Some functional equations originating from number theory

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.     

A functional equation having monomials as solutions

For each n=1,2,3, we obtain the general solution and the stability of the functional equation

f(2x+y)+f(2x-y)=2^n-2[f(x+y)+f(x-y)+6f(x)].     

Effect of Biodiesel-derived Raw Glycerol on 1,3-Propanediol Production by Different Microorganisms

The microbial production of 1,3-propanediol (1,3-PD) from raw glycerol, a byproduct of biodiesel production, is economically and environmentally advantageous. Although direct use of raw glycerol without any pretreatment is desirable, previous studies have reported that this could cause inhibition of microbial growth. In this study, we investigated the effects of raw glycerol type, different microorganisms, and pretreatment of raw glycerol on the production of 1,3-PD. Raw glycerol from waste vegetable-oil-based biodiesel production generally caused more inhibition of 1,3-PD production and microbial growth compared to raw glycerol from soybean-oil-based biodiesel production. In addition, two raw glycerol types produced from two biodiesel manufacturers using waste vegetable oil exhibited different 1,3-PD production behavior, partially due to different amounts of methanol included in the raw glycerol from the two biodiesel manufacturers. Klebsiella strains were generally resistant to all types of raw glycerol while the growth of Clostridium strains was variably inhibited depending on the type of raw glycerol. The 1,3-PD production of the Clostridium strains using acid-pretreated raw glycerol was significantly enhanced compared to that with raw glycerol, demonstrating the feasibility of using raw glycerol for 1,3-PD production by various microorganisms.     

Endothelial progenitor cell transplantation decreases lymphangiogenesis and adverse myocardial remodeling in a mouse model of acute myocardial infarction

Cardiac lymphatic system in the remodeling after acute myocardial infarction (AMI) has been overlooked. We wanted to investigate the role of bone marrow-derived endothelial progenitor cells (EPCs) and their contribution to lymphatic distribution in myocardial remodeling after AMI. Mouse (C57bl/6J) MI models were created by ligation of the left anterior descending coronary artery and were treated with phosphate buffered saline (PBS) or EPCs. Real-time RT-PCR with 2- to 4-week myocardial tissue samples revealed that lymphangiogenetic factors such as vascular endothelial growth factor (VEGF)-C (8.5 fold, P < 0.05), VEGF-D (6.1 fold, P < 0.05), Lyve-1 (15 fold, P < 0.05), and Prox-1 (11 fold, P < 0.05) were expressed at significantly higher levels in the PBS group than the EPC group. The PBS group also showed a significantly higher density of lymphatic vessels in the peri-infarction area. Echocardiography showed that from 2 weeks after the treatment, left ventricle (LV) dimensions at both systole and diastole were significantly smaller in the EPC group than in the PBS group (P < 0.01) and LV fractional shortening was higher in the EPC group accordingly (P < 0.01). Lymphangiogenic markers increased in a mouse MI model. EPC transplantation decreased lymphangiogenesis and adverse ventricular remodeling after AMI. These novel findings suggest that new lymphatic vessels may be formed in severely damaged myocardium, and may be involved in adverse myocardial remodeling after AMI.     

A functional equation originating from quadratic forms

In this paper, we obtain the general solution and the stability of the 2-variable quadratic functional equation

f(x+y,z+w)+f(x−y,z−w)=2f(x,z)+2f(y,w).     

石墨烯/二氯化镁负载钛系齐格勒-纳塔催化剂制备及其乙烯聚合性能

石墨烯自2004年发现以来,由于其独一无二的优异性迅速成为科学家们的研究热点.由于石墨烯具有极其优异的电学、力学和热学等性能,因此被广泛应用于高性能聚合物基复合材料的制备.众所周知,纳米填料在聚合物中的分散状态以及与基体间的界面作用是构筑高性能聚合物纳米复合材料的关键因素.由于石墨烯极易团聚,难以通过传统的熔融共混法制备均匀分散的石墨烯增强-聚烯烃纳米复合材料.另一方面,聚烯烃通常需要在较高温度下才能溶于部分有毒溶剂(如:三氯苯和二甲苯等),因此溶液共混法也不适用于聚烯烃-石墨烯纳米复合材料的制备.有鉴于此,本文开发了一种共沉积法制备石墨烯/二氯化镁负载钛系齐格勒-纳塔催化剂的路线.通过原位聚合直接制备出石墨烯均匀分散的聚烯烃/石墨烯纳米复合材料.考察了石墨烯的加入量对催化剂形态及其催化乙烯聚合行为的影响.当石墨烯加入量较低时,多个石墨烯片被包裹于较大的催化剂粒子中.随着石墨烯加入量的增加,催化剂趋向于在石墨烯表面聚集.继续增加石墨烯量将导致石墨烯包裹催化剂粒子,降低过渡金属钛的负载效率.通过三乙基铝活化后,所制备的催化剂具有非常高的乙烯催化活性,所生成的聚乙烯/石墨烯纳米复合材料复制了催化剂的片状结构.同时,通过对所制备的聚乙烯/石墨烯纳米复合材料进行电子显微镜和X射线衍射分析可知,石墨烯均匀分散于聚乙烯基体中,并且没有任何团聚现象发生.该复合材料的热重分析表明,仅加入非常少量的石墨烯就可以使其具有比纯聚乙烯更高的热稳定性,当石墨烯加入量为0.66 wt%时,其5 wt%热分解温度较纯聚乙烯升高了54°C.同时,所制备聚乙烯/石墨烯纳米复合材料具有更优异的机械性能.因此,本研究提供了一个简单高效的高性能聚烯烃/石墨烯纳米复合材料的制备方法.     

Thermal–electrical–structural performances of hot heat exchanger with different internal fins of thermoelectric generator for low power generation application

Journal of Thermal Analysis and Calorimetry - In this study, an electro-thermo-structural coupled numerical analysis is conducted to evaluate the thermal, electrical, and structural performances of...