Step-like contrast structure of singularly perturbed optimal control problem

In this paper, the existence of step-like contrast structure for a class of singularly perturbed optimal control problem is shown by the contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. Finally, an example is presented to show the result

An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation

The multiterm fractional differential equation has a wide application in engineering problems. Therefore, we propose a method to solve multiterm variable order fractional differential equation based on the second kind of Chebyshev Polynomial. The main idea of this method is that we derive a kind of operational matrix of variable order fractional derivative for the second kind of Chebyshev Polynomial. With the operational matrices, the equation is transformed into the products of several dependent matrices, which can also be viewed as an algebraic system by making use of the collocation points. By solving the algebraic system, the numerical solution of original equation is acquired. Numerical examples show that only a small number of the second kinds of Chebyshev Polynomials are needed to obtain a satisfactory result, which demonstrates the validity of this method

Unraveling the Complex Trait of Harvest Index with Association Mapping in Rice (Oryza sativa L.)

Harvest index is a measure of success in partitioning assimilated photosynthate. An improvement of harvest index means an increase in the economic portion of the plant. Our objective was to identify genetic markers associated with harvest index traits using 203 O. sativa accessions. The phenotyping for 14 traits was conducted in both temperate (Arkansas) and subtropical (Texas) climates and the genotyping used 154 SSRs and an indel marker. Heading, plant height and weight, and panicle length had negative correlations, while seed set and grain weight/panicle had positive correlations with harvest index across both locations. Subsequent genetic diversity and population structure analyses identified five groups in this collection, which corresponded to their geographic origins. Model comparisons revealed that different dimensions of principal components analysis (PCA) affected harvest index traits for mapping accuracy, and kinship did not help. In total, 36 markers in Arkansas and 28 markers in Texas were identified to be significantly associated with harvest index traits. Seven and two markers were consistently associated with two or more harvest index correlated traits in Arkansas and Texas, respectively. Additionally, four markers were constitutively identified at both locations, while 32 and 24 markers were identified specifically in Arkansas and Texas, respectively. Allelic analysis of four constitutive markers demonstrated that allele 253 bp of RM431 had significantly greater effect on decreasing plant height, and 390 bp of RM24011 had the greatest effect on decreasing panicle length across both locations. Many of these identified markers are located either nearby or flanking the regions where the QTLs for harvest index have been reported. Thus, the results from this association mapping study complement and enrich the information from linkage-based QTL studies and will be the basis for improving harvest index directly and indirectly in rice

Phase relations in the Ta2O5-WO3-SiO2 system

Subsolidus relations and liquidus boundaries in the TaO-WO-SiO system at temperatures ranging from 1200 °C to 1500 °C were investigated. Phase diagrams were constructed. Compounds with stoichiometries of TaWO, TaWO and TaWO formed in the TaO-WO subsystem at 1200 °C. SiO was compatible with each of the compounds. A solid solution with a formula of (1 − x) TaO·xWO formed on the TaO-WO line in the compositional range of TaO:WO > 11:4. SiO had a maximum solubility of 25% SiO in the solid solution. Liquid phase first appeared in the WO-rich corner at 1300 °C. As the temperature was increased up to 1500 °C, the liquidus area boundary gradually expanded towards the SiO- and the TaO-rich corners

The Riddle of the Sphinx: Progress in Leptomeningeal Metastasis of Non–Small Cell Lung Cancer

Leptomeningeal metastasis (LM) is a serious complication of advanced non–small cell lung cancer (NSCLC), and the incidence of LM has been increasing yearly in recent times. There is no consensus on the best treatment modality for LM, which underscores a difficult problem in the management of advanced NSCLC patients. The existing treatments include molecular targeted therapy, systemic chemotherapy, local radiotherapy, antivascular tumor therapy, intrathecal chemotherapy, and immunotherapy, but their efficacy is not satisfactory. In this article, we briefly describe the clinical manifestations, diagnosis, and treatment of NSCLC-LM and discuss progress regarding evaluation of the efficacy of LM treatment to better provide a necessary reference for clinical practice and clinical trial evaluation