Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

线性规划的符号跟踪算法

分析了只含一个约束条件的线性规划最优基变量的特征，将其运用到搜寻含m个约束条件的线性规划的最优基变量，从而提出了线性规划的符号跟踪算法，为线性规划求解提供了新途径。     

模糊半群上的模糊同余及其扩张

给出模糊半群上的模糊同余的概念，并进一步研究它的一些基本代数性质。同时研究带有模糊半群上的模糊同余扩张性质(FCEPF)的半群类，得到一个半群有模糊半群上的模糊同余扩张性质、有模糊同余扩张性质(FCEP)、有同余扩张性质(CEP)三个条件是等价的。     

Spectral Analysis of Powers of the Operator (Vf)(x)=q(x)∫0 xw(t)f(t),dt

Mathematical Notes -     

Security Applications of Optical Face Recognition System: Access Control in E-Learning

The educational system has gradually shifted from a face-to-face to an e-learning system, which has become prevalent in advanced countries with the advance of information technology, and connection of global networks. Accordingly, a growing demand is emerging for more reliable individual certification with technical precision in order to measure and record learning achievements and credentials of participants. The present system has a limit in terms of registration capacity, therefore, its accuracy has often been questioned. Against this background, an individual certification system is proposed particularly for access control in e-learning. Under our proposed system, a compact optical correlator for facial recognition is employed. This correlator was previously tested for of biometrics authentication accuracy and proved highly reliable, having recorded remarkably low error rates (below 1%). The recorded error rate is sufficiently robust that the system itself can be regarded as a valid and practical viable attestation system.     

Searching for new conditions for fermion N-representability

New elements of the dual cone of the set of fermion N-representable 2-density operators are proposed. So far, the explicit form of the corresponding necessary conditions for N-representability is obtained for N = 3. In this case the new condition is stronger than the known B- and C-conditions for 3-representability. The results provide evidence that in the spectral decomposition of the N-representable 2-density operator there exists an intrinsic relation between the eigenvalue and the corresponding eigenfunction.     

Analysis of the characteristics of a two-fiber sensor for monitorship of a turbid medium

Summary Certain characteristics of a two-fiber sensor device, of the type proposed by Papaet al. for sea water turbidity monitorship, are examined. The extension of medium from which most of the received backscattered power originates is investigated, together with possible effects of multiple scattering on the received power. Laboratory measurements testing the results of the analysis are reported.

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Riassunto Sono esaminate alcune caratteristiche di un sensore a due fibre, del tipo di quello proposto da Papaet al. per il monitoraggio della torbidità dell'acqua di mare. è stata studiata l'estensione della zona del mezzo da cui proviene la maggior parte della radiazione retrodiffusa ricevuta. Sono stati considerati effetti di diffusione multipla. I risultati dell'analisi sono stati controllati con misure in laboratorio.

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Резюме Исследуются некоторые характеристики дву-qh-нитевого датчика, предложенного Папа и др. для мониторирования мутности морской воды. Исследуется расширение зоны в среде, из которой формируется основная часть рассеянного назад излучения. Также рассматриваются эффекты многократного рассеяния. На основе лабораторных измерений проводится проверка результатов анализа.

     

聚丙烯微孔膜的等离子体接枝聚合改性

利用拉伸时的晶型转变致孔特性,从β晶相聚丙烯经单向或双向拉伸制得了新型聚丙烯微孔膜、用等离子体接枝聚合技术接上了亲水性聚合物如聚丙烯酸、聚丙烯腈等。研究了等离子体处理时间、单体性质对得到的亲水膜的亲水性、离子/溶质渗透性的影响。发现接枝聚丙烯酸的双向拉伸膜对Na~+、Mg~(++),尿素有较大的渗透性,并具有优良的形状稳定性。     

A method for determining optical constants, dimensions, and concentrations of “soft” absorbing particles in the brightening band region

We investigate the possibilities of creating a method for estimating the optical constants, dimensions, and concentrations of “soft” absorbing particles by applying a theoretical analysis of the angular dependence of the intergrated indicatrix, overall characteristics of light scattering, and absorption on the phase shift and diffraction parameter of particles in the brightening band region. We show that using the investigated optical characteristics, it is possible to determine the unknown parameters of a suspension from experimental data. Institute of Biophysics, Siberian Branch of the Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 6, pp. 807–812, November–December, 1997.     

Helmholtz potentiality conditions for systems of difference-differential equations

For operators corresponding to systems ofμth-order difference-differential equations of neutral type, necessary and sufficient conditions for potentiality with respect to the classical bilinear form are obtained. These results are applied to first-order quasilinear systems. Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 437–442, September, 1998. The author wishes to express his thanks to V. M. Savchin for fruitful discussions and useful remarks.