近红外光谱和人工神经网络的金苦荞氨基酸快速测定

荞麦籽粒中富含谷类作物比较缺乏的赖氨酸,使其不同于其他作物,具有较高经济价值。传统氨基酸测定费时且昂贵,为满足金苦荞育种工作的需要,选用近红外光谱技术结合人工神经网络的算法建立快速检测金苦荞叶片中氨基酸含量的近红外模型。使用氨基酸含量差异较大的样品255个,扫描光谱后测定其化学值。研究发现样品苏氨酸(Thr)含量范围是5.307~14.374 mg·g-1;缬氨酸(Val)含量范围是6.137~16.204 mg·g-1;甲硫氨酸(Met)含量范围是0.308~3.049 mg·g-1;异亮氨酸(Ile)含量范围是5.259~14.134 mg·g-1;亮氨酸(Leu)含量范围是9.730~26.061 mg·g-1;苯丙氨酸(Phe)含量范围是5.936~17.223 mg·g-1;赖氨酸(Lys)含量范围是6.640~17.280 mg·g-1;谷氨酸(Glu)含量范围是10.984~27.740 mg·g-1;天冬氨酸(Asp)含量范围是6.437~17.280 mg·g-1;丝氨酸(Ser)含量范围是3.467~8.312 mg·g-1;精氨酸(Arg)含量范围是4.937~14.772 mg·g-1;丙氨酸(Ala)含量范围是3.329~6.885 mg·g-1;组氨酸(His)含量范围是1.946~4.798 mg·g-1;甘氨酸(Gly)含量范围是4.196~9.264 mg·g-1;脯氨酸(Pro)含量范围是1.024~5.672 mg·g-1;酪氨酸(Tyr)含量范围是0.176~1.173 mg·g-1;半胱氨酸(Cys)含量范围是0.422~1.926 mg·g-1。每次随机选取50个样品建设模型,以4∶1的比例随机分为训练集和测试集。数据进行归一化处理后,使用神经网络结构1102-9-1进行模型建设。利用多次学习的方式建立了较优模型,其中Arg和Asp近红外模型的仿真测试结果最好,预测值与真实值的相关系数(R2)均大于0.97,平均相对误差(RSD)也小于10%;另外Leu,Val,Tyr,Ile,Ser,Ala,Thr,His,Phe,Gly和Lys模型的R2均大于0.90,模型仿真测试数据的RSD小于10%,模型均可用;Met与Cys的模型进行仿真测试时,其预测值与真实值的R2均大于0.78,但RSD大于10%,模型不可用。结果表明,金苦荞叶片的氨基酸含量高,有极高应用价值,近红外光谱技术结合人工神经网络的分析方法可应用于金苦荞氨基酸含量的预测,为高品质荞麦育种工作提供了便利。     

Nonlocal nonreciprocal optomechanical circulator

A nonlocal circulator protocol is proposed in a hybrid optomechanical system. By analogy with quantum communication, using the input-output relationship, we establish the quantum channel between two optical modes with long-range. The three-body nonlocal interaction between the cavity and the two oscillators is obtained by eliminating the optomechanical cavity mode and verifying the Bell-CHSH inequality of continuous variables. By introducing the phase accumulation between cyclic interactions, the unidirectional transmission of quantum state between the optical mode and two mechanical modes is achieved. The results show that nonreciprocal transmissions are achieved as long as the accumulated phase reaches a certain value. In addition, the effective interaction parameters in our system are amplified, which reduces the difficulty of the implementation of our protocol. Our research can provide potential applications for nonlocal manipulation and transmission control of quantum platforms.     

Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits

We rigorously study a recent algorithm due to Davidchack and Lai (DL) [Davidchack RL, Lai Y-C. Phys Rev E 1999;60(5):6172–5] for efficiently locating complete sets of hyperbolic periodic orbits for chaotic maps. We give theorems concerning sufficient conditions on convergence and also describing variable sized basins of attraction of initial seeds, thus pointing out a particularly attractive feature of the DL-algorithm. We also point out the true role of involutary matrices which is different from that implied by Schmelcher and Diakonos [Schmelcher P, Diakonos FK. Phys Rev E 1998;57(3):2739–46] and propagated by Davidchack and Lai.     

奇异摄动反应扩散方程的后验误差估计及自适应算法

研究了一类奇异摄动半线性反应扩散方程的自适应网格方法.在任意非均匀网格上建立迎风有限差分离散格式,并推导出离散格式的后验误差界,然后用该误差界设计自适应网格移动算法.数值实验结果证明了所提出的自适应网格方法的有效性.     

符号函数在积分运算中常见的错误分析

符号函数sgnx是数学分析中一个特殊的分段函数,在积分运算中,经常被误认为是常值函数,被提到积分符号的前面,从而导致结果错误．本文将通过具体的例子来分析常见的错误．     

Parameter space of the Rulkov chaotic neuron model

The parameter space of the two dimensional Rulkov chaotic neuron model is taken into account by using the qualitative analysis, the co-dimension 2 bifurcation, the center manifold theorem, and the normal form. The goal is intended to clarify analytically different dynamics and firing regimes of a single neuron in a two dimensional parameter space. Our research demonstrates the origin that there exist very rich nonlinear dynamics and complex biological firing regimes lies in different domains and their boundary curves in the two dimensional parameter plane. We present the parameter domains of fixed points, the saddle-node bifurcation, the supercritical/subcritical Neimark–Sacker bifurcation, stability conditions of non hyperbolic fixed points and quasiperiodic solutions. Based on these parameter domains, it is easy to know that the Rulkov chaotic neuron model can produce what kinds of firing regimes as well as their transition mechanisms. These results are very useful for building-up a large-scale neuron network with different biological functional roles and cognitive activities, especially in establishing some specific neuron network models of neurological diseases.     

A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

Ulam–Hyers–Mittag-Leffler stability of fractional-order delay differential equations

In this paper, we first prove two existence and uniqueness results for fractional-order delay differential equation with respect to Chebyshev and Bielecki norms. Secondly, we prove the above equation is Ulam–Hyers–Mittag-Leffler stable on a compact interval. Finally, two examples are also provided to illustrate our results.     

Wilson元特征值下逼近准确特征值

该文讨论矩形域上Laplace算子特征值问题有限元近似.证明了Wilson非协调有限元特征值下逼近准确特征值,从而解决了有限元法中长期存在的一个猜想.