Lattice-Valued Convergence Spaces: Weaker Regularity and p

By using some lattice-valued Kowalsky’s dual diagonal conditions, some weaker regularities for Jäger’s generalized stratified L-convergence spaces and those for Boustique et al’s stratified L-convergence spaces are defined and studied. Here, the lattice L is a complete Heyting algebra. Some characterizations and properties of weaker regularities are presented. For Jäger’s generalized stratified L-convergence spaces, a notion of closures of stratified L-filters is introduced and then a new p-regularity is defined. At last, the relationships between p-regularities and weaker regularities are established

Single Machine Scheduling to Maximize Number of Batch of Jobs with Uncertain Processing Times

The paper studies single-machine scheduling to maximize number of batch of jobs with uncertain processing times. Firstly, an expected value model to maximize number of batch of jobs processed is given based on uncertainty theory. Then, the model is transformed into a deterministic integer programming model and its properties are provided. Further, its arithmetic, called Man-computer Alternant Arithmetic, is presented. Finally, a numerical example on the model is given

Comparative mapping of chalkiness components in rice using five populations across two environments

BACKGROUND: Chalkiness is a major constraint in rice production because it is one of the key factors determining grain quality (appearance, processing, milling, storing, eating, and cooking quality) and price. Its reduction is a major goal, and the primary purpose of this study was to dissect the genetic basis of grain chalkiness. Using five populations across two environments, we also sought to determine how many quantitative trait loci (QTL) can be consistently detected. We obtained an integrated genetic map using the data from five mapping populations and further confirmed the reliability of the identified QTL. RESULTS: A total of 79 QTL associated with six chalkiness traits (chalkiness rate, white core rate, white belly rate, chalkiness area, white core area, and white belly area) were mapped on 12 chromosomes using five populations (two doubled haploid lines and three recombinant inbred lines) across two environments (Hainan in 2004 and Wuhan in 2004). The final integrated map included 430 markers; 58.3% of the QTL clustered together (QTL clusters), 71.4% of the QTL clusters were identified in two or more populations, and 36.1% of the QTL were consistently detected in the two environments. The QTL could be detected again and showed dominance (qWBR1, qWBR8, qWBR12, and qCR5) or overdominance effects (qWCR7) for the rate of the white belly or white core, respectively, and all four QTL clusters derived from Zhenshan 97 controlling white belly rate were stably and reliably identified in an F(2) population. CONCLUSIONS: Our results identified 79 QTL associated with six chalkiness traits using five populations across two environments and yielded an integrated genetic map, indicating most of the QTL clustered together and could be detected in different backgrounds. The identified QTL were stable and reliable in the F(2) population, and they may facilitate our understanding of the QTL related to chalkiness traits in different populations and various environments, the relationships among the various chalkiness QTL, and the genetic basis for chalkiness. Thus, our results may be immediately used for map-based cloning of important QTL and in marker-assisted breeding to improve grain quality in rice breeding

Expression profiling and integrative analysis of the CESA/CSL superfamily in rice

