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In this paper, we carry out in-depth research centering around the Harnack inequality for positive solutions to nonlinear heat equation on Finsler metric measure manifolds with weighted Ricci curvature Ric ∞ bounded below. Aim on this topic, we first give a volume comparison theorem of Bishop-Gromov type. Then we prove a weighted Poincaré inequality by using Whitney-type coverings technique and give a local uniform Sobolev inequality. Further, we obtain two mean value inequalities for positive subsolutions and supersolutions of a class of parabolic differential equations. From the mean value inequality, we also derive a local gradient estimate for positive solutions to heat equation. Finally, as the application of the mean value inequalities and weighted Poincaré inequality, we get the desired Harnack inequality for positive solutions to heat equation. [ABSTRACT FROM AUTHOR]

We study functional and geometric inequalities on complete Finsler measure spaces with the weighted Ricci curvature Ric ∞ bounded below. We first obtain some local uniform Poincaré inequalities and Sobolev inequalities. Then, we prove a mean value inequality for nonnegative subsolutions of elliptic equations. Further, we derive local and global Harnack inequalities for positive harmonic functions. Finally, we establish a global gradient estimate for positive harmonic functions on forward complete non-compact Finsler measure spaces. Besides, as an application of the mean value inequality, we prove a Liouville type theorem for harmonic functions. [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce and study the weakly weighted Einstein–Finsler metrics. First, we show that weakly weighted Einstein–Kropina metrics must be of isotropic S-curvature with respect to the Busemann–Hausdorff volume form under a certain condition about the weight constants. Then we characterize weakly weighted Einstein–Kropina metrics completely via their navigation expressions or via α and β , respectively. In particular, when ν ≠ 0 (or ν = κ = 0 , respectively) and S-curvature with respect to the Busemann–Hausdorff volume form is isotropic, we prove that a Kropina metric determined by navigation data (h, W) is a weakly weighted Einstein metric if and only if the Riemann metric h is a weighted Einstein–Riemann metric. [ABSTRACT FROM AUTHOR]

The potato tuberworm, Phthorimaea operculella Zeller, is an oligophagous pest feeding on crops mainly belonging to the family Solanaceae. It is one of the most destructive pests of potato worldwide and attacks foliage and tubers in the field and in storage. However, the lack of a high-quality reference genome has hindered the association of phenotypic traits with their genetic basis. Here, we report on the genome assembly of P. operculella at the chromosomal level. Using Illumina, Nanopore and Hi-C sequencing, a 648.2 Mb genome was generated from 665 contigs, with an N50 length of 3.2 Mb, and 92.0% (596/648.2 Mb) of the assembly was anchored to 29 chromosomes. In total, 16619 genes were annotated, and 92.4% of BUSCO genes were fully represented. The chromosome-level genome of P. operculella will provide a significant resource for understanding the genetic basis for the biological study of this insect, and for promoting the integrative management of this pest in future. Measurement(s) whole genome sequencing Technology Type(s) Illumina NovaSeq. 6000 • Oxford Nanopore Sequencing Sample Characteristic - Organism Phthorimaea operculella Sample Characteristic - Location Yunnan Province, Southwest China [ABSTRACT FROM AUTHOR]

Complexes containing rare-earth ions attract great attention for their technological applications ranging from spintronic devices to quantum information science. While charged rare-earth coordination complexes are ubiquitous in solution, they are challenging to form on materials surfaces that would allow investigations for potential solid-state applications. Here we report formation and atomically precise manipulation of rare-earth complexes on a gold surface. Although they are composed of multiple units held together by electrostatic interactions, the entire complex rotates as a single unit when electrical energy is supplied from a scanning tunneling microscope tip. Despite the hexagonal symmetry of the gold surface, a counterion at the side of the complex guides precise three-fold rotations and 100% control of their rotational directions is achieved using a negative electric field from the scanning probe tip. This work demonstrates that counterions can be used to control dynamics of rare-earth complexes on materials surfaces for quantum and nanomechanical applications. Rare-earth elements are vital to advanced technological applications ranging from spintronic devices to quantum information science. Here, the authors formed charged rare-earth complexes on a material surface and demonstrated atomically precise control on their rotational dynamics. [ABSTRACT FROM AUTHOR]

Motivated by the emerging practices of China's major e-commerce platforms, we investigate the effect of consumer's valuation change, deposit expansion and return policy on retailer's advance booking decisions. We establish the retailer's expected profit based on a two-stage newsvendor model and derive his optimal deposit and order quantity decisions under different scenarios. Our conclusions show that: (1) the retailer gains further profit under the advance selling strategy with a deposit, due to the reduction of inventory risk and exploitation of consumer's valuation uncertainty; (2) the retailer benefits more from advance selling when he has a lower profit margin or the consumers have low-level prior valuations; (3) the effectiveness of advance selling on exploiting consumer's valuation uncertainty will be weakened if the retailer allows customers to return products; (4) a lower deposit expansion rate leads to higher deposit and expected profit. [ABSTRACT FROM AUTHOR]

