Dirichlet’s theorem, including the uniform setting and asymptotic setting, is one of the most fundamental results in Diophantine approximation. The improvement of the asymptotic setting leads to the well-approximable set (in words of continued fractions)

$$ \begin{align*} \mathcal{K}(\Phi):=\{x:a_{n+1}(x)\ge\Phi(q_{n}(x))\ \textrm{for infinitely many }n\in \mathbb{N}\}; \end{align*} $$

$$ \begin{align*} \mathcal{G}(\Phi):=\{x:a_{n}(x)a_{n+1}(x)\ge\Phi(q_{n}(x))\ \textrm{for infinitely many }n\in \mathbb{N}\}. \end{align*} $$

$\Phi _{1},\Phi _{2}:[1,+\infty )\rightarrow \mathbb {R}^{+}$

$\mathcal {G}(\Phi _{1})\!\setminus\! \mathcal {K}(\Phi _{2})$

$\mathcal {G}(\Phi )$

$\mathcal {K}(\Phi )$

$\Phi $

$\mathcal {G}(\Phi _{1})\!\setminus\! \mathcal {K}(\Phi _{2})$

$\Phi _1$

Business process management (BPM) has been the main driver behind company optimization and operational efficiency. However, the digitization era we live in necessitates that organizations be agile and adaptable. Delivering unprecedented rates of automation-fueled agility is necessary to be a part of this digital revolution. On the other hand, BPM automation cannot be done only by concentrating on procedure space and traditional planning methodologies. With the introduction of BPM, where the deployment of BPM with cloud computing has undergone enormous development lately, cloud computing has been considered a particularly active topic of study. Cloud computing points to the provision of dependable computing environments based on improved infrastructure availability and service quality without imposing a significant cost load. This research aims to discover the relationship between technical factors, financial factors, environmental factors, security of the cloud-based information systems, and the agile development of industrial BPM (IBPM). The present study aims to fill this gap and show how partial least squares structural equation modeling (SEM) can be employed in this field. Importance–performance map analysis (IPMA) evaluated the importance and performance of factors in the SEM. IPMA enables the identification of factors with relatively low performance but relatively high importance in shaping dependent variables. The empirical findings showed that four key factors (technical, financial, environmental, and security) positively influence the agile development of IBPM.

This 62-d research aimed to evaluate the effects of dietary lysine levels (DLL) and salinity on growth performance and nutrition metabolism of genetically improved farmed tilapia (GIFT) juveniles (Oreochromis niloticus). Six diets with lysine supplementation (1·34, 1·70, 2·03, 2·41, 2·72 and 3·04 % of DM) were formulated under different cultured salinities in a two-factorial design. The results indicated that supplemental lysine improved the specific growth rate (SGR) and weight gain (WG) and decreased the feed conversion ratio (FCR). Meanwhile, the fish had higher SGR and WG and lower FCR at 8 ‰ salinity. Except for moisture, the whole-body protein, lipid and ash content of GIFT were increased by 8 ‰ salinity, which showed that DLL (1·34 %) increased the whole-body fat content and DLL (2·41 %) increased whole-body protein content. Appropriate DLL up-regulated mRNA levels of protein metabolism-related genes such as target of rapamycin, 4EBP-1 and S6 kinase 1. However, 0 ‰ salinity reduced these protein metabolism-related genes mRNA levels, while proper DLL could improve glycolysis and gluconeogenesis mRNA levels but decrease lipogenesis-related genes mRNA levels in liver. 0 ‰ salinity improved GLUT2, glucokinase and G6 Pase mRNA levels; however, sterol regulatory element-binding protein 1 and fatty acid synthase mRNA levels were higher at 8 ‰ salinity. Moreover, 8 ‰ salinity also increased plasma total protein and cholesterol levels and decreased glucose levels. These results indicated that the recommended range of lysine requirement under different salinity was 2·03–2·20 % (0 ‰) and 2·20–2·41 % (8 ‰) and 8 ‰ salinity resulted in higher lysine requirements due to changes in the related nutrient metabolism, which might provide useful information for designing more effective feed formulations for GIFT cultured in different salinity environment.

