A new Monte Carlo model for predicting the mechanical properties of fiber yarns

Understanding the complicated failure mechanisms of hierarchical composites such as fiber yarns is essential for advanced materials design. In this study, we developed a new Monte Carlo model for predicting the mechanical properties of fiber yarns that includes statistical variation in fiber strength. Furthermore, a statistical shear load transfer law based on the shear lag analysis was derived and implemented to simulate the interactions between adjacent fibers and provide a more accurate tensile stress distribution along the overlap distance. Simulations on two types of yarns, made from different raw materials and based on distinct processing approaches, predict yarn strength values that compare favorably with experimental measurements. Furthermore, the model identified very distinct dominant failure mechanisms for the two materials, providing important insights into design features that can improve yarn strength.     

Odd length for even hyperoctahedral groups and signed generating functions

We define a new statistic on the even hyperoctahedral groups which is a natural analogue of the odd length statistic recently defined and studied on Coxeter groups of types $A$ and $B$. We compute the signed (by length) generating function of this statistic over the whole group and over its maximal and some other quotients and show that it always factors nicely. We also present some conjectures.     

Mathematics students’ next steps after graduation

This article is about what happens to newly minted mathematics graduates. It explores data from the first destination statistics from the perspective of mathematics lecturers and others involved in institutions that provide a higher education in mathematics. It also looks at reasons why this issue is important to those engaged in the higher education of mathematics undergraduates. A key finding is that the employment of mathematics graduates is concentrated in the sector of the economy that includes banking, property and financial services which makes the employment prospects for new graduates in mathematics vulnerable to recession in that sector.     

The distribution of length of N random unit vectors for a von Mises population

Greenwood and Durand (1955) have expressed the distribution function (d.f.) of the length $\text{R}$ of N random unit vectors for a von Mises population as a double integral. This double integral is simplified herein by calculating analytically one of the integrals. Hence a numerical calculation for large parameter values now becomes possible.     

Monte-Carlo simulation of laser diode sub-Poissonian light generation

When laser diodes are driven by high-impedance electrical sources, the variance of the number of photo-detection events counted over large time durations is less than the average number of events (sub-Poissonian light). This paper presents a Monte-Carlo simulation that keeps track of each level occupancy (0 or 1) in the conduction and valence bands, and of the number of light quanta in the optical cavity. When there is good electron–lattice thermal contact, the electron and hole temperatures remain equal to that of the lattice. In that case, the elementary laser-diode noise theory results are accurately reproduced by the simulation. But when the thermal contact is poor (or, almost equivalently, at high power levels), new effects occur (spectral-hole burning, temperature fluctuations, statistical fluctuations of the optical gain) that are difficult to handle theoretically. Our numerical simulation shows that the frequency domain over which the photo-current spectral density is below the shot-noise level becomes narrower as the optical power increases.     

Dependence Properties of Multivariate Mixture Distributions and Their Applications

Consider a multivariate mixture model where the random variables X ₁, ..., X _n given (₁, ..., _n ), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X _i 's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models.     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

概率论与数理统计课程改革的创新机制

针对课程改革的目的,结合教学实践,就概率统计课程建设和教学改革的必要性进行综合分析并主张：通过讲述概率统计理论发展史,引导学生明确学习重点;借助多媒体教学,整合教学大纲内容,系统教学;将理论与实际相联系,激发学生学习兴趣;立足基本理论,开设统计学软件实验课程．     

Speckle interferometry for measurement of continuous deformations

Improvements of a method for measurement of continuous displacements and deformations with digital phase shifting speckle pattern interferometry are presented. The method is based on an algorithm that, with the knowledge of the initial phase, only needs one image at a time to evaluate continuos phase changes due to object deformations. In the improved method, the initial random phase of the speckle pattern is evaluated using a number of phase-shifted images before the deformation under study. This is used for increasing the accuracy of the initial phase estimation and reducing influences from image noise and other measurement disturbances. The phase-shifted speckle patterns are used as references for comparison with the speckle patterns of the deformed object, thereby increasing the reliability and accuracy of the phase estimations of the deformed patterns. The technique can be used for measuring deformations such as transients and other dynamic events, heat expansion as well as other phenomena where it is difficult to accomplish phase shifting during deformation.