APPLICATIONS OF THE BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE NORM OF MERCER KERNEL MATRICES

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.

APPLICATIONS OF BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE COVERING NUMBER

The paper deals with estimates of the covering number for some Mercer kernel Hilbert space with Bernstein-Durrmeyer operators. We first give estimates of l2- norm of Mercer kernel matrices reproducing by the kernelsK（α,β）（x,y）：=∑∞k=0 Ck（α,β）（x）Qk（α,β）（y）,where Qk（α,β） （x） are the Jacobi polynomials of order k on （0, 1 ）, Ck（α,β） 〉 0 are real numbers, and from which give the lower and upper bounds of the covering number for some particular reproducing kernel Hilbert space reproduced by Kα,β （x, y）.

The Tate Kernel of the Number Field Q (-3)

A complete characterization of Tate kernel of the number field Q (-3) is given.Our method can also be used in other fields.

Identification of QTL for kernel number-related traits in a rice chromosome segment substitution line and fine mapping of qSP1

A chromosome segment substitution line (CSSL) is a powerful tool for combining quantitative trait locus (QTL) mapping with the pyramiding of desirable alleles. The rice CSSL Z1364 with increased kernel number was identified in a BC3F8 population derived from a cross of Nipponbare as the recipient with Xihui 18 as the donor parent. Z1364 carried three substitution segments distributed on chromosomes 1, 6, and 8. The mean substitution length was 1.19 Mb. Of 17 QTL identified on the substitution segments, qSP1 for spikelets per panicle, qSSD1 for seed-set density, and qNSB1 for number of secondary branches explained respectively 57.34%, 87.7%, and 49.44% of the corresponding phenotypic variance and were all linked to RM6777. Chi-square analysis showed that the increased kernel number in Z1364 was inherited recessively by a single gene. By fine mapping, qSP1 was delimited to a 50-kb region on the short arm of chromosome 1. Based on DNA sequence, a previously uncharacterized rice homolog of Arabidopsis thaliana AT4G32551 was identified as a candidate gene for qSP1 in which mutation increases the number of spikelets and kernels in Z1364. qSP1 was expressed in all tissues, but particularly in 1-cm panicles. The expression levels of OsMADS22, GN1A, and DST were upregulated and those of LAX2, GNP1, and GHD7 were downregulated in Nipponbare. These results provide a foundation for functional research on qSP1.

ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES

Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.

Quantifying.Associations among Dimensions of Ears and Their Form Factors in Maize(Zea Mays)Using Dimensional Analysis

Ear morphological traits such as volume and shape are important features of maize and the quantitative associations among them can help understand kernel yield determination. 150 mature ears each of 4 maize cultivars were collected from field experiments, and ear length(L), diameter(D), area(S) and volume(V) were recorded for individual ears, kernel weight per ear also recorded for a portion of the examined ears. Following principles of dimensional analysis, 8 theoretical equations of 3 sets,which relate ear higher dimensions to its length and diameter, were developed and parameterized and validated with the field observations. The 3 optimized equations showed that the shape of ears in maize can be featured with 3 dimensionless form factors, namely diameter-to-length ratio(c=D/L), areal form factor(b=S/L/D), and volumetric form factor(a=V/L/D/D). Statistically,all of them were significantly different among cultivars, and a's values varied from 0.582 to 0.612, and b's 0.839-0.868, and c's 0.242-0.308. Volumetric form factor and areal form factor could estimate precisely ear volume and area respectively, but diameter-to-length ratio was not suitable to estimate ear diameter by its length. Ear volume explained almost all variation of ear kernel weight and product L*D*D did the same substantially. Dimensional analysis proved to be promising in understanding relationship among morphological traits of ears in maize. Its application in crop researches should improve our knowledge of the physical properties of crop plants.

CALCULATION FOR KERNEL OF INTERVAL GREY NUMBER BASED ON BARYCENTER APPROACH

The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.

