Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning

In this paper, we propose a modification of Benson’s algorithm for solving multiobjective linear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson’s original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of -nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjective linear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method.     

Some problems in metric fixed point theory

Three papers, published coincidentally and independently by Felix Browder, Dietrich G?hde, and W. A. Kirk in 1965, triggered a branch of mathematical research now called metric fixed point theory. This is a survey of some of the highlights of that theory, with a special emphasis on some of the problems that remain open. Dedicated to Felix Browder on the occasion of his 80th birthday     

多道次搅拌摩擦加工对5083-O铝合金组织性能的影响

在不同轴肩直径、搅拌头转速和搅拌头行进速度下,对27mm厚5083-O铝合金进行了多道次搅拌摩擦加工(multi passfrictionstirprocessing),搭接率为100%,共进行3道次搅拌摩擦加工.研究结果表明,加工区由细小的再结晶组织组成;随着加工道次的增加,加工区内部缺陷体积减少,晶粒进一步细化,析出相细化并均匀分布,力学性能提高,加工区最高抗拉强度可达360MPa,延伸率也优于母材;其中,第二道次加工对材料组织和性能的影响最为明显.     

一种基于同步性的听觉滤波信号关联度分析方法

受听觉系统运行机制的启发,提出一种以同步性为线索的信号分量间关联度的分析方法.首先对信号进行带通滤波、逆序滤波和半波整流,继而提取一次、二次和三次极值点,并生成三种单位序列.基于单位序列分别计算相邻滤波通道同步性和一、二次极值点同步性,这两种同步性可描述信号分量间的波形吻合程度和波动关联性.分析了带有侧隙的齿轮振动信号,结果表明所提方法可发现具有较高关联性的信号分量,有助于缩减数据量和揭示被测对象的动力行为特性.     

北京市轨道交通票制票价改革研究

为了发挥轨道交通票价的杠杆作用,进一步完善地面公交与轨道交通衔接,优化交通结构,增加客票收入,本文通过分析国内外大都市票制体系、票价优惠策略及北京市轨道交通发展状况,提出北京市轨道交通票价改革方案。在重点分析客流量、运营成本和城市人均收入水平的基础上,确定单一票价水平为4元;实施高低峰分时定价策略,通过分析三峰时间分布及高峰客流构成,用Logit模型计算出高低峰票价分别为6元、2元;提出制定月票的策略,以及其他一系列辅助票制来保障上班族、老人等的权益。该研究为实现北京市轨道交通可持续发展提供了理论基础。     

西藏边境贸易的历史演进与现实情况分析

西藏地方边境贸易发展历史悠久,在发展中形成了自身特点。西藏边境贸易一方面推动了藏区畜牧业产品和其他农副产品大量流入其他周边国家和地区,同时其他地区的茶叶、绢、布、陶瓷、米面、调料、茜草及手工产品也大量进入藏区,边民之间互设贸易,互通有无,促进了双方畜牧业、手工等产业的发展,增强了边民间以及我国与相邻国家和地区的文化交流和睦邻友好关系。文章追本溯源阐述了西藏边境贸易的历史,分析了现存问题,并提出了大力加强边贸市场的基础设施建设、改善通关环境;优化结构,发展特色产业,提高产品质量及附加值;加大对边境旅游的扶持力度;注重制度体系建设力度等对策建议。     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

Raman spectroscopic study of the molecular structure of the uranyl mineral zippeite from Jáchymov (Joachimsthal), Czech Republic

Raman spectra at 298 and 77K and infrared spectra of the uranyl sulfate mineral zippeite from Jáchymov (Joachimsthal), Czech Republic, K(0.6)(H(3)O)0.4[(UO(2))6(SO(4))3(OH)7].8H2O, were studied. Observed bands were tentatively attributed to the (UO(2))2+ and (SO(4))2- stretching and bending vibrations, the OH stretching vibrations of water molecules, hydroxyls and oxonium ions, and H(2)O, oxonium, and delta U-OH bending vibrations. Empirical relations were used for the calculation of U-O bond lengths in uranyl R (A)=f(nu(3) or nu(1)(UO(2))2+). Calculated U-O bond lengths are in agreement with U-O bond lengths from the single crystal structure analysis and those inferred for uranyl anion sheet topology of uranyl pentagonal dipyramidal coordination polyhedra. The number of observed bands supports the conclusion from single crystal structure analysis that at least two symmetrically distinct U6+ (in uranyls) and S6+ (in sulfates), water molecules and hydroxyls may be present in the crystal structure of the zippeite studied. Strong to very weak hydrogen bonds present in the crystal structure of zippeite studied were inferred from the IR spectra.     

A novel method for flow injection analysis of total antioxidant capacity using enzymatically produced ABTS and biamperometric detector containing interdigitated electrode

Application of interdigitated array microelectrodes as electrochemical sensors for determination of antioxidant capacity is reported. Electrochemical measurements with interdigitated electrodes (IDE) were studied in both stationary solutions and the flow system. The method is based on biamperometric measurements using ABTS⁺|ABTS redox couple in phosphate buffer solution, pH 7.40. During analysis, the ABTS radical cation was enzymatically produced by peroxidase in a tubular flow-through reactor. The performance of bioreactor was tested at different concentrations of immobilized enzyme, ABTS and hydrogen peroxide. The influence of flow rate on proper operation of the bioreactor was also studied. The results of antioxidant activity were determined using Trolox as a standard. The applied IDE detector accomplished good sensitivity of 0.3 nA/μM of Trolox and offered linear range between 20 to 500 μM of Trolox.The comparison of results (R² = 0.9915) for antioxidant activity between spectroscopic and FIA biamperometric measurements by interdigitated electrodes confirmed the applicability of the proposed method for determination of antioxidant capacity.     

Synthesis of lariat organochalcogenoethers based on azacalix[3]arenes for the potentiometric detection of [UO2] ions

The syntheses of organochalcogen-supported azacalix[3]arenes are described in a one-pot manner in satisfactory yields. A remarkably selective potentiometric response was accomplished for uranyl ions over a variety of other metal ions, including alkali (Na⁺, K⁺), alkaline-earth (Mg²⁺, Ca²⁺, Ba²⁺), transition and heavy metal ions (Co²⁺, Ni²⁺, Cu²⁺, Ag⁺, Fe³⁺, Zn²⁺, Cd²⁺ and Pb²⁺) using an ion-selective electrode based on compound 3 incorporated into a polymeric (PVC) membrane.