Improved analysis for SRS- and XPM-induced crosstalk in SCM-WDM transmission link in the presence of HOD

In this paper, the improved analysis for SRS- and XPM-induced crosstalk has been reported. The modified expression for XPM-induced crosstalk has been obtained and SRS- and XPM-induced crosstalks have been reported at varied walkoff parameter, modulation frequency, input optical power and transmission distance. It has been observed that there is exponent decrease in SRS-induced crosstalk with the increase in modulation frequency from 0 to 2.0 GHz. It varies with the increase in length and lie in the range of (−114 to −122.4) dB and (−115.5 to −124.4) dB at 20 and 100 km, respectively. Moreover, it increases exponentially with the increase in input optical power and lies in the range of (−121.6 to −130.6) dB at 10 mW and grows exponentially up to the range of (−114 to −122.8) dB at 60 mW optical powers at walkoff parameter of (13.6, 27.2, 54.4 and 81.6) ps/km. It has been observed that the XPM-induced crosstalk increases exponentially with the increase in transmission distance and modulation frequency for 2OD and 3OD. Furthermore, it has been found that the total SRS- and XPM-induced crosstalk rises exponentially with fluctuations with the increase in modulation frequency and transmission length in the presence of combined effect of 2OD and 3OD at varied walkoff parameters.     

高阶效应对超短艾里-高斯脉冲相互作用的影响

本文运用分步傅里叶变换,对满足高阶耦合非线性薛定谔方程的超短艾里脉冲与超短高斯脉冲,利用MATLAB数值模拟了在高阶效应下两脉冲相互作用后的演化过程以及时域上的强度变化。结果表明：负三阶色散效应使超短脉冲相互作用能传输更远距离;正三阶色散效应会减慢超短脉冲相互作用的传输。自陡峭效应通过孤子分裂现象的形式使超短脉冲相互作用产生时域位移,内拉曼效应可以将超短脉冲相互作用的能量由前沿处转移到后沿处。     

Positive solutions of higher-order nonlinear fractional differential systems with nonlocal boundary conditions

The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.     

基于温度变量的四维荧光光谱的石油类污染物测定

三维荧光光谱结合多元校正分析对石油类污染物复杂多组分体系测定方法多谱图混叠,且易受到空白荧光和干扰物荧光影响降低了测定准确性。提出在三维荧光光谱中增加一维温度信息构造激发波长-发射波长-温度-样品（EEM-temperature data array）的四维荧光光谱数据阵列,应用四线性成分模型建立高维荧光光谱定性定量分析的方法。实验证明在15～25 ℃温度范围内,矿物油荧光光谱轮廓形状不随温度变化,而其强度随温度线性变化,满足四线性要求,这为构建四维荧光光谱发展高维数据的三阶校正提取更丰富的有效信息提供了可能。三阶校正不仅可以在干扰物共存的情况下对感兴趣组份进行定量测定,即具有“二阶优势”,还具有更高的选择性和灵敏性,可以对高共线性和背景干扰的重叠光谱表现更好的解析能力,即“三阶优势”。对0#柴油、97#汽油和机油为混合油待测组分,腐殖酸为水体干扰组分组成的复杂体系污染油样品为进行实验,得到的三维荧光光谱利用平行因子（PARAFAC）算法和交替惩罚三线性分解（APTLD）算法进行二阶校正分析,将三维荧光光谱在温度方向上堆叠构成增加温度维度的四维荧光光谱数阵,并将其利用四维平行因子算法（4-PARAFAC）和交替惩罚四线性分解（APQLD）算法进行三阶校正分析,比较,0#柴油、97#汽油和机油的预测结果表明增加了影响荧光光谱的温度因素构造的四维荧光光谱提高了有效信息提取能力,四维荧光光谱结合高阶校正算法能提高油种光谱识别和浓度精确检测,较传统的三维荧光光谱分析提高了回收率（recovery rate）和预测均方根误差（root mean square error of prediction,RMSEP）,有利于石油类污染物的有效,准确,实时,绿色环保检测。同时指出了4-PARAFAC和APQLD算法各自的特点及其不同适用环境,为油类污染物检测具体情况提供算法选择依据。引入温度参量的四维荧光光谱结合三阶校正算法的检测技术较三维荧光光谱技术,在组分光谱定性分辨和浓度定量检测方面能对复杂体系油类污染物实现快速有效,绿色无污染地检测,实现“数学分离”更有效代替“化学分离”。     