In this study, we focus on the temporal behaviors – speed and rhythm – of outward foreign direct investment (OFDI) by emerging multinational enterprises (EMNEs) and examine the effect of such behaviors on innovation performance. Using a learning perspective, we argue that OFDI speed has an inverted U-shaped effect on EMNEs’ innovation performance, whereas the relationship between the uneven rhythm of OFDI and innovation performance is negative. The results, based on OFDI panel data of 1,092 Chinese firms, support our predictions that a moderate OFDI speed and a more regular pattern of OFDI expansion provide sources of competitiveness and contribute to firms’ innovation performance.

Sustainability encompasses social, economic and environmental issues with the primary aim to fulfil the needs of the present society without compromising the potential needs of future generations. Product design has been identified to greatly influence the sustainability of New Product Development. This study aims to identify and review the fundamental factors in which product design has the ability to influence and improve the overall environmental sustainability of a product. A comprehensive literature review has been performed to establish trends over the past four decades. The factors that have significant potential, such as the 6Rs, waste and energy, which aid designers in the implementation of environmental sustainability during the product design process have been identified and discussed. Through this analysis, a new conceptual framework has been conceived, facilitating designers in implementing environmental sustainability during product development. In addition, future research opportunities have been identified.

Athetis lepigone Möschler (Lepidoptera, Noctuidae) is a common maize pest in Europe and Asia. However, there is no long-term effective management strategy is available yet to suppress its population. Adults rely heavily on olfactory cues to locate their optimal host plants and oviposition sites. Pheromone-binding proteins (PBPs) are believed to be responsible for recognizing and transporting different odorant molecules to interact with receptor membrane proteins. In this study, the ligand-binding specificities of two AlepPBPs (AlepPBP2 and AlepPBP3) for sex pheromone components and host plant (maize) volatiles were measured by fluorescence ligand-binding assay. The results demonstrated that AlepPBP2 had a high affinity with two pheromones [(Z)-7-dodecenyl acetate, Ki = 1.11 ± 0.1 μM, (Z)-9-tetradecenyl acetate, Ki = 1.32 ± 0.15 μM] and ten plant volatiles, including (-)-limonene, α-pinene, myrcene, linalool, benzaldehyde, nonanal, 2-hexanone, 3-hexanone, 2-heptanone and 6-methyl-5-hepten-2-one. In contrast, we found that none of these chemicals could bind to AlepPBP3. Our results clearly show no significant differences in the functional characterization of the binding properties between AlepPBP2 and AlepPBP3 to sex pheromones and host plant volatiles. Furthermore, molecular docking was employed for further detail on some crucial amino acid residues involved in the ligand-binding of AlepPBP2. These findings will provide valuable information about the potential protein binding sites necessary for protein-ligand interactions which appear as attractive targets for the development of novel technologies and management strategies for insect pests.

Primitive lamprophyres in orogenic belts can provide crucial insights into the nature of the subcontinental lithosphere and the relevant deep crust–mantle interactions. This paper reports a suite of relatively primitive lamprophyre dykes from the North Qiangtang, central Tibetan Plateau. Zircon U–Pb ages of the lamprophyre dykes range from 214 Ma to 218 Ma, with a weighted mean age of 216 ± 1 Ma. Most of the lamprophyre samples are similar in geochemical compositions to typical primitive magmas (e.g. high MgO contents, Mg no. values and Cr, with low FeOt/MgO ratios), although they might have experienced a slightly low degree of olivine crystallization, and they show arc-like trace-element patterns and enriched Sr–Nd isotopic composition ((87Sr/86Sr)i = 0.70538–0.70540, ϵNd(t) = −2.96 to −1.65). Those geochemical and isotopic variations indicate that the lamprophyre dykes originated from partial melting of a phlogopite- and spinel-bearing peridotite mantle modified by subduction-related aqueous fluids. Combining with the other regional studies, we propose that slab subduction might have occurred during Late Triassic time, and the rollback of the oceanic lithosphere induced the lamprophyre magmatism in the central Tibetan Plateau.

