棱柱和Mobius梯的Tutte多项式

棱柱是圈C_(n)和路P_(2)的笛卡尔积,也可以看作两端连接的梯图.Mobius梯的结构与棱柱相似,可看作扭曲后两端连接的梯图,并且自然地嵌入Mobius带.图的Tutte多项式是一个双变量多项式图不变量,通过对变量赋值或变换可以得到生成树数目、连通生成子图数目、色多项式和可靠多项式等许多图不变量.本文运用Tutte多项式的删除-收缩运算,获得了棱柱和Mobius梯的Tutte多项式.

一类柱面与Mobius带的匹配多项式

给两条n个点的路,其顶点从左向右分别标记为1,2,…,n和1′,2′,…,n′.将这两条路上的点i和i′(i=1,2,…,n)分别用一条边连接,得到的图记为L_(n,n),称为梯子.将图L_(n,n)的顶点1和n,1′和n′分别用一条边连接得到的图记为Z_(n,n),称为柱面.将图L_(n,n)的顶点1和n′,1′和n分别用一条边连接得到的图记为M_(n,n),称为Mobius带.即L_(n,n)=Pn×P2,Z_(n,n)=Cn×P2分别表示梯子与柱面图.本文利用递推关系和生成函数的方法分别给出了L_(n,n),M_(n,n)和Z_(n,n)的匹配多项式及完美匹配数目的计算公式.

Mobius自动验证系统在容积旋转调强放疗验证中的应用研究

目的探究Mobius自动验证系统在容积旋转调强放射治疗(Volumetric Modulated Arc Therapy,VMAT)计划验证的应用可行性。方法随机选择2021年4月至2022年1月在西安交通大学第一附属医院接受VMAT的不同部位肿瘤患者90例,分别实行Mobius和Delta4两种方法验证,统计不同部位两种算法靶区剂量学差异与多个标准下γ通过率,评估Mobius软件在不同部位VMAT计划验证中的精确性与可行性。结果两种系统不同算法下靶区平均剂量和90%覆盖度之间的差异均满足临床剂量学差异要求(<3%),不同部位差异有统计学意义(P<0.05),其中盆腔部位剂量差异最小;3%/3mm标准时两种验证设备VMAT验证γ通过率均能满足临床验证要求(γ>95%),除胸部计划外,Mobius与Delta4设备在3%/3 mm、3%/2 mm、2%/2 mm这3种γ评估标准下均具有良好的一致性(P>0.05),但验证未能通过2%/2 mm临床标准(γ<90%)。结论3%/3 mmγ评估标准下,Mobius自动验证系统与基于模体的Delta4验证设备具有良好的一致性,可以应用于VMAT计划验证,但不同部位肿瘤计划间差异需要注意。

基于Mobius 3D的舌癌IMRT计划的初步应用与探讨

目的 研究独立三维剂量验证系统Mobius 3D在舌癌放疗调强适形放射治疗(Intensity-Modulated Radiation Therapy,IMRT)计划中二次验算的可行性。方法 随机选取上海交通大学医学院附属第九人民医院在2021年1—12月收治的50例舌癌放疗患者的定位CT图像,分别在Monaco 5.11和Eclipse1 5.5计划系统进行9野等分IMRT计划设计,计划达到临床要求后分别将计划传入Mobius 3D中进行剂量二次验算。统计两种计划系统在传输过程中靶区和危及器官的体积变化和剂量差异,二次验算剂量前后行非参数Wilcoxon秩和检验,并使用γ通过率综合评估计划,验证三维剂量验证系统应用的可行性。结果 Monaco传输至Mobius中各感兴趣区域(Region of Interest,ROI)体积差异均小于Eclipse,最大变化差异ROI均为左腮腺(0.7%和1.34%)。经二次验算,两种计划系统的靶区和剂量差异均在0.6%内,但Eclipse计划系统二次验算剂量结果差异大于Monaco计划系统。Monaco计划系统与Mobius 3D二次验算后,计划靶区(Planning Target Volume,PTV54)的Dmean验算前后差异有统计学意义(P<0.05);Eclipse计划系统与Mobius 3D二次验算后,PTV60、左腮腺和右腮腺的Dmean在验算前后差异有统计学意义(P<0.05)。各结构和计划的γ通过率均值均大于97%,在整体计划γ通过率中,Monaco的通过率略高于Eclipse。结论 使用独立三维剂量验证Mobius 3D系统对舌癌IMRT计划进行二次验算具有可行性,结果准确清晰,使用简便,可将该系统作为计划二次核查使用,提高调强计划剂量验证的效率与准确性。