Simultaneous Representation and Approximation Formulas and High-Order Sobolev Embedding Theorems on Stratified Groups

We give various integral representation formulas simultaneously for a function and its derivatives in terms of vector field gradients of the function of appropriately high order. When the function has compact support, simpler formulas can be derived. Many of the results proved here appear to be new even in the special case of classical Euclidean space. For instance, Theorem 2.2 below reduces to the following result in the usual Euclidean case: Let B be a ball in R^N with radius r(B), let m be a positive integer, and let f\in W^m,1(B). Then there is a polynomial P=_m(B,f) of degree m-1 such that for any integers i, j with 0 j < i m and a.e. x\in B, |\nabla^j(f-P)(x)| C\int_{B}\frac{|\nablaⁱf(y)|}{|x-y|^N-(i-j)} dy +Cr(B)^i-j-N\int_B|\nablaⁱf(y)| dy. Moreover, if 0 < i-j N, then for a.e. x \in B we have the more refined formula |\nabla^j(f-P)(x)| C\int_B\frac{|\nablaⁱf(y)|}{|x-y|^N-i+j} dy.     

Higher-order diffraction images in photorefractive materials

We report some photorefractive higher-order diffraction phenomena of a liquid crystal polymer composite. The photorefractive composite consists of the polymer poly[N-vinylcarbazole] (PVK) doped with the chromophore 4,4′-n-entylcyanobiphenyl (5CB) and the sensitizer C₆₀. In two-wave coupling experiments, the signal beam was interfered by a mutually coherent reference beam within composite materials at a small incident angle. Results are given when the composite was placed behind the focal plane, in front of the focal plane, and in the focal plane. Higher-order diffraction images were obtained by amplification and reduction. A theory of the properties of higher-order diffraction images in a photorefractive liquid crystal polymer composite is developed. The theory is in good agreement with the results of experimental work. The experiments demonstrate the feasibility of optical image processing.     

Activity coefficients for ternary systems: VI. The system HCl + MgCl2 + H2O at different temperatures; application of Pitzer's equations

Electromotive-force measurements have been made on HCl–MgCl₂–H₂O mixtures at 5, 15, 25, 35 and 45°C at eleven different ionic strengths from 0.1–5.0 mol-kg ^–1 . The results are interpreted in terms of the simple Harned's equations, as well as the more complicated Pitzer ion-component treatment of multicomponent electrolyte mixtures. Activity coefficients for HCl in the salt mixtures obey Harned's rule up to and including I=5.0. For the salt in the acid mixtures, Harned's rule holds true up to and including I=0.5. The contribution of higher-order electrostatic terms (E and E') in the Pitzer equations is important for accurate evaluations of unlike cation-cation interactions (_H,Mg), and cation-anion-cation interactions (_H,Mg,Cl). The values of^S_H,Mg and _H,Mg,Cl (determined with E and E'), _H,Mg and _H,Mg,Cl (determined without E and E'), as well as the trace activity coefficients of HCl, _tr ^A , in solutions of MgCl₂ (where ionic strength fraction of the salt,y _B = 1) at all the experimental temperatures and ionic strengths, are reported. Results of this study are compared with those for similar systems. At I=0.1 and 25°C, the results of the Brönsted-Guggenheim specific interaction theory are discussed briefly.     

Application of least square method to arbitrary-order problems with separated boundary conditions

In this paper, differential equations of arbitrary order with separated boundary conditions are converted into an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. In fact it will be shown that for every ε>0$\epsilon >0$, there exists an approximate solution _vε$v_{\epsilon }$ of B-spline functions such that the corresponding least square error is less than ε>0$\epsilon >0$, and also _vε$v_{\epsilon }$ satisfies the exact boundary conditions. Some examples are given and the optimal errors are obtained for the sake of comparison.