Rapid Determination of Seed Number and Thousand Kernel Weight of Asparagus officinalis L.Using Image Processing Method

Asparagus officinalis L.is favored by its high health function,but its hybrid seeds are expensive.The amount of seed,seed plumpness and germination rate are related to the production costs of breeding enterprises and large growers.Therefore,it is necessary to investigate the seed number and thousand kernel weight of A.officinalis L.This study developed a quick and accurate method to measure the seed number and thousand kernel weight of A.officinalis L.using image processing technology.Seed sample of A.officinalis L.was scanned with 200 dpi resolution,and the seed number was then obtained using Image-ProPlus software.After weighing the seeds,thousand kernel weight was finally calculated.By recording‘macro’,the batch processing of the samples can also be realized.This method is simple and accurate,and can greatly save the time of investigation.

Dynamics of Brix and pH of Flag Leaf Sap of Winter Wheat Cultivars and Their Relationship with Grain Yield Components

Plant tissue sap analysis is becoming an established tool for crop fertilization recommendation. Few research was conducted to use it as screening tools in crop breeding. With introduction of hhand-held sap analysis meters, sap analysis is becoming a promising tool for genotype screening. In this study, we measured Brix and pH of flag leaf juice of 10 winter wheat genotypes after heading stage. Brix value tended to increase during the measurement period. Brix value of flag leaf sap was negatively correlated with kernel number per spike and grain yield per spike, positively correlated with kernel weight. The pH values of flag leaf sap were negatively correlated with kernel number per spike and grain yield per spike, positively correlated with kernel weight.

Effect of Planting Density, Irrigation Regimes, and Maize Hybrids with Varying Ear Size on Yield, and Aflatoxin and Fumonisin Contamination Levels

Corn (maize, Zea mays L.) hybrids expressing the flexibility trait in ear size (number of kernels per ear) are marketed for ability to give higher yields under adverse conditions. Altered kernel number is associated with altered number of silk, a major route for infection of kernels by aflatoxin-producing fungi such as Aspergillus flavus. The effect of plant density and irrigation level on yield and accumulation of aflatoxins and fumonisins in harvested grain was compared in a fixed-ear hybrid (Pioneer 33K81), a semi-flexible ear hybrid (Pioneer 3223) and a flexible ear hybrid (Golden Acres 8460) over a range of seeding densities (49,400, 61,750, 74,700, 86,450, and 98,800 seeds·ha–1) in non-irrigated, moderately-irrigated (6.4 cm soil water deficit) and well-irrigated plots (3.8 cm soil water deficit), during three years with variable rainfall. Irrigation increased yields in all hybrids, but in the absence of irrigation, yields were highest with the semi-flexible ear trait hybrid. In general, the hybrid with the flexible ear trait had lower optimal seeding densities than the other hybrids for each soil water regime. In general, kernel number was least affected by seeding density in the hybrid with fixed-ear trait compared to the semi- and flexible ear hybrids. The lowest levels of aflatoxin and of fumonisin contamination in harvested grain were associated with the flexible ear trait at all rainfall and irrigation levels, but there was no evidence that reducing stress by lowering seeding density reduced mycotoxin contamination. Inoculation with A. flavus resulted in much higher levels of aflatoxin and significantly higher levels of fumonisin contamination in grain of all hybrids under most conditions of rainfall and irrigation, suggesting that factors that promote A. flavus infection can affect production of both mycotoxins.

Kernel(λ)之元的辛平延之积

在局部环上对辛群的生成问题进行研究,给出了辛变换的亏失数概念,将局部环上辛群的Kernel(λ)的元表示为辛平延之积.

Natural variations of HvSRN1 modulate the spike rachis node number in barley

Grain number,one of the major determinants of yield in Triticeae crops,is largely determined by spikelet number and spike rachis node number(SRN).Here,we identified three quantitative trait loci(QTLs)for SRN using 145 recombinant inbred lines derived from a barley R90/1815D cross.qSRN1,the major-effect QTL,was mapped to chromosome 2H and explained up to 38.77%of SRN variation.Map-based cloning revealed that qSRN1 encodes the RAWUL domain-containing protein HvSRN1.Further analysis revealed that two key SNPs in the HvSRN1 promoter region(-2 kb upstream of the transcription start site)affect the transcript level of HvSRN1 and contribute to variation in SRN.Similar to its orthologous proteins OsLAX2 and ZmBA2,HvSRN1 showed protein–protein interactions with HvLAX1,suggesting that the LAX2–LAX1 model for spike morphology regulation may be conserved in Poaceae crops.CRISPR-Cas9-induced HvSRN1 mutants showed reduced SRN but increased grain size and weight,demonstrating a trade-off effect.Our results shed light on the role of HvSRN1 variation in regulating the balance between grain number and weight in barley.

