Optimal parameter for the SOR-like iteration method for solving the system of absolute value equations

The SOR-like iteration method for solving the absolute value equations~(AVE) of finding a vector $x$ such that $Ax - |x| - b = 0$ with $\nu = \|A^{-1}\|_2 < 1$ is investigated. The convergence conditions of the SOR-like iteration method proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]) are revisited and a new proof is given, which exhibits some insights in determining the convergent region and the optimal iteration parameter. Along this line, the optimal parameter which minimizes $\|T_\nu(\omega)\|_2$ with $$T_\nu(\omega) = \left(\begin{array}{cc} |1-\omega| & \omega^2\nu \\ |1-\omega| & |1-\omega| +\omega^2\nu \end{array}\right)$$ and the approximate optimal parameter which minimizes $\eta_{\nu}(\omega) =\max\{|1-\omega|,\nu\omega^2\}$ are explored. The optimal and approximate optimal parameters are iteration-independent and the bigger value of $\nu$ is, the smaller convergent region of the iteration parameter $\omega$ is. Numerical results are presented to demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math. Lett.}, 97:107--113, 2019]). In some situation, the SOR-like itration method with the optimal parameter performs better, in terms of CPU time, than the generalized Newton method (Mangasarian, [{\em Optim. Lett.}, 3:101--108, 2009]) for solving the AVE.Comment: 23 pages, 7 figures, 7 table

Germanium doping of Si substrates for improved device characteristics and yield

During the last decade the 300 mm Si wafer has been optimized and one is already studying 450 mm crystals and wafers. The increasing silicon crystal diameter shows two important trends with respect to substrate characteristics: the interstitial oxygen concentration is decreasing while the size of grown in voids (COP's) in vacancy-rich crystals is increasing. The first effect is due the suppression of melt movements by the use of magnetic fields leading to a more limited transport of oxygen to the crystal. This and the decreasing thermal budget of advanced device processing leads to reduced internal gettering capacity. The increasing COP size is due to the combination of decreasing pulling rate and thermal gradient leading to a decreased void nucleation and increased thermal budget for void growth. The effect of Ge doping in the range between 10(16) cm(-3) and 10(19) cm(-3) on both COP's and oxygen precipitation will be discussed

Optimization of hole spacing for cut-top blasting based on new hole-sealing technology

In order to solve the problem of stress concentration on the roof of the mining trench, reduce the risk of sudden collapse of the roof overburden and disturbance, improve the control effect of the surrounding rock of the roof cutting and retaining roadway, and reduce the construction cost of mining tunnels, a new type of pouch sealing technology has been developed. By using on-site testing methods, the optimal sealing material ratio was optimized, and the crack propagation law and roof cutting effect of the 11503 W working face in Zhaizhen Coal Mine, Shandong Province were studied under hole spacing of 0.7, 1.0, and 1.1 meters and different sealing methods. The results show that using 1.5 m single pouch sealing technology in the blasting test, when the water cement ratio of the sealing material is 1:1, the required sealing strength and sealing temperature can be achieved, and there will be no punching phenomenon. When the spacing between holes is 1 m, the blasting effect is optimal, with a single hole effectively reaching a cutting seam length of about 0.5 m. There are obvious through cracks in the cave, with a total length of about 7 meters. After using the new pouch sealing technology for blasting, the displacement and bottom drum volume on both sides of the tunnel are lower than those of the traditional yellow mud sealing method, and the bottom drum volume is reduced by 37% and 53%, respectively. Based on comprehensive theoretical analysis and on-site experiments, the optimal hole spacing is determined to be 1 m, and the pouch sealing effect is good

One-Pot Synthesis of Biocompatible CdSe/CdS Quantum Dots and Their Applications as Fluorescent Biological Labels

We developed a novel one-pot polyol approach for the synthesis of biocompatible CdSe quantum dots (QDs) using poly(acrylic acid) (PAA) as a capping ligand at 240°C. The morphological and structural characterization confirmed the formation of biocompatible and monodisperse CdSe QDs with several nanometers in size. The encapsulation of CdS thin layers on the surface of CdSe QDs (CdSe/CdS core–shell QDs) was used for passivating the defect emission (650 nm) and enhancing the fluorescent quantum yields up to 30% of band-to-band emission (530–600 nm). Moreover, the PL emission peak of CdSe/CdS core–shell QDs could be tuned from 530 to 600 nm by the size of CdSe core. The as-prepared CdSe/CdS core–shell QDs with small size, well water solubility, good monodispersity, and bright PL emission showed high performance as fluorescent cell labels in vitro. The viability of QDs-labeled 293T cells was evaluated using a 3-(4,5-dimethylthiazol)-2-diphenyltertrazolium bromide (MTT) assay. The results showed the satisfactory (>80%) biocompatibility of as-synthesized PAA-capped QDs at the Cd concentration of 15 μg/ml

Genotypic differences in shoot silicon content and the impact on grain arsenic accumulation in rice

Silicon in rice has been demonstrated to be involved in resistance to lodging, tolerance to both drought and salinity, and also enhances resistance to pests and diseases. The aim of this study was to determine the range of silicon content in a set of rice (Oryza sativa L.) accessions, and to determine if the natural variation of shoot silicon is linked to the previously identified silicon transporters (Lsi genes). Silicon content was determined in 50 field-grown accessions, representing all sub-populations of rice, with all accessions being genotyped with 700K SNPs. SNPs within 10 kb of the Lsi genes were examined to determine if any were significantly linked with the phenotypic variation. An XRF method of silicon determination compared favourably with digestion and colorimetric analysis. There were significant genotypic differences in shoot silicon ranging from 16.5 – 42.4 mg g-1 of plant dry weight, there was no significant difference between the rice sub-populations. Plants with different alleles for SNPs representing Lsi2 and Lsi3 were significantly different for shoot silicon content. Shoot silicon correlated negatively with grain arsenic in the tropical and temperate japonica sub-population, suggesting that accessions with high shoot silicon have reduced grain arsenic. This study indicates that alleles for Lsi genes are excellent candidate genes for further study to explain the natural variation of shoot silicon in rice