab initio calculations, and the possible structure of the H:Si(100) surface is discussed based on available data.     

Catalysis of redox reactions by Ag@TiO<Subscript>2</Subscript> and Fe<Superscript>3+</Superscript>-doped Ag@TiO<Subscript>2</Subscript> core–shell type nanoparticles

Ag nanoparticles encapsulated by TiO₂ shells have the ability to catalyze redox reactions on their surface. By continually monitoring by use of UV–visible spectroscopy it was found that the surface charge of both TiO₂-coated and uncoated colloidal silver particles changed after chemical electron injection. The charging and discharging process of Ag@TiO₂ vary, depending on the different Ag content of the core–shell nanoparticles. In order to enhance the stability of Ag@TiO₂ colloids, Fe³⁺ was doped into the lattice of the TiO₂ shells. The experimental results showed that the Fe³⁺ ions have the capacity to store and transfer electrons. Furthermore, the charging and discharging rate can be controlled by changing the thickness of the TiO₂ shells, because they are limited by the diffusion distance of electrons through the TiO₂ shells.     

Test compounds for detecting the silanol effect on the elution of ionized amines in reversed‐phase LC

The effectiveness of several basic compounds for testing silica‐based stationary phases was reviewed by applying them to recent columns for reversed‐phase HPLC. Most octadecylsilylated (C18) stationary phases, prepared as a base‐deactivated material from high‐purity silica gel with endcapping, provided excellent peak shape and column efficiency for the bases including benzylamine and amitriptyline that once caused problems and were subsequently employed for testing silanol activities. However, a cyclic tertiary amine, dextrometorphan, was eluted as an acceptable peak from only a few columns at neutral pH. Such a more sensitive probe is expected to contribute to further improvement of the stationary phase for reversed‐phase HPLC.     

Coloring–decoloring behavior of fluoroalkyl end‐capped 2‐acrylamido‐2‐methylpropanesulfonic acid oligomer/acetone composite in methanol

A reddish‐brown fluoroalkyl end‐capped 2‐acrylamido‐2‐methylpropanesulfonic acid (AMPS) oligomer/acetone composite was prepared by heating the white oligomer powder with acetone at 80 °C for 3 h. The color was not observed in the corresponding non‐fluorinated AMPS oligomer/acetone composite, which was prepared under similar conditions. The coloring was probably caused by the formation of acetone polyaldol condensation products in the fluorinated oligomeric gel network cores. The colored R_F‐(AMPS)_n‐R_F/acetone composite powders were stable and did not exhibit any color change after 2 years in natural light at room temperature. The colored composite powders dissolved in methanol to give a reddish‐brown solution at room temperature. However, the retro‐polyaldol condensation decolored the solution after 1 day at room temperature. This is the first example of the retro‐aldol polycondensation of acetone under mild conditions. The decoloration increased by between 38‐ and 70‐fold under UV irradiation, compared with that in dark conditions. The coloring–decoloring behavior was consistent and repeatable; therefore our fluorinated oligomer/acetone composites are promising candidates for new fluorinated coloring materials. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2555–2564     

Electronic structure characteristic of carbon nanotubules

Electronic structure near the Fermi energy of single-shell carbon nanotubules has been studied within the framework of the tight-binding approximation. The electronic density of states (DOS) of tubules shows a structure consisting of many spike-like peaks. An analytical expression in a π-electron model is derived which predicts not only the energy gap (E _g ) of semiconducting tubules, but also the energy positions of those spike-like peaks in the π-DOS near the Fermi energy in any tubule. The limitation of the π-electron model in tubules is discussed by investigating the effect of σ-πmixing. The position of σ component edge in the DOS is also investigated as a function of tubule radius (R) and chiral angle (θ). It is found that this edge energy is very sensitive to θ and largely changes with R, because the dominant contribution of θ to its change is given by g(θ)/R in contrast to f(θ)/R ² for E _g .