具有等级约束的三台机排序问题的可中断在线算法

研究具有等级约束的三台机在线排序问题．机器和工件的等级数均为1或2,工件只能在等级数不超过自身等级的机器上加工,且加工允许中断,目标是极小化最大工件完工时间．如果有两台机器等级为1,给出竞争比为3／2的在线算法,并证明算法是最好可能的;如果只有一台等级为1的机器,也给出竞争比为3／2的在线算法．     

Nonlinear inversion of ultrasonic guided waves for in vivo evaluation of cortical bone properties

Ultrasonic guided waves (UGWs), which propagate throughout the entire thickness of cortical bone, are attractive for the early diagnosis of osteoporosis. However, this is challenging due to the impact of soft tissue and the inherent difficulties related to multiparametric inversion of cortical bone quality factors, such as cortical thickness and bulk wave velocity. Therefore, in this research, a UGW-based multi-parameter inversion algorithm is developed to predict strength-related factors. In simulation, a free plate (cortical bone) and a bilayer plate (soft tissue and cortical bone) are used to validate the proposed method. The inversed cortical thickness (CTh), longitudinal velocity (V_L) and transverse velocity (V_T) are in accordance with the true values. Then four bovine cortical bone plates were used in in vitro experiments. Compared with the reference values, the relative errors for cortical thickness were 3.96%, 0.83%, 2.87%, and 4.25%, respectively. In the in vivo measurements, UGWs are collected from the tibias of 10 volunteers. The theoretical dispersion curves depicted by the estimated parameters (V_T, V_L, CTh) match well with the extracted experimental ones. In comparison with dual-energy x-ray absorptiometry, our results show that the estimated transverse velocity and cortical thickness are highly sensitive to osteoporosis. Therefore, these two parameters (CTh and V_T) of long bones have potential to be used for diagnosis of bone status in clinical applications.     

可转包两台流水作业机排序的近似算法

研究可转包的两台流水作业机排序问题, 目标是极小化最大完工时间和总外包费用之和. 首先给出最坏情况界为2的近似算法, 接着对工件满足有序化约束的情形给出最坏情况界为\frac{3}{2}的改进算法, 以上算法界均为紧界.     

Amplitude modulation excitation for cancellous bone evaluation using a portable ultrasonic backscatter instrumentation

The ultrasonic backscatter (UB) has the advantage of non-invasively obtaining bone density and structure, expected to be an assessment tool for early diagnosis osteoporosis. All former UB measurements were based on exciting a short single-pulse and analyzing the ultrasonic signals backscattered in bone. This study aims to examine amplitude modulation (AM) ultrasonic excitation with UB measurements for predicting bone characteristics. The AM multiple lengths excitation and backscatter measurement (AM-UB) functions were integrated into a portable ultrasonic instrument for bone characterization. The apparent integrated backscatter coefficient in the AM excitation (AIB_AM) was evaluated on the AM-UB instrumentation. The correlation coefficients of the AIB_AM estimating volume fraction (BV/TV), structure model index (SMI), and bone mineral density (BMD) were then analyzed. Significant correlations (|R| = 0.82-0.93, p < 0.05) were observed between the AIB_AM, BV/TV, SMI, and BMD. By growing the AM excitation length, the AIB_AM values exhibit more stability both in 1.0-MHz and 3.5-MHz measurements. The recommendations in AM-UB measurement were that the avoided length (T1) should be lower than AM excitation length, and the analysis length (T2) should be enough long but not more than AM excitation length. The authors conducted an AM-UB measurement for cancellous bone characterization. Increasing the AM excitation length could substantially enhance AIB_AM values stability with varying analyzed signals. The study suggests the portable AM-UB instrument with the integration of real-time analytics software that might provide a potential tool for osteoporosis early screening.     

Structure and Photoluminescence of Polycrystalline MgxZn1-xO Films

Different photoluminescence （PL） spectra are observed for rf magnetron sputtered polycrystalline Mg0.25Zn0.75O and Mg0.37Zn0.63O films on silicon substrates when excited by different wavelengths. When the excitation wavelength is 280nm, a UV emission peak at 370nm and a blue peak at 462nm are generated for the Mg0.25Zn0.75O film, and those two peaks for the Mg0.37Zn0.63O film shift to 366nm and 466nm, respectively. The wavelengths of the PL peaks are related to the excitation wavelength. The stronger peak is obtained in the blue band due to a large number of oxygen vacancies caused by excess Zn and Mg atoms, while the weaker peak is obtained in the ultraviolet band.     

Modelling of passively Q-switched lasers with intracavity Raman conversion

We present a model of passively Q-switched Raman lasers by utilizing the rate equations. The intracavity fun-damental photon density, Raman photon density and the initial population-inversion density of the gain medium are assumed to be of Gaussian spatial distributions. These rate equations are normalized by introducing some synthetic parameters and solved numerically, and a group of general curves are generated. Prom these curves we can understand the dependence of the Raman laser pulse characteristics on the parameters about the pumping, the gain medium, the Raman medium and the resonator. An illustrative calculation for a passively Q-switched Nd^3＋：GdVO4 self-Raman laser is presented to demonstrate the usage of the curves and related formulas.[第一段]     

第十七届莫斯科中等学校数学竞赛

数学竞赛这种活动,对于我国来说,还是创举。以前我们很少介绍这方面的材料,以致老师对它很陌生。自从数学竞赛委员会成立以来,老师们纷纷来信反映,希望能在这项工作中供献出自己的一份力量,但是因为知道的不多,无法具体工作。根据老师们的这些反映,我刊这期关出专栏介绍苏联和波兰的数学竞赛的性质和作法,供老师们参考。