Heisenberg double as braided commutative Yetter-Drinfel'd module algebra over Drinfel'd double in multiplier Hopf algebra case

Based on a pairing of two regular multiplier Hopf algebras $A$ and $B$, Heisenberg double $\mathscr{H}$ is the smash product $A \# B$ with respect to the left regular action of $B$ on $A$. Let $\mathscr{D}=A\bowtie B$ be the Drinfel'd double, then Heisenberg double $\mathscr{H}$ is a Yetter-Drinfel'd $\mathscr{D}$-module algebra, and it is also braided commutative by the braiding of Yetter-Drinfel'd module, which generalizes the results in [10] to some infinite dimensional cases.Comment: 18 pages. arXiv admin note: text overlap with arXiv:math/0404029 by other author

Parametric representations of BiHom-Hopf algebras

summary:The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new $n$-monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras

Tutorial on big spectrum data analytics for space information networks

Abstract Space information network (SIN) is an integrated network system of various space information platforms (e.g., satellites, stratospheric airships, manned or unmanned aerial vehicles) to enable real-time sensing, collection, transmission, and processing of various space information, as well as to realize both global and localized tailor-made systematized information services. Spectrum usage and management becomes a more and more serious issue in SIN mainly for the following reasons: (i) the paradox between spectrum shortage and spectrum under-utilization, (ii) the complex electromagnetic spectrum environment with tremendous spectrum devices and ubiquitous spectrum interference, and (iii) the spectrum disorder and spectrum attack. In this paper, we propose to empower SIN with big spectrum data analytics for dynamic spectrum sharing, real-time spectrum monitoring, and intelligent spectrum control. Specifically, we first identify critical spectrum issues in developing SIN and highlight that spectrum data analytics is the key solution to address these issues via spectrum sensing, spectrum data statistical inference and knowledge discovery, spectrum data-driven decision optimization, and spectrum experiment validation and evaluation, etc. Then, we introduce the concept of big spectrum data in SIN and analyze its characteristics, including volume, value, variety, viability, veracity, and velocity. Next, we discuss the emerging use cases and highlight research frontiers

Identifying the Influencing Factors of Plastic Film Mulching on Improving the Yield and Water Use Efficiency of Potato in the Northwest China

Potato is an important crop in the Northwest China, however, its production is constrained by water scarcity. Plastic mulching film is an efficient technical measure to alleviate potato production restrictions. Therefore, studying the response of potato yield and water use efficiency to plastic mulching film is of great significance. The study conducted a meta-analysis to quantify the effect of plastic film on potato yield and water use efficiency in the Northwest. The study then quantified the effects of different levels of natural conditions (mean annual precipitation, mean annual accumulated temperature ≥ 10 °C), fertilizer application (nitrogen fertilizer, phosphate fertilizer, potassium fertilizer), cultivation measures (planting density, cultivation method, mulching method), and mulching properties (mulching color, mulching thickness) through subgroups analysis. Finally, the random forest model was used to quantify the importance of factors. Plastic film mulching increased yield by 27.17% and water use efficiency by 27.16%, which had a better performance under relatively lower mean annual precipitation, low mean annual accumulated temperature ≥ 10 °C, relatively lower fertilizer application, planting density of 15,000–45,000 plants·ha−1, ridge, and black mulching. Natural conditions, fertilization measures were vital to improve productivity. The research results can provide reference for agricultural management strategies of potato cultivation using plastic film in the Northwest China and other potato-producing areas

Maize basal internode development significantly affects stalk lodging resistance

Stalk lodging in maize causes yield and quality losses worldwide. This could potentially be prevented through breeding and improved crop management. Breeding efforts and management optimization are however, hampered by the lack of an internode growth model and an indicator for stalk lodging resistance. With this study, we aim to contribute to a solution for this problem. We report on the results of a two-year field study in which we measured and analyzed plant traits assumed to be related to stalk lodging resistance, in five cultivars. These traits include plant and basal internode morphology, dry matter constituents accumulation, and mechanical strength of basal internode. Results from a logistic regression analysis indicate that, the stalk lodging incidence was significantly affected by the development process of the basal internode. The rapid accumulation duration of lignin, internode plumpness and cellulose were found to be the most important contributors to mechanical strength of basal internode. The correlation between Rind penetration strength (PS) and stalk lodging rate was found to be higher than the correlation between bending strength (BS) and the stalk lodging rate. In addition, PS was found to be more stable than BS over development stages and years. Dry matter constituents accumulation in the basal internode, especially lignin accumulation, were found to be the dominant process determining the mechanical strength of the basal internode. Breeding and crop management strategies aiming to prolong the duration of rapid lignin and dry matter accumulation in the basal internode may thus significantly contribute to improved lodging resistance in future maize cultivars