Resonant waveguide grating: Analysis of polarization independent filtering

We investigate the property of polarization independent reflection using a 1D grating. It is shown to be possible, by choosing the correct parameters of the structure and angle of incidence to adjust the bandwidth of the reflection curves for both polarizations in such a way that these coincide. We expect that the found polarization-independent narrow band filter can be used as a component for WDM applications.     

核－核碰撞的独立源模型及中心快度区末态产生粒子横能量分布

将强子－核碰撞的独立源模型推广到核－核碰撞，给出了核－核碰撞末态产生粒子横能量分布方程，将其与ＣＥＲＮ的ＮＡ３５合作组得到的实验数据相比较，模型较好地解释了实验结果．     

Massive and massless neutrinos on unbalanced seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM).A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)L x U(1)y gauge symmetry.The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix.Given p＞q,the rank of M is in general equal to 2q,corresponding to 2q non-zero mass eigenvalues.The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model,independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M,and the q x q heavy Majorana neutrino mass matrix MR.In other words,the numbers of massive left- and right-handed neutrinos are fairly matched.A good example to illustrate this "seesaw fair play rule"is the minimal seesaw model with p ＝ 3 and q ＝ 2,in which one masslese neutrino sits on the unbalanced seesaw.     

Influence of saddle-splay deformation on lyotropic chromonic liquid crystals confined between two coaxial cylinders

ABSTRACT

A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-? plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K_24。     

On the Lower Tail Probabilities of Some Random Sequences in <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We investigate the behaviour of the logarithmic small deviation probability of a sequence (σ _n θ _n ) in l _p , 0<p≤∞, where (θ _n ) are i.i.d. random variables and (σ _n ) is a decreasing sequence of positive numbers. In particular, the example σ _n ∼n ^−μ (1+log n)^−ν is studied thoroughly. Contrary to the existing results in the literature, the rate function and the small deviation constant are expressed expli- citly in the present treatment. The restrictions on the distribution of θ ₁ are kept to an absolute minimum. In particular, the usual variance assumption is removed. As an example, the results are applied to stable and Gamma-distributed random variables.     

On Lower Bounds for Lp Norms in the Central Limit Theorem for Independent and m-Dependent Random Variables

We derive lower bounds for L_p norms , in the central limit theorem for independent and m–dependent random variables with finite fifth order absolute moments and for independent and m–dependent identically distributed random variables with fourth order moments.     

NOTES ON ERDOS' CONJECTURE

Let Xn,n 1,be a sequence of independent random variables satisfying P(Xn = O) = 1 － P(Xn = an) = 1 － 1/pn,where an,n 1,is a sequence of real numbers,andpn isthenthprime,setFN(x)=P(N∑Xnn=1 x).The authors investigate a conjecture of Erdos in probabilistic number theory and show that in order for the sequence FN to be weakly convergent,it is both sufficient and necessary that there exist three numbers x0 and x1 ＜ x2 such that limsup(FN(x2) －FN(x1)) ＞ 0 holds,and Lo =N→∞ lim FN(x0) exists.Moreover,the authors point ont that they can also obtain the same N→∞ result in the weakened case of liminfP(Xn = 0) ＞ 0.n→∞     

Correlation‐assisted nearest shrunken centroid classifier with applications for high dimensional spectral data

High throughput data are frequently observed in contemporary chemical studies. Classification through spectral information is an important issue in chemometrics. Linear discriminant analysis (LDA) fails in the large‐p‐small‐n situation for two main reasons: (1) the sample covariance matrix is singular when p > n and (2) there is an accumulation of noise in the estimation of the class centroid in high dimensional feature space. The Independence Rule is a class of methods used to overcome these drawbacks by ignoring the correlation information between spectral variables. However, a strong correlation is an essential characteristic of spectral data. We proposed a new correlation‐assisted nearest shrunken centroid classifier (CA‐NSC) to incorporate correlation information into the classification. CA‐NSC combines two sources of information [class centroid (mean) and correlation structure (variance)] to generate the classification. We used two real data analyses and a simulation study to verify our CA‐NSC method. In addition to NSC, we also performed a comparison with the soft independent modeling of class analogy (SIMCA) approach, which uses only correlation structure information for classification. The results show that CA‐NSC consistently improves on NSC and SIMCA. The misclassification rate of CA‐NSC is reduced by almost half compared with NSC in one of the real data analyses. Generally, correlation among variables will worsen the performance of NSC, even though the discriminatory information contained in the class centroid remains unchanged. If only correlation structure information is used (as in the case of SIMCA), the result will be satisfactory only when the correlation structure alone can provide sufficient information for classification. Copyright © 2015 John Wiley & Sons, Ltd.     

Feasibility study on qualitative and quantitative analysis in tea by near infrared spectroscopy with multivariate calibration

This study attempted the feasibility to use near infrared (NIR) spectroscopy as a rapid analysis method to qualitative and quantitative assessment of the tea quality. NIR spectroscopy with soft independent modeling of class analogy (SIMCA) method was proposed to identify rapidly tea varieties in this paper. In the experiment, four tea varieties from Longjing, Biluochun, Qihong and Tieguanyin were studied. The better results were achieved following as: the identification rate equals to 90% only for Longjing in training set; 80% only for Biluochun in test set; while, the remaining equal to 100%. A partial least squares (PLS) algorithm is used to predict the content of caffeine and total polyphenols in tea. The models are calibrated by cross-validation and the best number of PLS factors was achieved according to the lowest root mean square error of cross-validation (RMSECV). The correlation coefficients and the root mean square error of prediction (RMSEP) in the test set were used as the evaluation parameters for the models as follows: R = 0.9688, RMSEP = 0.0836% for the caffeine; R = 0.9299, RMSEP = 1.1138% for total polyphenols. The overall results demonstrate that NIR spectroscopy with multivariate calibration could be successfully applied as a rapid method not only to identify the tea varieties but also to determine simultaneously some chemical compositions contents in tea.     

A New Series of C‐6 Unsubstituted Tetrahydropyrimidines: Convenient One‐Pot Chemoselective Synthesis,Aggregation‐Induced and Size‐Independent Emission Characteristics

A new series of C‐6 unsubstituted tetrahydropyrimidines 6 have been directly synthesized via a convenient urea‐catalyzed chemoselective five‐component reaction (5CR) under mild conditions. Compounds 6 show typical aggregation‐induced emission enhancement (AIEE) characteristics because they are practically no emissive in solution but emit blue or green fluorescence in aggregates with fluorescence yield up to 93 %. One of the 5CR products, 6 aa , exhibits blue‐ and green‐fluorescence aggregates (bf‐ and gf‐aggregates). The bf‐ and gf‐aggregates are prepared under different conditions and proved to result from different J‐aggregations by single‐crystal X‐ray analysis. In addition, the bf‐ and gf‐aggregates of 6 aa show unusual size‐independent emission (SIE) characteristics because their maximum emission wavelengths in different sizes (suspension particles, film, powder and crystals) are the same, 434 and 484 nm, respectively. Based on the obtained experimental results, the 5CR mechanism, the origins of AIEE and SIE characteristics are discussed.