Few surges on the Central Tibetan Plateau have been reported. Here, we report observations of a recent surging event of the Gangjiaquba Glacier in the Geladandong Peak region using surface velocity and morphology changes that were extracted from Landsat MSS/TM/ETM+/OLI images obtained from 1973 to 2019. The results reveal that the active surge of this glacier initiated at the end of summer in 2014 and terminated in 2016. The surge resulted in a total advance of 500 ± 11.2 m and many fresh crevasses in the surging zone. The maximum velocity was 1100 m a−1 during the active surge phase, which is much smaller than those observed in Karakoram but similar to observations in West Kunlun.

The study was conducted to determine the effects of three dietary Se sources, such as sodium-selenite (S-S), seleno-yeast (S-Y) and seleno-methionine (S-M), on Se concentration, glutathione peroxidase (GPX) and TXNRD activities, and mRNA expression of fifteen representative selenoproteins, and protein expression of four endoplasmic reticulum-resided selenoproteins in a wide range of tissues of yellow catfish. Compared with S-S and S-M groups, dietary S-Y significantly decreased growth performance and feed utilisation of yellow catfish. Dietary Se sources significantly influenced Se contents in the spleen, dorsal muscle and the kidney, GPX activities in spleen, kidney, intestine, muscle and mesenteric fat, and TXNRD activities in the heart, intestine and mesenteric fat. Among ten tested tissues, dietary Se sources influenced mRNA expression of GPX4 and SELENOK in three tissues; GPX3, SELENOS and TXNRD2 in four tissues; SELENOF, SELENON and DIO2 in five tissues; SELENOM, GPX1/2 and TXNRD3 in six tissues; SELENOW in seven tissue and SELENOP and SELENOT in eight tissues. Based on these observations above, S-S and S-M seem to be suitable Se sources for improving growth performance and feed utilisation of yellow catfish. Dietary Se sources differentially influence the expression of selenoproteins in various tissues of yellow catfish. For the first time, we determined the expression of selenoproteins in fish in responses to dietary Se sources, which contributes to a better understanding of the functions and regulatory mechanisms of selenoporteins.

Salicylic acid (SA), a phytohormone, has been considered to be a key regulator mediating plant defence against pathogens. It is still vague how SA activates plant defence against herbivores such as chewing and sucking pests. Here, we used an aphid-susceptible wheat variety to investigate Sitobion avenae response to SA-induced wheat plants, and the effects of exogenous SA on some defence enzymes and phenolics in the plant immune system. In SA-treated wheat seedlings, intrinsic rate of natural increase (rm), fecundity and apterous rate of S. avenae were 0.25, 31.4 nymphs/female and 64.4%, respectively, and significantly lower than that in the controls (P < 0.05). Moreover, the increased activities of phenylalanine-ammonia-lyase, polyphenol oxidase (PPO) and peroxidase in the SA-induced seedlings obviously depended on the sampling time, whereas activities of catalase and 4-coumarate:CoA ligase were suppressed significantly at 24, 48 and 72 h in comparison with the control. Dynamic levels of p-coumaric acid at 96 h, caffeic acid at 24 and 72 h and chlorogenic acid at 24, 48 and 96 h in wheat plants were significantly upregulated by exogenous SA application. Nevertheless, only caffeic acid content was positively correlated with PPO activity in SA-treated wheat seedlings (P = 0.031). These findings indicate that exogenous SA significantly enhanced the defence of aphid-susceptible wheat variety against aphids by regulating the plant immune system, and may prove a potential application of SA in aphid control.

Over recent decades, Chinese giant salamanders Andrias spp. have declined dramatically across much of their range. Overexploitation and habitat degradation have been widely cited as the cause of these declines. To investigate the relative contribution of each of these factors in driving the declines, we carried out standardized ecological and questionnaire surveys at 98 sites across the range of giant salamanders in China. We did not find any statistically significant differences between water parameters (temperature, dissolved oxygen, ammonia, nitrite, nitrate, salinity, alkalinity, hardness and flow rate) recorded at sites where giant salamanders were detected by survey teams and/or had been recently seen by local respondents, and sites where they were not detected and/or from which they had recently been extirpated. Additionally, we found direct and indirect evidence that the extraction of giant salamanders from the wild is ongoing, including within protected areas. Our results support the hypothesis that the decline of giant salamanders across China has been primarily driven by overexploitation. Data on water parameters may be informative for the establishment of conservation breeding programmes, an initiative recommended for the conservation of these species.