二维矩形Strip Packing问题的算法研究与改进

二维矩形Strip Packing问题的约束条件及目标函数与基本型二维矩形Packing问题类似,都是在有限的矩形容器中,有效地摆放各个矩形块,以最大化容器利用率为目标。为了解决这一NP-hard问题,该文在邓见凯、王磊提出的拟人型全局优化算法的基础上进行了深入的算法研究与改进。针对Strip Packing问题特点,提出了QHG(Quasi-Human Group)算法,其核心改进涵盖了多个方面,包括扩充初始点集合、删除和替换评价标准以及扩大邻域空间搜索范围。和单个局部极小值点的迭代相比,对局部极小值点集合进行迭代所生成布局优度更高,跳坑策略用于跳出局部极小值点,将搜索引向有希望的区域,优美度枚举有望进一步提高布局优度。通过这些措施,QHG算法更好地模拟人类决策过程,提高了全局搜索的效率。为评估QHG算法性能,对8组标准问题实例(C组、N组、NT组、CX组、NP组、ZDF组、2sp组、bwmv组)进行了大量实验。实验结果表明,QHG算法生成的布局优度优于当前国际文献中的几种较先进算法,展现了其在Strip Packing问题上的卓越性能。

A dual-RPA based lateral flow strip for sensitive,on-site detection of CP4-EPSPS and Cry1Ab/Ac genes in genetically modified crops

Traditional transgenic detection methods require high test conditions and struggle to be both sensitive and efficient.In this study,a one-tube dual recombinase polymerase amplification(RPA)reaction system for CP4-EPSPS and Cry1Ab/Ac was proposed and combined with a lateral flow immunochromatographic assay,named“Dual-RPA-LFD”,to visualize the dual detection of genetically modified(GM)crops.In which,the herbicide tolerance gene CP4-EPSPS and the insect resistance gene Cry1Ab/Ac were selected as targets taking into account the current status of the most widespread application of insect resistance and herbicide tolerance traits and their stacked traits.Gradient diluted plasmids,transgenic standards,and actual samples were used as templates to conduct sensitivity,specificity,and practicality assays,respectively.The constructed method achieved the visual detection of plasmid at levels as low as 100 copies,demonstrating its high sensitivity.In addition,good applicability to transgenic samples was observed,with no cross-interference between two test lines and no influence from other genes.In conclusion,this strategy achieved the expected purpose of simultaneous detection of the two popular targets in GM crops within 20 min at 37°C in a rapid,equipmentfree field manner,providing a new alternative for rapid screening for transgenic assays in the field.

Soybean maize strip intercropping:A solution for maintaining food security in China

The practice of intercropping leguminous and gramineous crops is used for promoting sustainable agriculture,optimizing resource utilization,enhancing biodiversity,and reducing reliance on petroleum products.However,promoting conventional intercropping strategies in modern agriculture can prove challenging.The innovative technology of soybean maize strip intercropping(SMSI)has been proposed as a solution.This system has produced remarkable results in improving domestic soybean and maize production for both food security and sustainable agriculture.In this article,we provide an overview of SMSI and explain how it differs from traditional intercropping.We also discuss the core principles that foster higher yields and the prospects for its future development.