<p>Abstract</p> <p>Background</p> <p>The cellulose synthase and cellulose synthase-like gene superfamily (<it>CESA</it>/<it>CSL</it>) is proposed to encode enzymes for cellulose and non-cellulosic matrix polysaccharide synthesis in plants. Although the rice (<it>Oryza sativa </it>L.) genome has been sequenced for a few years, the global expression profiling patterns and functions of the <it>OsCESA</it>/<it>CSL </it>superfamily remain largely unknown.</p> <p>Results</p> <p>A total of 45 identified members of <it>OsCESA</it>/<it>CSL </it>were classified into two clusters based on phylogeny and motif constitution. Duplication events contributed largely to the expansion of this superfamily, with Cluster I and II mainly attributed to tandem and segmental duplication, respectively. With microarray data of 33 tissue samples covering the entire life cycle of rice, fairly high <it>OsCESA </it>gene expression and rather variable <it>OsCSL </it>expression were observed. While some members from each <it>CSL </it>family (<it>A1</it>, <it>C9</it>, <it>D2</it>, <it>E1</it>, <it>F6 </it>and <it>H1</it>) were expressed in all tissues examined, many of <it>OsCSL </it>genes were expressed in specific tissues (stamen and radicles). The expression pattern of <it>OsCESA</it>/<it>CSL </it>and <it>OsBC1L </it>which extensively co-expressed with <it>OsCESA</it>/<it>CSL </it>can be divided into three major groups with ten subgroups, each showing a distinct co-expression in tissues representing typically distinct cell wall constitutions. In particular, <it>OsCESA1, -3 & -8 </it>and <it>OsCESA4, -7 & -9 </it>were strongly co-expressed in tissues typical of primary and secondary cell walls, suggesting that they form as a cellulose synthase complex; these results are similar to the findings in <it>Arabidopsis</it>. <it>OsCESA5</it>/<it>OsCESA6 </it>is likely partially redundant with <it>OsCESA3 </it>for OsCESA complex organization in the specific tissues (plumule and radicle). Moreover, the phylogenetic comparison in rice, <it>Arabidopsis </it>and other species can provide clues for the prediction of orthologous gene expression patterns.</p> <p>Conclusions</p> <p>The study characterized the <it>CESA</it>/<it>CSL </it>of rice using an integrated approach comprised of phylogeny, transcriptional profiling and co-expression analyses. These investigations revealed very useful clues on the major roles of <it>CESA</it>/<it>CSL</it>, their potentially functional complement and their associations for appropriate cell wall synthesis in higher plants.</p

Soil chemistry, metabarcoding, and metabolome analyses reveal that a sugarcane—Dictyophora indusiata intercropping system can enhance soil health by reducing soil nitrogen loss

IntroductionGreater amounts of fertilizer are applied every year to meet the growing demand for food. Sugarcane is one of the important food sources for human beings.MethodsHere, we evaluated the effects of a sugarcane—Dictyophora indusiata (DI) intercropping system on soil health by conducting an experiment with three different treatments: (1) bagasse application (BAS process), (2) bagasse + DI (DIS process), and (3) the control (CK). We then analyzed soil chemistry, the diversity of soil bacteria and fungi, and the composition of metabolites to clarify the mechanism underlying the effects of this intercropping system on soil properties.Results and discussionSoil chemistry analyses revealed that the content of several soil nutrients such as nitrogen (N) and phosphorus (P) was higher in the BAS process than in the CK. In the DIS process, a large amount of soil P was consumed by DI. At the same time, the urease activity was inhibited, thus slowing down the loss of soil in the DI process, while the activity of other enzymes such as β-glucosidase and laccase was increased. It was also noticed that the content of lanthanum and calcium was higher in the BAS process than in the other treatments, and DI did not significantly alter the concentrations of these soil metal ions. Bacterial diversity was higher in the BAS process than in the other treatments, and fungal diversity was lower in the DIS process than in the other treatments. The soil metabolome analysis revealed that the abundance of carbohydrate metabolites was significantly lower in the BAS process than in the CK and the DIS process. The abundance of D(+)-talose was correlated with the content of soil nutrients. Path analysis revealed that the content of soil nutrients in the DIS process was mainly affected by fungi, bacteria, the soil metabolome, and soil enzyme activity. Our findings indicate that the sugarcane–DIS intercropping system can enhance soil health

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer&rsquo;s diagonal condition, the other approach extends the G&auml;hler&rsquo;s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures

Stratified lattice-valued neighborhood tower group

In this paper, by generalizing Höhle and Šostak's stratified L-fuzzy neighborhood system, the notion of stratied L-neighborhood tower space is introduced. Then by enriching a group structure on a stratied L-neighborhood tower space, the notion of stratied L-neighborhood tower group is proposed. It is proved that this notion can be regarded as a natural extension of stratied L-neighborhood group discussed by Ahsanullah et al. Indeed, the category of stratied L-neighborhood tower groups includes the category of stratied L-neighborhood groups as a concretely reflective (resp., coreflective) full subcategory. Furthermore, it is shown that the group operations enrich a stratied L-neighborhood tower space to be topological (generally, stratied L-neighborhood tower space is not topological). This means that there is no difference between stratied L-neighborhood tower group and topologically stratied L-neighborhood tower group.Mathematics Subject Classification (2010): 54A40, 54H11, 54B30Keywords: Fuzzy topological group, lattice-valued topological group, L-neighborhood system, stratied L-neighborhood tower grou