基于区间数PROMETHEE的智能制造能力评价研究

智能制造是当今时代的发展趋势,也是制造企业的竞争优势。智能制造能力评价能够帮助企业准确掌握智能制造发展状况,为企业之后发展与转型提供有效、合理的依据。针对多属性决策中存在指标间补偿以及指标取值不确定的问题,提出一种基于区间数PROMETHEE的智能制造能力评价方法。首先,构建智能制造能力评价指标体系;其次,依据专家评分构造区间数评分集合矩阵;然后,根据核密度估计拟合出区间数集合的概率密度矩阵,基于Wasserstein距离构建PROMETHEE偏好函数;最后,利用该偏好函数计算出各个方案的净流量,得到最终的智能制造能力评价结果。通过实证研究,与其他方法进行对比,验证了该方法的科学性与有效性。

Conditional QTL mapping of three yield components in common wheat(Triticum aestivum L.)

Spike number per m^2(SN),kernel number per spike(KNPS) and thousand-kernel weight(TKW)are the three main components determining wheat(Triticum aestivum L.) yield.To evaluate the relationships among them a doubled haploid(DH) population consisting of 168 lines grown at three locations for three years was analyzed by unconditional and conditional QTL mapping.Thirty-three unconditional QTL and fifty-nine conditional QTL were detected.Among them,two QTL(QSN-DH-2B and QSN-DH-3A-1.1) improved SN,with no effect on KNPS.QKNPS-DH-2B-2.1 improved KNPS,with no effect on SN.QKNPS-DH-1A-1.1,QKNPS-DH-2D-1.1and QKNPS-DH-6A improved KNPS,with no effect on SN or TKW.QKNPS-DH-6B was associated with increased SN and TKW.In addition,QTKW-DH-4B,QTKW-DH-5B and QTKW-DH-7B increased TKW without decreasing KNPS.These results provide useful information for marker assisted selection(MAS) and improvement in wheat yield.

Development of high-oil maize haploid inducer with a novel phenotyping strategy

Doubled haploid(DH) technology is important in modern maize breeding. Haploid inducers determine the efficiency of both haploid induction and identification. It has taken decades to improve the efficiency,haploid induction rate(HIR), from the ~2% of the ancestor haploid inducer, stock6, to the ~10% of modern haploid inducers. Improvement of kernel oil content(KOC) would further enhance haploid identification efficiency. Using molecular marker-assisted selection, in combine with the number of haploids per ear as phenotypic criterion, we developed a new high-oil haploid inducer line, CHOI4, with a mean HIR of 15.8%and mean KOC of 11%. High KOC of CHOI4 can achieve a mean accuracy greater than 90% in identification of haploids of different backgrounds, with reduced false discovery rates and false negative rates in comparison with the previous high-oil haploid inducer line, CHOI3. Comparison of phenotypic selection strategies suggested that the number of haploids per ear can be used as a phenotyping criterion during haploid inducer line development. CHOI4 could further increase the efficiency of large-scale DH breeding programs with lower cost.

Activity of Corn Silk at Different Days after Silk Emergence

This study was carried out to evaluate the changes in silk activity of two corn cultivars Xundan 518 and Yongyou 618 after silk emergence. Artificial pollination was conducted at different days after silk emergence, and the ear length, ear diameter,barren tip length, 100-grain weight, grain number per ear and grain weight per ear were measured at harvest. The results showed that with the delay of pollination, the number and weight of grains per ear increased at first, peaked at D2 to D4, and decreased subsequently; ear diameter and 100-grain weight showed a downward trend. Correlation analysis revealed that grain number per ear and grain weight per ear were most closely correlated. Rapid silk extrusion and long-lasting silk activity proved that the two corn cultivars Xundan 518 and Yongyou 618 are tolerant to high temperature.