Molecular investigation into the transformation of recalcitrant dissolved organic sulfur in refinery sour water during stripping process

Refinery sour water primarily originates from the tops of towers in various units and coker condensate,and cannot be discharged directly to a wastewater treatment plant due to high levels of chemical oxygen demand(COD)and organic sulfur contents.Even after the recovery of H_(2)S from the sour water by the stripping process,the effluent still contains a high concentration of dissolved organic sulfur(DOS),which can have a huge bad influence.While chemical composition of dissolved organic matter(DOM)in refinery wastewater has been extensively studied,the investigation of recalcitrant DOS from sour waters remains unclear.In the present study,chemical composition of sour water DOMs(especially DOS)was investigated using fluorescence spectroscopy(excitation-emission matrix,EEM)and mass spectrometry,including gas chromatography-mass spectrometry(GC-MS)and high-resolution Orbitrap MS.The GC-MS and EEM results showed that volatile and low-aromaticity compounds were effectively removed during the stripping process,while compounds with high hydrophilicity and humification degree were found to be more recalcitrant.The Orbitrap MS results showed that weak-polar oxygenated sulfur compounds were easier to be removed than oxygenated compounds.However,the effluent still contained significant amounts of sulfur-containing compounds with multiple sulfur atoms,particularly in the form of highly unsaturated and aromatic compounds.The Orbitrap MS/MS results of CHOS-containing compounds from the effluent indicate that the sulfur atoms may exist as sulfonates,disulfide bonds,thioethers.Understanding the composition and structure of sour water DOS is crucial for the development of effective treatment processes that can target polysulfide compounds and minimize their impact on the environment.

A simple route for preparation of TRIP-assisted Si-Mn steel with excellent performance using direct strip casting

The complex producing procedures and high energy-consuming limit the large-scale production and application of advanced high-strength steels(AHSSs).In this study,the direct strip casting(DSC)technology with unique sub-rapid solidification characteristics and cost advantages was applied to the production of low-alloy Si-Mn steel with the help of quenching&partitioning(Q&P)concept to address these issues.Compared this method with the conventional compact strip production(CSP)process,the initial microstructure formed under different solidification conditions and the influence of heat treatment processes on the final mechanical properties were in-vestigated.The results show that the initial structure of the DSC sample is a dual-phase structure composed of fine lath martensite and bainite,while the initial structure of the CSP sample consists of pearlite and ferrite.The volume fraction and carbon content of retained austenite(RA)in DSC samples are usually higher than those in CSP samples after the same Q&P treatment.DSC samples typically demonstrate better comprehensive mechanical properties than the CSP sample.The DSC sample partitioned at 300℃ for 300 s(DSC-Pt300)achieves the best comprehensive mechanical properties,with yield strength(YS)of 1282 MPa,ultimate tensile strength(UTS)of 1501 MPa,total elongation(TE)of 21.5%,and product of strength and elongation(PSE)as high as 32.3 GPa·%.These results indicate that the excellent mechanical properties in low-alloy Si-Mn steel can be obtained through a simple process(DSC-Q&P),which also demonstrates the superiority of DSC technology in manufacturing AHSSs.

Effect of phosphorus content on interfacial heat transfer and film deposition behavior during the high-temperature simulation of strip casting

The interfacial wettability and heat transfer behavior are crucial in the strip casting of high phosphorus-containing steel.A hightemperature simulation of strip casting was conducted using the droplet solidification technique with the aims to reveal the effects of phosphorus content on interfacial wettability,deposited film,and interfacial heat transfer behavior.Results showed that when the phosphorus content increased from 0.014wt%to 0.406wt%,the mushy zone enlarged,the complete solidification temperature delayed from1518.3 to 1459.4℃,the final contact angle decreased from 118.4°to 102.8°,indicating improved interfacial contact,and the maximum heat flux increased from 6.9 to 9.2 MW/m2.Increasing the phosphorus content from 0.081wt%to 0.406wt%also accelerated the film deposition rate from 1.57 to 1.73μm per test,resulting in a thickened naturally deposited film with increased thermal resistance that advanced the transition point of heat transfer from the fifth experiment to the third experiment.

High-resolution imaging of magnetic fields of banknote anti-counterfeiting strip using fiber diamond probe

Counterfeiting of modern banknotes poses a significant challenge,prompting the use of various preventive measures.One such measure is the magnetic anti-counterfeiting strip.However,due to its inherent weak magnetic properties,visualizing its magnetic distribution has been a longstanding challenge.In this work,we introduce an innovative method by using a fiber optic diamond probe,a highly sensitive quantum sensor designed specifically for detecting extremely weak magnetic fields.We employ this probe to achieve high-resolution imaging of the magnetic fields associated with the RMB 50denomination anti-counterfeiting strip.Additionally,we conduct computer simulations by using COMSOL Multiphysics software to deduce the potential geometric characteristics and material composition of the magnetic region within the anti-counterfeiting strip.The findings and method presented in this study hold broader significance,extending the RMB 50 denomination to various denominations of the Chinese currency and other items that employ magnetic anti-counterfeiting strips.These advances have the potential to significantly improve and promote security measures in order to prevent the banknotes from being counterfeited.

