It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

Soil organic carbon (SOC) mineralization is closely related to carbon source or sink of terrestrial ecosystem. Understanding soil organic carbon (SOC) mineralization under plum plantation is essential for improving our understanding of SOC responses to land-use change in karst rocky desertification ecosystem. In this study, 2-y, 5-y and 20-y plum plantations and adjacent woodland were sampled and a 90-day incubation experiment was conducted to investigate the effect of plum plantation with different years on SOC mineralization in subtropical China. Results showed that: (1) there was no significant difference in SOC content between different planting years, but there were significant differences in accumulative SOC mineralization (C_t) and potential SOC mineralization (C₀); (2) the dynamics of the SOC mineralization was a good fit to a first-order kinetic model. Both C₀ and C_t in calcareous soil of this study was several to ten folds lower than that in other soils, indicating that SOC in karst region has higher stability. (3) Correlation analysis revealed that both C_t and C₀ was significantly correlated with soil calcium (Ca) and C/N, indicating the important role of Ca and C/N in SOC mineralization in karst rocky desertification area.

Methylsilsesquioxane aerogels with uniform mesopores have been facilely prepared via a sol–gel process followed by microwave drying with methyltrimethoxysilane (MTMS) as precursor, hydrochloric acid (HCl) as catalyst, water and methanol as solvents, hexadecyltrimethylammonium chloride (CTAC) as surfactant and template and propylene oxide (PO) as gelation agent. The microstructure, chemical composition and pore structures of the resultant MSQ aerogels were investigated in detail to achieve controllable preparation of MSQ aerogels, and the thermal stability of MSQ aerogels was also analyzed. The gelation agent, catalyst, solvent and microwave power have important roles on pore structures of MSQ aerogels. Meanwhile, microwave drying method is found to not only have a remarkable effect on improving production efficiency, but also be conducive to avoid the collapse of pore structure especially micropores during drying. The resulting MSQ aerogel microwave-dried at 500 W possesses a specific surface area up to 821 m2/g and a mesopore size of 20 nm, and displays good thermal stability.

Laminopathies are a spectrum of diseases caused by LMNA mutations. In familial partial lipodystrophy of Dunnigan (FPLD), LMNA plays role in the differentiation and development of adipocytes and lipid metabolism. Changes in LMNA predict not only the differentiation of adipose-derived mesenchymal stem cells (AD-MSCs) but also the transformation of cancer cells. Hence, our in-depth study aimed to identify the molecular connection between disordered lipid metabolism and hepatic carcinogenesis. We first discovered significant positive correlations between pLMNA and two key rate-limiting enzymes in de novo fatty acid synthesis, acetyl-CoA-carboxylase 1 (ACC1) and fatty acid synthase (FASN), in the liver tissue but not in adipose tissue of obese model rats. Moreover, LMNA knockdown (KD) in rat AD-MSCs prevented the differentiation and maturation of adipocytes. To clarify the mechanistic relationship with lipogenesis, gain- and loss-of-function experiments in which functional changes and the related molecular pathways were investigated in a normal hepatocyte line (7701 cells). Adenosine 5'-monophosphate activated protein kinase α (AMPKα) was found to be activated by abnormalities in the LMNA structure under conditions of LMNA deletion, farnesyltransferase inhibitor (FTI) treatment and LMNA mutations associated with clinical FPLD pathogenic phenotype. Active AMPKα could directly phosphorylate ACC1 and thus inhibit lipid synthesis but induced glycolysis in both HCC cells and normal cells. The HCC cells could not survive with LMNA knockout (KO) or even KD. Lonafarnib (an FTI) combined with low-glucose conditions significantly decreased the proliferation of HepG2 and MHCC cells by inhibiting glycolysis and the maturation of prelamin A.

In this paper, the effects of different food-grade enzymes on the antigenicity of casein (CN), β- lactoglobulin (β-LG) and ɑ-lactalbumin (ɑ-LA) in natural cow milk were studied. The degree of hydrolysis (DH), SDS-PAGE and molecular mas (MW) distribution of cow milk (CM) hydrolysates was assessed. Additionally, the residual antigenicity of CM hydrolysates was evaluated by using ELISA and western blotting with anti-CN, anti-β-LG and anti-ɑ-LA rabbit polyclonal antibody. The results showed that Alcalase and Protamex hydrolysis could efficiently reduce the antigenicity of CN, β-LG, ɑ-LA, showed a higher DH and the loss of density of CM proteins, as indicated by SDS-PAGE. The increasing of the low MW (<3 kDa) in CM hydrolysates was also presented. It was also found that Protamex, Alcalase could be more efficiently hydrolyzed major allergenic of CM than other enzymes for the development of hypoallergenic cow milk. Our research will lay a theoretical foundation for the study of hypoallergenic cow milk.