Multivariate Cluster and Principle Component Analyses of Selected Yield Traits in Uzbek Bread Wheat Cultivars

Investigation of genetic diversity of geographically distant wheat genotypes is a useful approach in wheat breeding providing efficient crop varieties. This article presents multivariate cluster and principal component analyses (PCA) of some yield traits of wheat, such as thousand-kernel weight (TKW), grain number, grain yield and plant height. Based on the results, an evaluation of economically valuable attributes by eigenvalues made it possible to determine the components that significantly contribute to the yield of common wheat genotypes. Twenty-five genotypes were grouped into four clusters on the basis of average linkage. The PCA showed four principal components (PC) with eigenvalues > 1, explaining approximately 90.8% of the total variability. According to PC analysis, the variance in the eigenvalues was the greatest (4.33) for PC-1, PC-2 (1.86) and PC-3 (1.01). The cluster analysis revealed the classification of 25 accessions into four diverse groups. Averages, standard deviations and variances for clusters based on morpho-physiological traits showed that the maximum average values for grain yield (742.2), biomass (1756.7), grains square meter (18,373.7), and grains per spike (45.3) were higher in cluster C compared to other clusters. Cluster D exhibited the maximum thousand-kernel weight (TKW) (46.6).

基于纹理特征与深度学习的小麦图像中的穗粒分割与计数

穗粒数是小麦产量构成的重要因素和估测产量的参数之一,传统的人工计数方法耗时费力,人为因素影响大。为了实现对小麦穗粒数的智能、快速监测,以百农307、新麦26、稷麦336这3个小麦品种为试验材料,利用智能手机于小麦灌浆后期拍摄麦穗图像,随后对麦穗图像进行预处理并归一化为480×480像素大小,结合深度学习和迁移学习机制,构建基于冻结-解冻机制的HRNet模型的小麦小穗图像分割计数深度学习模型,利用图像处理算法、小麦小穗图像纹理特征确定小穗像素数与穗粒数之间的关系阈值,构建小穗粒数预测模型,实现对小麦穗粒的预测计数。结果表明,对比同样采用冻结-解冻机制的PSPNet模型、DeeplabV3+分割模型、U-Net模型及无冻结解冻机制的HRNet模型,采用基于冻结-解冻机制的HRNet模型对小麦小穗的分割效果更优,且具有更好的鲁棒性,分割精确度为0.9594,平均交并比(mIoU)为0.9119,类别平均像素准确率(mPA)为0.9419,召回率为0.9419;通过3个不同品种小麦的麦穗图像对小穗进行计数,所得决定系数(R2)为0.92,平均绝对误差为0.73,平均相对误差为2.89%;籽粒计数的R2为0.92,平均绝对误差为0.43,平均相对误差为5.51%。由研究结果可知,基于冻结-解冻机制得出的HRNet模型的小麦小穗图像分割算法能够有效分割小麦图像中的小穗,并获得更加丰富的语义信息,可用于解决小目标图像分割困难及训练欠拟合问题,通过粒数预测模型可以快速、精确地对小麦的籽粒数进行预测,从而为小麦高效、智能化估产提供算法支撑。

枣仁安神颗粒联合耳穴揿针疗法对三四类大手术前患者焦虑情绪的影响

目的 研究旨在探讨枣仁安神颗粒联合耳穴揿针疗法对三四类大手术患者术前焦虑的影响。方法 采用随机数字表法,将患者分为对照A组35例,对照B组35例,试验组37例,其中对照A组给予枣仁安神颗粒治疗,对照B组给予耳穴揿针治疗,试验组则采用枣仁安神颗粒联合耳穴揿针疗法。比较3组患者焦虑(S-AI)评分、术前睡眠质量及血压水平。结果 治疗后3组患者焦虑水平、收缩压及睡眠疗效比较均存在统计学差异(P<0.05),试验组的焦虑水平及收缩压低于对照A、B组,睡眠疗效优于对照A、B组。结论 枣仁安神颗粒联合耳穴揿针能减轻三四类大手术患者术前的焦虑情绪,并改善术前睡眠及稳定术前血压,具备一定临床应用价值。

部分Motzkin路的计数

一条长为n的部分Motzkin路是从(0,0)到(n,k)的一条经过整点的格路径,它由上步U=(1,1),下步D=(1,-1)以及水平步H=(1,0)构成,且从不走到x轴的下方.从(0,0)到(n,0)的Motzkin路的个数叫做第n个Motzkin数.利用核方法得到了Motzkin数的发生函数及部分Motzkin路径数的Riordan矩阵的表示.基于递推关系和线性代数方法给出了高度受限的部分Motzkin路的发生函数,并给出了相关示例.