Circular Scale of Time and Its Use in Calculating the Schrödinger Perturbation Energy of a Non-Degenerate Quantum State

The paper presents a circular scale of time—and its diagrams—which can be successfully applied in calculating the Schrödinger perturbation energy of a non-degenerate quantum state. This seems to be done in a more simple way than with the aid of any other of the perturbation approaches of a similar kind. As an example of the theory suitable to comparison is considered the Feynman diagrammatic method based on a straight-linear scale of time which represents a much more complicated formalism than the present one. All diagrams of the approach outlined in the paper can obtain as their counterparts the algebraic formulae which can be easily extended to an arbitrary Schrödinger perturbation order. The calculations and results descending from the perturbation orders N between N = 1 and N = 7 are reported in detail.

Talk about Several Time Periodic Pulse Electroosmotic Flow of Maxwell Fluid in a Circular Microchannel

Using the method of Laplace transform, analytical expressions are derived for the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid in circular microchannel. The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations of inverse Laplace transform, the effects of electrokinetic width K, relaxation time and pulse width a on the above several pulse EOF velocities are investigated. In addition, we focused on the comparison and analysis of the formulas and graphs between the triangle and sawtooth pulse EOF with the rectangle pulse EOF. The study found that there are obvious differences in formulas and graphs between triangle and sawtooth pulse EOF with rectangle pulse EOF, and the difference mainly depends on the different definitions of the three kinds of time periodic pulse waves. Finally, we also studied the stability of the above three kinds of pulse EOF and the influence of relaxation time on pulse EOF velocity under different pulse widths is discussed. We find that the rectangle pulse EOF is more stable than the triangle and sawtooth pulse EOF. For any pulse, as the pulse width a increases, the influence of the relaxation time on the pulse EOF velocity will be weakened.

Circular Scale of Time and Energy of a Quantum State Calculated from the Schrodinger Perturbation Theory

The main facts about the scale of time considered as a plot of a sequence of events are submitted both to a review and a more detailed calculation. Classical progressive character of the time variable, present in the everyday life and in the modern science, too, is compared with a circular-like kind of advancement of time. This second kind of the time behaviour can be found suitable when a perturbation process of a quantum-mechanical system is examined. In fact the paper demonstrates that the complicated high-order Schrodinger perturbation energy of a non-degenerate quantum state becomes easy to approach of the basis of a circular scale. For example for the perturbation order N = 20 instead of 19! ≈ 1.216 × 1017 Feynman diagrams, the contribution of which should be derived and calculated, only less than 218 ≈ 2.621 × 105 terms belonging to N = 20 should be taken into account to the same purpose.

Circular Scale of Time as a Way of Calculating the Quantum-Mechanical Perturbation Energy Given by the Schrodinger Method

The Schrodinger perturbation energy for an arbitrary order N of the perturbation has been presented with the aid of a circular scale of time. The method is of a recurrent character and developed for a non-degenerate quantum state. It allows one to reduce the inflation of terms necessary to calculate known from the Feynman’s diagrammatical approach to a number below that applied in the original Schrodinger perturbation theory.

Circular Scale of Time Applied in Classifying the Quantum-Mechanical Energy Terms Entering the Framework of the Schrodinger Perturbation Theory

The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.

Circular Scale of Time and Construction of the Schrodinger Perturbation Series for Energy Made Simple

Physically the examined perturbation problem can be regarded as a set of collision events of a time-independent perturbation potential with a quantum system. As an effect of collisions there is an expected definite change of energy of an initially unperturbed state of the system to some stationary perturbed state. The collision process certainly occupies some intervals of time which, however, do not enter the formalism. A striking property is the result of a choice of the sequence of collisions according to the applied circular scale of time: the scale produces almost automatically the energy terms predicted by the Schrödinger perturbation theory which usually is attained in virtue of complicated mathematical transformations. Beyond of the time scale and its rules—strictly connected with the perturbation order N introduced by Schrödinger—a partition process of the number N-1 is applied. This process, combined with contractions of the time points on the scale, provides us precisely with the perturbation terms entering the Schrödinger theory.

Circular Scale of Time as a Guide for the Schrodinger Perturbation Process of a Quantum-Mechanical System

We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .

双曲型法向圆弧齿轮传动的动力学分析

为探究啮合刚度、传动误差及侧隙对双曲型法向圆弧齿轮传动动态响应的影响,建立齿轮副的动力学方程,并在数值计算的基础上进行仿真分析。运用有限元方法,计算接触位置处的载荷及变形,并对时变啮合刚度、静态传动误差和侧隙进行量化分析。仿真结果表明:对振动位移响应影响最大的是侧隙,其次是时变啮合刚度;对动态啮合力影响最大的则是时变啮合刚度和侧隙。

绝对式圆时栅偏心状态自诊断测量方法研究

针对圆时栅传感器在安装过程中因定子和转子不同心而在整周测量结果中的较大1次谐波误差,影响传感器测量精度的问题,提出了一种基于多测头结构的绝对式圆时栅偏心状态自诊断测量方法。采用多测头结构在圆时栅转子的内外圈分别布置单个和4个独立的感应测头,根据内外圈感应信号的比相关系,判断传感器安装偏心程度,实现传感器在偏心状态下的自诊断功能。通过LabVIEW搭建的测量系统,能同时处理内圈单路感应信号和外圈4路感应信号的相位计数值,得到传感器的绝对位置信息并显示绝对角位移值。实验结果表明,传感器样机经过诊断指示调整安装后,整周测量误差精度可达±1″,有效提高了传感器的测量精度。

