Growth of Solutions of Some Linear Difference Equations with Meromorphic Coefficients

In this paper, we investigate the properties of solutions of some linear difference equations with meromorphic coefficients, and obtain some estimates on growth and value distribution of these meromorphic solutions.     

Effect of the Scanning Step on the Surface Quality of Microdevices in Femtosecond-Laser Micromachining and its Optimization

Direct writing technique is usually used in femtosecond-laser two-photon micromachining. The size of the scanning step has important influence on the surface quality and machining efficiency of microdevices. According to the mechanism of two-photon polymerization combining the distribution function of the light intensity and the free-radical-concentration theory, we establish the mathematical model of coverage of solidification unit and analyze the effect of coverage on the machining quality and efficiency of microdevices. Using the principle of exposure equivalence, we also obtain the analytic expression of the relationship between the surface-quality characteristic parameters of microdevices and the scanning step and carry out the numerical simulation and experiment. The results show that the scanning step has little influence on the surface quality of the line when it is much smaller than the size of the solidification unit. However, when the scanning step is gradually increasing, the smoothness of the line surface is reduced rapidly, and the surface quality becomes worse drastically. For stereo-device processing with different slopes, we propose a kind three-dimensional continuous-variable scanning method and provide the calculation expression of the scanning step. From the experimental example of fabricating a spherical structure, we show that, compared with the fixed-step scanning method, the continuous-variable scanning-step method should be used to improve the surface quality of microdevices.     

Transient and Recyclable Halogenation Coupling (TRHC) for Isoflavonoid Synthesis with Site-Selective Arylation

A transient and recyclable C−H iodination has been designed for the synthesis of isoflavonoids through the domino reactions of o-hydroxyphenyl enaminones and aryl boronic acids in the presence of catalytic KI and Pd catalyst. Instead of the conventional cross-coupling strategy employing pre-halogenated substrates, this method transforms raw C−H bond by means of a transient C−H halogenation to smoothly relay the subsequent C-arylation. Consequently, such a method avoids the pre-functionalization for C−halogen bond installation as well as the generation of stoichiometric halogen-containing waste following the cross-coupled product, disclosing an intriguing new coupling protocol to forge the C−C bond in the virgin area between classical C−X (X=halogen) bond cross coupling and the C−H activation.     

Preparation and Tribological Behaviors of Lubricants—Oil Based on Modified Microbial Oil with Nano-Schiff Base Copper Complex

A W/O microemulsion reactor was used to prepare four kinds of modified lubricants: (i) modified lubricant 1, modified epoxidized microbial oil + rape oil in volume ratio of 1:1; (ii) modified lubricant 2, modified esterified microbial oil + rape oil in volume ratio of 1:3; (iii) modified lubricant 3, modified epoxidized rape oil; and (iv) modified lubricant 4, modified PAO. The individual modified lubricants were further modified with 0%, 0.5%, 1%, and 2% content of nano-Schiff base copper complex (nano-SBCC). A microtribometer was used to evaluate the friction coefficient between ball/flat point contacts immersed in the modified lubricants and operated in reciprocating and linear sliding mode. A comparison of the values of the friction coefficient with the lubricants further modified with nano-SBCC with those of their individual 0% nano-SBCC counterparts indicated significant decrease: (i) almost 19.18% was obtainable for the modified lubricant 1 with 2% of nano-Schiff base copper complex, (ii) almost 16.5% was obtainable for the modified lubricant 2 with 0.5% of nano-Schiff base copper complex; (iii) almost 7.42% was obtainable for the modified lubricant 3 with 1% of nano-SBCC; and (iv) almost 7.01% was obtainable for the modified lubricant 4 with 0.5% of nano-SBCC. These suggested that the addition of nano-Schiff base copper complex can efficiently decrease the friction coefficient of epoxidized or esterified microbial oil. Analyses of two-dimensional images, average profiles (across the mid-section y = 0 of the reciprocating sliding path), and three-dimensional topographies by confocal white light microscope for the worn surfaces of flats immersed in modified lubricant 1 and modified lubricant 2 suggested better wear-resistance of the modified lubricant 2 than that of the modified lubricant 1. The ability of wear resistance for the modified lubricant became better with the increasing content of nano-Schiff base copper complex from 0% to 2%. The study revealed the modification of epoxidized microbial oil + rape oil (1:1 volume ratio) and esterified microbial oil + rape oil (1:3 volume ratio) with Cu(II) chelate of bis(salicylaldehyde)ethylenediamine, reducing the magnitude of friction and wear because of their respective wear self-repairing ability. Such self-repairing ability furnishes the suitability of epoxidized microbial oil or esterified microbial oil to be effectively modified by nano-Schiff base copper complex and to substitute ordinary base oil as a mixture with rape oil.     

Toward the natural didemnaketal A: total synthesis of the isomer of didemnaketal A

The total synthesis of isomer of didemnaketal A was achieved in 26 steps. The position of esters is switched at C7 and C8 with respect to their proposed position in natural didemnaketal A, which shows potent anti-HIV activity but so far has not been synthesized in the laboratory. Structural analysis of synthetic isomer of didemnaketal A indicates that the esters at C7 and C8 are correctly assigned, suggesting that the problems for the structural reassignment of natural didemnaketal A lie elsewhere.     

Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.