In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".

In the paper, the authors nd a new closed expression for the Fibonacci polynomials and, consequently, for the Fibonacci numbers, in terms of a tridiagonal determinant.

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify two families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind.

Hexabromocyclododecane (HBCD) was most important flame retardant in Expanded Polystyrene foam and Extruded Polystyrene foam in the past forty years in the world. China was the major producer and user of HBCD, and the total HBCD production was about 0.3 million tons. Although HBCD has been completely banned in China in 2021 because of its long-range transport, bioaccumulation and toxicity, there's still a lot of residues in environment. Therefore, we reviewed multiple studies concerning the distribution of HBCD in diverse environmental matrices, such as air, dust, soil, water, sediment and biota. Results revealed that HBCD levels in different environments in China present a geographical variation and were at high level compared with other countries. In all environmental media, relatively high HBCD concentrations have been found in industrial and urban areas. Industrialization and urbanization are two important factors that influence the concentration and distribution of HBCD in the environment. In terms of isomer, γ-HBCD was the dominant isomer in soil, water, and sediment, while in the biota, α-HBCD was the predominant isomer.

Properties of time domain parameters of the vibration signal have been extensively studied for the fault diagnosis of rolling element bearings (REB). Parameters like kurtosis and Envelope Harmonic-to-Noise Ratio are most widely applied in this field and some important progress has been made. However, since only one-sided information is contained in these parameters respectively, problems still exist in practice when the signals collected are of complicated structure and/or contaminated by strong background noises. A new parameter, named Shock pulse index (SPI), is proposed in this paper. It integrates the mutual advantage of both parameters above and can help effectively identify fault related impulse components under the interference of strong background noises, unrelated harmonic components and random impulses. The SPI optimizes the parameters of Maximum Correlated Kurtosis Deconvolution (MCKD), which is used to filter the signals under consideration. Finally, the interested transient information contained in the filtered signal can be highlighted through demodulation with Teager Energy Operator (TEO). Fault related impulse components can therefore be extracted accurately. Simulations and experiment analyses verify the effectiveness and correctness of the SPI.

Breeding early-maturing cultivars is one of the most important objectives for pear breeding. Very early-maturing pear provides an excellent parental material for crossing, while the immature embryo and low seed germination of its hybrid progenies often limit the selection and breeding of new early-maturing pear cultivars. In this study, we choose a very early maturing pear cultivar ‘Pearl Pear’ as study object, and investigate the effects of cold stratification, culture medium and seed coat on the germination and growth of early maturing pear seeds. Our results show that cold stratification (4℃) treatment could significantly improve the germination rates of early maturing pear seeds. A 100 days of low temperature pre-treatment and germination on White medium could increase the germination rate up to 84.54%. We also observe that seed coat removal could improve the germination activity of early maturing pear seeds, and middle seed coat removal (MSR) represents an optimal method with its high germination rate and low contamination. The results of our study established an improved protocol for seed germination of early-maturing pear seeds, which will greatly facilitate the breeding of new very early-maturing pear cultivars.

To understand the molecular mechanism underlying yellowing in pineapples during ripening, coupled with alterations in fruit quality, comprehensive metabolome and transcriptome investigations were carried out. These investigations were conducted using the pulp samples collected at three distinct stages of maturity: young fruit (YF), mature fruit (MF), and fully mature fruit (FMF). This study revealed a noteworthy increase in the levels of total phenols and flavones, coupled with a concurrent decline in lignin and total acid content, as the fruit transitioned from YF to FMF. Furthermore, the analysis yielded 167 differentially accumulated metabolites (DAMs) and 2194 differentially expressed genes (DEGs). Kyoto Encyclopedia of Genes and Genomes enrichment analysis based on DAMs and DEGs revealed that the biosynthesis of plant secondary metabolites, particularly the flavonol, flavonoid, and phenypropanoid pathways, plays a pivotal role in fruit yellowing. Additionally, a comprehensive regulatory network encompassing genes that contribute to metabolisms of flavones, flavonols, lignin, and organic acids was proposed. This network sheds light on the intricate processes that underlies fruit yellowing and quality alterations. These findings enhance our understanding of the regulatory pathways governing pineapple ripening and offer valuable scientific insight into the molecular breeding of pineapples.