Schubert Class and Cyclotomic NilHecke Algebras

Let (l) and n be positive integers such that l ≥ n,and let Gn,l be the Grassmannian which consists of the set of n-dimensional subspaces of Cl.There is a Z-graded algebra isomorphism between the cohomology H*(Gn,l,Z) of Gn,l and a nat-ural Z-form B of the Z-graded basic algebra of the type A cyclotomic nilHecke algebra(H)(0) =<ψ1,… ψn-1,y1,…,yn>.We show that the isomorphism can be chosen such that the image of each (geometrically defined) Schubert class (a1,...,an) coincides with the basis element bλ constructed by Hu and Liang by purely algebraic method,where 0 ≤ a1 ≤ a2 ≤ … ≤ an ≤ l-n with ai ∈ Z for each i,and λ is the l-multipartition of n associated to (l + 1-(an + n),l + 1-(an-1 + n-1),...,l + 1-(a1 + 1)).A similar correspondence between the Schubert class basis of the cohomology of the Grassmanni-an Gl-n,l and the bλ's basis (λ is an l-multipartition of n with each component being either (1) or empty) of the natural Z-form B of the Z-graded basic algebra of (H)(0)l,n is also obtained.As an application,we obtain a second version of the Giambelli formula for Schubert classes.     

电商平台主导的E-闭环供应链定价、服务决策与回收模式

E-闭环供应链(E-CLSC)管理须有科学的定价与服务决策支撑。针对集中和分散回收模式,构建电商平台主导的Stackelberg博弈模型,研究E-CLSC定价与平台服务决策。通过对产品销售价格、平台服务水平等均衡策略分析,揭示回收主体投资有效性、回收转移价格等对E-CLSC均衡策略影响。研究表明:集中回收模式优于分散回收模式;在分散回收模式下,若回收主体投资有效性相同,制造商、平台均偏好制造商回收模式;平台回收与第三方回收模式相比,产品销售价格、平台服务水平相同,前者回收渠道效率较高;平台回收模式下,单位佣金与回收转移价格负相关,产品销售价格、平台服务水平、废旧产品回收率均与回收转移价格无关;若回收主体投资有效性差异程度较大,制造商回收模式并非总是最优的,回收主体投资有效性差异显著影响产品销售价格、回收渠道效率、平台服务水平和E-CLSC各成员利润。上述结论通过数值仿真进行了验证。     

高光谱数据的刚竹毒蛾虫害程度检测

刚竹毒蛾虫害检测对毛竹的生长和竹业的发展起着至关重要的作用。根据高光谱冠层光谱信息与刚竹毒蛾虫害程度之间的关系,提取冠层光谱中与虫害紧密相关的特征波长、指数以及光谱参数等,利用Fisher判别分析法建立刚竹毒蛾虫害程度检测模型。分别以原始光谱的400～508,586～693和724～900 nm处的波长、包络线去除光谱的400～756 nm之间的特征波长、9种冠层光谱植被指数和7种冠层特征光谱参数作为Fisher判别函数自变量,构建判别函数。收集300组毛竹叶片虫害样本数据,随机划分为210组建模集与90组验证集,根据检测精度、Kappa系数以及判定系数R2作为检验标准,对建立的判别函数进行效果评价与对比。结果表明,以原始光谱、去包络线光谱、冠层指数、光谱参数为自变量建立的Fisher判别函数的检验精度分别为：84.4%,81.1%,79.7%,78.7%;Kappa系数分别为：0.79,0.74,0.74,0.76;R2分别为：0.89,0.88,0.88和0.85。由此可知,Fisher判别分析模型建立的函数具备很好的刚竹毒蛾虫害程度检测能力,而且基于冠层原始光谱建立的判别函数检测效果最佳。根据高光谱数据的冠层原始光谱建立的判别函数对福建省顺昌县大干镇武坊村的洋门和土垅村的上湖竹林进行刚竹毒蛾虫害程度检测。检测结果为：上湖两个样区的竹林以健康为主。洋门两个样区虫害程度以中度和重度为主。因此基于无人机高光谱遥感对于刚竹毒蛾虫害的大面积检测具有可行性,该方法可为虫害检测的探究提供参考,为基于冠层遥感虫害检测贡献理论支撑。     

刚竹毒蛾危害下的毛竹叶片光谱特征及虫害等级检测研究

探讨刚竹毒蛾危害下的毛竹叶片光谱特征可为建立竹林生态安全监测体系提供重要的理论指导。相比于传统的多光谱数据,高光谱遥感能够准确探测不同刚竹毒蛾危害等级间寄主光谱的细微变化。然而,当前有关此方面的研究甚少,其寄主的光谱变化机理还有待进一步总结。为此,基于实测的552条竹叶光谱,分析了健康、受刚竹毒蛾危害、小年叶片之间的光谱差异,选择可反映其健康状况的特征变量,并利用XGBoost模型建立了叶片尺度的刚竹毒蛾危害检测模型。研究结果显示：（1）随着虫害等级的上升,受害叶片在可见光范围内的反射率逐渐出现“绿低红高”的特征,其近红外波段的反射率则不断降低,而短波红外的反射率则明显高于健康叶片,尤其在两个水汽吸收波段（1 450和1 940 nm）的差异最为明显;（2）小年叶片于可见光-近红外波段的反射率显著高于健康、受害叶片;（3）根据不同受害类型叶片的光谱特征可知,较之健康叶片,缺刻型叶片的光谱并未出现太大的变化,红褐色病斑型叶片在红光波段的反射率出现了一定程度的上升,灰白色病斑型叶片则已经完全失去了植被的基本光谱特征;（4）根据XGBoost模型给出的变量重要性排序可知,各特征变量的贡献度依次为PRI（光化学反射率指数）＞FDVI_{576, 717}（植被健康程度评估指数）＞NPCI（归一化色素叶绿素指数）＞DSWI（疾病水胁迫指数）＞VOG 1（红边指数1）＞RVSI（红边植被胁迫指数）＞NDWI（归一化差值水分指数）;（5）模型对刚竹毒蛾危害识别的总平均精度为74.39%,其中健康叶片的识别精度达到了94.55%,轻度危害叶片为74.93%,重度危害为84.12%,小年叶片则为71.10%,而中度危害叶片的识别精度较差,仅为33.48%。     