The soft actuator is made of superelastic material and embedded flexible material. In this paper, a kind of soft tube was designed and used to assemble two kinds of pneumatic soft actuators. The experiment and finite element analysis are used to comprehensively analyze and describe the bending, elongation, and torsion deformation of the soft actuator. The results show that the two soft actuators have the best actuation performance when the inner diameter of the soft tube is 4 mm. In addition, when the twisting pitch of the torsional actuator is 24 mm, its torsional performance is optimized. Finally, a device that can be used in the production line was assembled by utilizing those soft actuators, and some operation tasks were completed. This experiment provides some insights for the development of soft actuators with more complex motions in the future.

Hypertension represents one of the most common pre-existing conditions and comorbidities in Coronavirus disease 2019 (COVID-19) patients. To explore whether hypertension serves as a risk factor for disease severity, a multi-centre, retrospective study was conducted in COVID-19 patients. A total of 498 consecutively hospitalised patients with lab-confirmed COVID-19 in China were enrolled in this cohort. Using logistic regression, we assessed the association between hypertension and the likelihood of severe illness with adjustment for confounders. We observed that more than 16% of the enrolled patients exhibited pre-existing hypertension on admission. More severe COVID-19 cases occurred in individuals with hypertension than those without hypertension (21% vs. 10%, P = 0.007). Hypertension associated with the increased risk of severe illness, which was not modified by other demographic factors, such as age, sex, hospital geological location and blood pressure levels on admission. More attention and treatment should be offered to patients with underlying hypertension, who usually are older, have more comorbidities and more susceptible to cardiac complications.

Fullerene dimers have attracted extensive attention due to their unique structures and fascinating properties. Here, fullerene dimer derivatives with four to six carbon atoms in the esters are designed and synthesized. The property differences that caused by the carbon number in the esters of the fullerene dimers are investigated by performing their electrochemical, optical, and photoelectric measurements. As the carbon atom numbers in the esters increase from four to five and six, the absorption intensities increase to 1.6- and 4.4-folds. The intensities of the fluorescence spectra increase to 1.8- and 5.2-folds. Their photocurrent increases to 2- and 7-folds under the irradiation of a 405-nm laser. The LUMO energy levels move downward slightly from −3.89 to −3.90 and −3.92 eV, respectively. Our results indicate that as the carbon number increases, the carbon chain lengths in the ester structures increase, very slight effects produced on the energy levels of the fullerene dimers, but strongly contribute to their chemical activities and thus the photoelectronic efficiencies.

This Research Reflection short review presents an overview of the effects of heat stress on dairy cattle udder health and discusses existing heat stress mitigation strategies for a better understanding and identification of appropriate abatement plans for future stress management. Due to high ambient temperatures with high relative humidity in summer, dairy cows respond by changes of physical, biochemical and biological pathways to neutralize heat stress resulting in decreased production performance and poorer immunity resulting in an increased incidence of intramammary infections (IMI) and a higher somatic cell count (SCC). In vitro studies on bovine polymorphonuclear cells (PMN) suggested that heat stress reduces the phagocytosis capacity and oxidative burst of PMN and alters the expression of apoptotic genes and miRNA which, together with having a negative effect on the immune system, may explain the increased susceptibility to IMI. Although there are limited data regarding the incidence rate of clinical mastitis in many countries or regions, knowledge of SCC at the cow or bulk tank level helps encourage farmers to improve herd health and to develop strategies for infection prevention and cure. Therefore, more research into bulk tank SCC and clinical mastitis rates is needed to explain the effect of heat stress on dairy cow udder health and functions that could be influenced by abatement plans.