Tocilizumab against interleukin-6 receptor (IL-6R) has been demonstrated to inhibit the progression of diverse cancers in vitro and in vivo. Nonetheless, evidence regarding the anti-tumor effects of Tocilizumab on human colorectal carcinoma (CRC) corresponding to IL-6R expression levels re-mains scarce. To investigate the influence of IL-6R expression, SW480 and HT-29 cells inoculated subcutaneously into NU/NU mice were used as our human CRC xenograft models with anti-IL-6R antibody (Tocilizumab) therapy. IL-6R expression levels, the histology of CRC growth/ invasiveness and tumor growth-related signaling pathway were estimated by H&E and immunohistochemical staining. SW480 tumor cells with higher IL-6R expression levels exerted better responsiveness in Tocilizumab therapy than the treated HT-29 group. Likewise, therapeutic effects of Tocilizumab on the proliferative ability with mitotic index and Ki-67 expressions, the invasiveness with MMP-9 proteinase expressions, ERK 1/2 and STAT3 signaling transduction in SW480 treatment group were superior to HT-29 treatment group. In light of our results, IL-6R is the key indicator for the efficacy of Tocilizumab treatment in CRC xenografts. From the perspective of precision medicine, tumor response to anti-IL-6R antibody therapy could be predicted on the basis of IL-6R expression levels. In this manner, Tocilizumab may serve as a targeted and promising anti-CRC therapy.

The aim of this systematic review is to describe and to identify prospect of β-Tricalcium Phosphate (β-TCP) as Alveolar Bone Grafting (ABG) in Cleft Lip/Palate (CL/P) or alveolar bone cleft defect. A systematic review protocol based on Preferred Reporting Items for Systematic Reviews and Meta Analyses 2020 (PRISMA 2020) was drafted. The literature search was conducted with MEDLINE/PubMed, Web of Science/ ISI-Web of Knowledge, Scopus and Cochrane Library with English language and no publication year limits. The keywords yielded a total of 5824 publications. There are 3196 suitable articles to evaluate after removing duplicates and languages. Afterward, 1315 studies left after doing title and abstract reading. In addition, 85 full-articles were assessed for eligibility. The read the complete texts of those papers and eventually chose 20 that matched the inclusion requirements. Thirteen of the twenty studies included in this systematic review had a low risk of bias, one had a high risk of bias, and six had moderate bias which not report the randomization. β-TCP as ABG is biocompatible, visible and practical, offers a less invasive procedure, and does not interfere with orthodontic treatment. β-TCP as synthetic ABG can be the alternative to autologous bone grafts with several terms and conditions. Improvement of β-TCP efficacy for ABG in CL/P or alveolar bone cleft defects can be done by a tissue engineering approach combining β-TCP with growth factor, mesenchymal stem cells, or other graft materials and modification of β-TCP physical properties.

The effects of environmental media on the corrosion fatigue fracture behavior of 25CrMo steel were investigated. The media include air, and a 3.5 wt.% and a 5.0 wt.% NaCl solutions. Experimental results indicate that the media induces the initiation of corrosion fatigue cracks at multiple sites. The multi-cracking sites cause the changes in the crack growth directions, the crack growth rate during the coupling action of the media and the stress amplitude. The coupling effects are important for engineering applications and research. The probability and predictions of the corrosion fatigue characteristic life can be estimated using the 3-parameter Weibull distribution function.

As a new plant slope protection technology, living stumps can effectively improve slope stability. The current study attemptes to investigate the mechanical characteristics of the root system of living stumps and their reinforcement mechanism on slopes by carrying out a three-dimensional living stump slope modeling test. Using ABS materials, a 3D model of a living elm stump was created by 3D printing and a slope model test was carried out. The reinforcement mechanism of the living stump was studied through a combination of model testing and numerical simulation. The results indicate that, due to the presence of living stumps in the lower and middle parts of the slope, the maximum shear stress area of the soil moved to a deeper direction. The stress state of the soil around the living stump was effectively improved due to the existence of the lateral root system.Living stumps in the lower part of the slope cross the potential sliding surface and transferred the soil shear stress gradually to the root system through root-soil interaction. Moreover, the tap roots and lateral roots of living stumps form a robust spatial structure that bears the shear stress of soil together, thus increasing the stability of the slope.