Global infimum of strictly convex quadratic functions with bounded perturbations

The problem of minimizing [(f)\tilde]=f+p{\tilde f=f+p} over some convex subset of a Euclidean space is investigated, where f(x) = x ^T Ax + b ^T x is strictly convex and |p| is only assumed to be bounded by some positive number s. It is shown that the function [(f)\tilde]{\tilde f} is strictly outer γ-convex for any γ > γ*, where γ* is determined by s and the smallest eigenvalue of A. As consequence, a γ*-local minimal solution of [(f)\tilde]{\tilde f} is its global minimal solution and the diameter of the set of global minimal solutions of [(f)\tilde]{\tilde f} is less than or equal to γ*. Especially, the distance between the global minimal solution of f and any global minimal solution of [(f)\tilde]{\tilde f} is less than or equal to γ*/2. This property is used to prove a roughly generalized support property of [(f)\tilde]{\tilde f} and some generalized optimality conditions.     

On a characterization of analytic compactifications for ℂ* × ℂ*

Let M be a minimal compact surface, let Γ ⊂ M be a compact analytic sub-variety. Assume that X:= M \ Γ is Stein. Then we will show that X admits algebraic compactifications M _i (resp. non algebraic compactifications $ \mathbb{M}_i $ \mathbb{M}_i ) which are not birationally equivalent (resp. not bimeromorphically equivalent) iff X is biholomorphic to      

pH‐sensing nanostar probe using surface‐enhanced Raman scattering (SERS): theoretical and experimental studies

Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm⁻¹ was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd.     

A new sinusoidal shear deformation theory for bending,buckling, and vibration of functionally graded plates

A new sinusoidal shear deformation theory is developed for bending, buckling, and vibration of functionally graded plates. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns and has strong similarities with classical plate theory in many aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. Equations of motion are derived from the Hamilton’s principle. The closed-form solutions of simply supported plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of functionally graded plates.     

Control of Metal–Organic Framework Crystallization by Metastable Intermediate Pre‐equilibrium Species

There is an increasing amount of interest in metal–organic frameworks (MOFs) for a variety of applications, from gas sensing and separations to electronics and catalysis. However, the mechanisms by which they crystallize remain poorly understood. Herein, an important new insight into MOF formation is reported. It is shown that, prior to network assembly, crystallization intermediates in the canonical ZIF‐8 system exist in a dynamic pre‐equilibrium, which depends on the reactant concentrations and the progress of reaction. Concentration can, therefore, be used as a synthetic handle to directly control particle size, with potential implications for industrial scale‐up and gas sorption applications. These findings enable the rationalization of apparent contradictions between previous studies of ZIF‐8 and opens up new opportunities for the control of crystallization in network solids more generally.     

Fabrication of Nano Flower‐shaped Platinum on Glassy Carbon Electrode as a Sensitive Sensor for Lead Electrochemical Analysis

Platinum nanoflowers modified glassy carbon electrodes (PtNFs/GCE) was fabricated simply for lead determination in water samples. The modified electrodes were prepared by electrodeposition in hexachloroplatinic acid solution at constant potential. The influence of deposition time and potential on surface morphology, chemical composition, electrochemical properties of electrode were investigated. At ?0.2 V of potential and 150 s of deposition duration, platinum developed as nanoflower shape and scattered densely all over the glassy carbon surface, producing the largest electrochemically active surface areas. The highest differential pulse stripping voltammetry (DPSV) signal of lead was obtained by using the prepared electrode. Under optimized experimental condition of electrolyte, accumulation potential and time, the peak current was found to be linear proportion to lead concentration in range of 1 to 100 μg L^?1 (slope=0.371) with a limit of detection of 0.398 μg L^?1. The method has good repeatability and reproducibility with relative standard deviations of 1.47 % and 4.83 %, respectively. The modified PtNFs/GCE also demonstrated an excellent long‐term stability with only 9 % decrease in Pb peak current over 30 days. Moreover, the performance of the modified PtNFs/GCE in determination of Pb(II) in two industrial wastewaters was good agreement with data obtained by a graphite furnace atomic absorption spectrometry (GFAAS) method.     

Synthesis and Magnetic Characteristics of Neodymium Ferrite Powders with Perovskite Structure

Russian Journal of Applied Chemistry - Nanopowders of neodymium ferrite with perovskite structure were synthesized by co-precipitation precipitation via hydrolysis of iron(III) and neodymium(III)...