We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop–Gromov type. As one of the applications, we obtain an upper bound for volumes of the Finsler manifolds. Further, when the S-curvature is bounded on the whole manifold, we obtain a theorem of Bonnet–Myers type on Finsler manifolds. Finally, we obtain a sharp Poincaré–Lichnerowicz inequality by using integrated Bochner inequality, from which we obtain a better lower bound for the first eigenvalue on the Finsler manifolds. [ABSTRACT FROM AUTHOR]

The fungus Isaria javanica is an important entomopathogen that parasitizes various insects and is effective for pest control. In this study, we sequenced and assembled the genomes (IJ1G and IJ2G) of two I. javanica strains isolated from different insects. The genomes were approximately 35 Mb in size with 11,441 and 11,143 protein-coding genes, respectively. Using a phylogenomic approach, we evaluated genome evolution across five entomopathogenic fungi in Cordycipitaceae. By comparative genome analysis, it was found that family S53 serine peptidases were expanded in Cordycipitaceae entomopathogens, particularly in I. javanica. Gene duplication events were identified based on phylogenetic relationships inferred from 82 S53 peptidases within six entomopathogenic fungal genomes. Moreover, we found that carbohydrate-active enzymes and proteinases were the largest secretory protein groups encoded in the I. javanica genome, especially chitinases (GH18), serine and aspartic peptidases (S53, S08, S10, A01). Pathogenesis-related genes and genes for bacterial-like toxins and secondary metabolites were also identified. By comparative transcriptome analysis, differentially expressed genes in response to insect nutrients (in vitro) were identified. Moreover, most S53 peptidases were detected to be significantly upregulated during the initial fungal infection process in insects (in vivo) by RT-qPCR. Our results provide new clues about understanding evolution of pathogenic proteases and may suggest that abundant S53 peptidases in the I. javanica genome may contribute to its effective parasitism on various insects. [ABSTRACT FROM AUTHOR]

For an ( α, β)-metric (non-Randers type) of isotropic S-curvature on an n-dimensional manifold with non-constant norm ║ β║, we first show that n = 2, and then we characterize such a class of two-dimensional ( α, β)-manifolds with some PDEs, and also construct some examples for such a class. [ABSTRACT FROM AUTHOR]

In this paper, we study a special class of Finsler metrics, called ( α, β)-metrics, which are defined by F = αϕ( β/α), where α is a Riemannian metric and β is a 1-form. We show that if ϕ = ϕ( s) is a polynomial in s, it is Einstein if and only if it is Ricci-flat. We also determine the Ricci-flat ( α, β)-metrics which are not of the type F = ( α + ɛβ)/ α. [ABSTRACT FROM AUTHOR]

This paper summarizes the results of our study of the pinewood nematode ( Bursaphelenchus xylophilus). By population genetic analysis, it was determined that there was no genetic bottle caused by the founder effect and genetic drift in the Chinese invasive population. Multiple invasions with large amounts of nematodes from different sources led to rich genetic diversity in the invasive population. Keeping high genetic diversity in the invasive process may be one of the genetic mechanisms in its successful invasion. By testing interspecies competition, it was shown that, with high fecundity and a strong competitive ability, B. xylophilus outcompeted the native species B. mucronatus in the natural ecosystem during the invasion process. Competitive displacement may be one of the ecological mechanisms of B. xylophilus’s invasion. In addition, an unequal interspecific hybridization with introgress was in favor of the invasive species which also accelerated the replacement of B. mucronatus by B. xylophilus. The structures, functions and evolutions of a few important genes that are closely related to the ecological adaptation of pinewood nematodes were studied to explore the molecular mechanism of its ecological adaptations. Further, the resistance and resilience mechanism of the pine ecosystem invaded by pinewood nematodes was also investigated. The results of these studies uncovered a portion of the genetic and ecological mechanisms of PWN’s successful invasion and laid a foundation for further study to obtain a comprehensive interpretation of the mechanisms of the nematode invasion. The results also provided a scientific basis for effectively controlling the occurrence and spread of pine wilt disease which is caused by nematodes. Various aspects requiring further investigation are considered. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We characterize these metrics with isotropic S-curvature. [ABSTRACT FROM AUTHOR]

Based on the sequence analysis of 5.8S subunit and internal transcribed spacers (ITS) of ribosomal RNA gene (rDNA), the molecular phylogenetic tree of representative species of Pipizini and three groups of Syrphidae with different feeding habits (seven species belong to six genera) was constructed. Meanwhile, the phylogenetic tree of tribes (including Pipizini and other 17 tribes of Syrphidae) was constructed using morphological characteristics of adults and larvae and the number of chromosomes. Both the results show that the relationship between Pipizini and predatory groups is closer than that between Pipizini and saprophagous groups. So it is suggested that Pipizini be transferred from Milesiinae to Syrphinae. [ABSTRACT FROM AUTHOR]