Analysis of spot defects on the surface of a cold-rolled Fe-36%Ni alloy strip

Many spot defects were found on the surface of a cold-rolled Fe-36%Ni alloy strip produced in a factory,which seriously affected the surface quality of the product.Through metallographic microscopy and scanning electron microscopy analyses,it was found that the spot defects were caused by the residual oxide layer on the surface of the cold-rolled Fe-36%Ni alloy strip after hydrogen annealing.By properly increasing the grinding amount of the blank before cold rolling to remove the oxide layer,the spot defects on the surface of the cold-rolled strip were effectively eliminated,and the surface quality of the product was ensured.

Similarity evaluation model for the internal defect detection of strip steel

An internal defect meter is an instrument to detect the internal inclusion defects of cold-rolled strip steel.The detection accuracy of the equipment can be evaluated based on the similarity of the multiple detection data obtained for the same steel coil.Based on the cosine similarity model and eigenvalue matrix model,a comprehensive evaluation method to calculate the weighted average of similarity is proposed.Results show that the new method is consistent with and can even replace artificial evaluation to realize the automatic evaluation of strip defect detection results.

Mobius变换的推广及其几何性质

先引入Mobius变换,讨论了此变换在复平面中的一些性质,接着把Mobius变换的实数形式推广到了n维空间,并证明了此推广即为共形变换.最后,讨论了Mobius变换在n维空间中的球几何和微分度量.

三维非初等离散Mobius群的必要条件

本文利用Ｃｌｉｆｆｏｒｄ矩阵及三维Ｍｏｂｕｓ变换的分类及判别法研究了三维Ｍｏｂｉｕｓ群．得到了：三维Ｍｏｂｉｕｓ变换ｆ和ｇ生成非初等离散群且ｆ是抛物或双曲元素时的必要条件：｜ｔｒ￣２－４｜＋｜ｔｒ［ｆ，ｇ］－２｜≥１．并由此推导出几个重要的结果．

基于三维Mobius变换的图像置乱方法

利用三维Mobius变换,结合混沌序列具有容易生成、对初始条件敏感以及具有白噪声的统计特性等特点,提出一种数字图像置乱方法.该置乱方法在位置空间进行,具有随机性和变化多样性.仿真表明,用本文方法得到了较好的置乱效果.

Mobius氏综合征一例

Mobius综合征是一种少见的疾病,主要表现为多对颅神经损害和伴发多部位的先天畸形,作者通过1的报告及文献复习,介绍了此病的临床特征、病因、鉴别诊断以及治疗方法。

新型陈-Mobius模拟通信系统的计算机仿真与分析

针对新型陈-Mobius模拟通信系统,以基于MATLAB的Simulink作为软件工具,对该系统的性能进行了仿真和分析.并且提供了大量的仿真实验数据作为说明.

陈-Mobius多路载波数字通信系统及性能仿真

将几种常用数字波形的陈-Mobius逆变换作为多路载波数字通信系统数字输入信号的编码波形函数族,由其对二进制输入信号进行调制后直接叠加在一起在一个物理信道上进行传输;在接收端,用与各调制编码波形对应的正交的数字波形对各路信号进行同步相干解调,从而构成新的相干调制解调系统;而调制编码波形与解调波形函数族这两个函数族内部本身却是非正交的;而后应用MATALAB平台对这种新型多路载波数字通信系统进行性能仿真,在大量仿真平均的基础上,绘出了使用各函数族的系统的位错率对信噪比曲线,并与传统的相干调制解调系统的仿真结果相比较;结果表明,该系统具有更优异的抗强噪声与干扰的性能,可实现多路载波数字通信的直接叠加,节约系统的初始投资与运行费用。