Nanoimprinted substrates for high-yield production of topological insulator nanoribbons

We present a growth process mediated by nanoimprinted nanostructures specifically for producing bismuth selenide (Bi₂Se₃) topological insulator nanoribbons with a high yield. In this process, topological insulator nanostructures are grown on nanoimprinted gratings by using a nanoparticle-catalyzed vapor–liquid–solid mechanism. In comparison with the growth processes performed on flat and randomly rough substrates, such a nanograting-mediated growth method produces topological insulator nanoribbons with a higher yield (～15?000 nanoribbons/mm²), a narrower average ribbon width (w _avg<60 nm), and a higher uniformity in ribbon width (σ<30 nm); effectively suppresses the formation of other unwanted morphologies; and also results in the axial growth of nanoribbons along specific in-plane directions relative to pre-structured gratings. Such technical merits of nanograting-mediated growth are attributed to the preferential nucleation of Bi₂Se₃ crystal seeds and the concomitant pinning of catalytic nanoparticles at ordered grating edges. Finally, Aharonov–Bohm interference oscillations in the magnetoresistance were observed and demonstrated the coherent transport of electrons through topological surface states of Bi₂Se₃ nanoribbons. This growth process in combination with large-area nanoimprint lithography could serve as an important foundation for nanomanufacturing topological insulator nanoribbons with controllable feature size, large-area uniformity, and ordering, suitable for applications in future low-dissipation nanoelectronics.     

EADC Values in Diagnosis of Renal Lesions by 3.0 T Diffusion-Weighted Magnetic Resonance Imaging: Compared with the ADC Values

Exponential apparent diffusion coefficient (EADC) is an indicator of diffusion-weighted imaging (DWI) and reflects the pathological changes of tissues quantitatively. However, no study has been investigated in the space-occupying kidney disease using EADC values. This study aims to evaluate the diagnostic role of EADC values at a high magnetic field strength (3.0 T) in kidney neoplastic lesions, compared with that of the ADC values. Ninety patients with suspected renal tumors (including 101 suspected renal lesions) and 20 healthy volunteers were performed MRI scanning. Diffusion-weighted imaging was performed with a single-shot spin-echo echo-planar imaging (SE-EPI) sequence at a diffusion gradient of b = 500 s/mm². We found renal cell carcinoma (RCC) can be distinguished from angiomyolipoma, and clear cell carcinoma can be distinguished from non-clear cell carcinoma by EADC value. There was significant difference in overall EADC values between renal cell carcinoma (0.150 ± 0.059) and angiomyolipoma (0.270 ± 0.108) when b value was 500 s/mm². When receiver operating characteristic (ROC) was higher than 0.192, the sensitivity and specificity of EADC value of renal cell carcinoma were 84.6 and 81.1 %, respectively. In conclusion, EADC map shows the internal structure of the kidney tumor more intuitively than the ADC map dose, and is also in line with the observation habits of the clinicians. EADC can be used as an effective imaging method for tumor diagnosis.     

初态对光波导阵列中连续量子行走影响的研究

本文使用近邻耦合模型得到的解析解,分析了周期性波导中输入态对量子行走的粒子数的概率分布函数 和二阶相干性的影响.结果表明:输入态的对称性质对量子行走过程的二阶相干度有影响, 而对粒子数的概率分布函数影响不大. 关键词： 周期性光波导阵列 量子行走 二阶相干度 纠缠态     

光电振荡器产生宽带混沌光的时延特征分析

理论分析与数值研究了光电振荡器输出的混沌激光特性, 基于自相关分析方法, 详细研究了光电振荡器的直流偏置相移和反馈强度等工作参数对输出信号时延信息的影响. 数值研究表明: 增加反馈强度可以使时延信息变得更加微弱甚至消除; 相同条件下, 直流偏置相移对应的工作点越接近马赫-曾德尔调制器传输特性曲线的极值点, 时延信息越弱; 直流偏置相移为0时可以有效地抑制时延信息. 研究还发现, 当直流偏置相移和反馈调制产生的相移变化π/2时, 自相关曲线上对应于延迟时间处的相关系数符号发生变化. 关键词： 宽带混沌激光 延迟时间 光电振荡器     

一种直接用示波器观测单变量非线性系统状态的新方法

为解决用示波器观测单变量非线性系统难的问题, 本文提出了一种45°线法, 该方法能将随时间变化的连续信号以特殊的方式转换成直角坐标上45°线上的点图, 并可用通用双踪示波器 (模拟或数字均可)直接显示出来, 从而达到直接方便地观测和分析单变量被测系统运行时的各种状态, 如周期稳定态, 局部和全局不稳定态. 文中详细阐述了该方法的机理. 同时, 研究和解决了设计实现该方法物理电路的关键问题, 即从连续变化的信号中提取出能反映系统状态的有用信号. 由于蔡氏电路是典型的非线性系统, 且能随参数的变化产生各种丰富的状态, 本文选用该电路作为被测系统进行了大量的物理实验, 实验结果证实了该方法的有效性和实用性. 关键词： 45°线法 单变量系统 系统状态 双踪示波器