输电线路单导线覆冰形状对直流大电流融冰时间的影响

直流大电流融冰是输电线路冰灾防御的有效手段。根据实际运行条件下输电线路单导线覆冰形状在导线各处不一的情况,计算分析单导线圆形覆冰和翼形覆冰的直流大电流融冰时间。计算结果表明,翼形冰融冰时间仅为圆形冰融冰时间的10%左右。在重庆大学雪峰山能源装备安全国家野外观测研究站对LGJ—300/50和LGJ—400/35两种型号单导线进行直流大电流融冰实验。实验结果表明:LGJ—300/50导线翼形冰融冰时间为圆形冰融冰时间的10.6%,LGJ—400/35导线翼形冰融冰时间为圆形冰融冰时间的8.3%。基于此,该文提出抑制导线形成圆形冰促使其生长为翼形冰可降低直流大电流融冰时间,减少融冰能量消耗。

Time-history responses on the surface by regularly distributed enormous embedded cavities:Incident SH-waves

The time-history responses of the surface were obtained for a linear elastic half-plane including regularly distributed enormous embedded circular cavities subjected to propagating obliquely incident plane SH-waves. An advanced numerical approach named half-plane time-domain boundary element method（BEM）, which only located the meshes around the cavities, was used to create the model. By establishing the modified boundary integral equation（BIE）independently for each cavity and forming the matrices, the final coupled equation was solved step-by-step in the timedomain to obtain the boundary values. The responses were developed for a half-plane with 512 cavities. The amplification patterns were also obtained to illustrate the frequencydomain responses for some cases. According to the results,the presence of enormous cavities affects the scattering and diffraction of the waves arrived to the surface. The introduced method can be recommended for geotechnical/mechanical engineers to model structures in the fields of earthquake engineering and composite materials.

Design of S-Band Circularly Polarized Double-Layer Microstrip Antenna

This paper proposes a compact polarization microstrip antenna based on double-layer structure.The bandwidth of the whole antenna is widened by expanding the top and bottom layers respectively.After the design of antenna structure and adjustment of size,the proposed antenna can achieve both the left-and right-hand circular polarizations in 2.33 GHz-2.97 GHz.Measurement results indicate that the effective bandwidth is 640 MHz in S-band and the relative bandwidth can achieve 24% with 11 S less than 15 dB.

Can the Physics of Time Be Helpful in Solving the Differential Eigenequations Characteristic for the Quantum Theory?

The main differential equations of quantum theory are the eigenequations based on the energy operator;they have the energy as eigenvalues and the wave functions as eigenfunctions. A usual complexity of these equations makes their accurate solutions accessible easily only for very few physical cases. One of the methods giving the approximate solutions is the Schrödinger perturbation theory in which both the energies and wave functions of a more complicated eigenproblem are approached with the aid of similar parameters characteristic for a less complicated eigenproblem. No time parameter is necessary to be involved in these calculations. The present paper shows that the Schrödinger perturbation method for non-degenerate stationary quantum states, i.e. the states being independent of time, can be substantially simplified by applying a circular scale of time separately for each order of the perturbation theory. The arrangement of the time points on the scale, combined with the points contractions, gives almost immediately the series of terms necessary to express the stationary perturbation energy of a given eigenproblem. The Schrödinger’s method is compared with the Born-Heisenberg-Jordan perturbation approach.

应用圆形分布法分析阴道分娩经产妇的分娩时间规律

目的随着生育政策的调整,探索分析阴道分娩的经产妇分娩信息的变化及分娩时间是否存在集中趋势,为助产士人力资源配置提供依据。方法选取2013年1月1日至2022年12月31日在北京市某三级甲等综合医院住院分娩的2808名阴道分娩经产妇的分娩信息,应用圆形分布法分析经产妇的分娩时间是否存在集中趋势。结果经产妇年龄为22~54(33.74±3.80)岁,高龄经产妇百分比呈上升趋势,经产妇的分娩时间主要集中在11~12时(P<0.001)。结论随着生育政策的调整,经产妇和高龄经产妇百分比逐年增加,经产和高龄是导致不良分娩结局的因素,对母婴的健康和安全造成威胁,对助产士的能力提出更高的要求,需要加强培训和演练,做好助产士人才梯队储备。

Low Voltage Daily Energy Demand Temperature Dependent Representation by Using Circular Statistics

In this work, a tool that allows visualizing the probability of the power demand according to the temperature and the hours of the day is presented. This aim contributes to the decision making support for the transformer and its service administration. The objective is to represent the demand accurately as a color statistical map based on two variables: the time of day and the ambient temperature. Since the daily energy consumption is periodic regarding the hours of the day in terms of several days, its representation with Gaussian models becomes difficult, but it is simplified when working with circular statistics. The circular statistics used here is the Von Mises distribution, which has the parameters mean address and kappa concentration. Results obtained from measurements made over a year in a medium-voltage transformer with intervals of 60 minutes are shown.

基于时变啮合力的非圆齿轮传动动态磨损研究

由非圆齿轮变速比传动特性引起的时变啮合力对轮齿传动磨损具有重要影响,以精梳机中关键核心部件的椭圆齿轮副为研究对象,应用Hertz基础理论和Archard磨损公式,建立了基于时变啮合力的齿轮磨损计算模型,采用当量齿数法对非圆齿轮的啮合刚度进行求解,分析了单个齿廓的时变啮合力和磨损量的变化规律;在此基础上,研究了阶数和偏心率对椭圆齿轮时变啮合力及磨损量的影响。结果表明,齿轮时变啮合力和齿面磨损量随着偏心率和椭圆齿轮阶数的增加呈现不同程度的增加;时变啮合力在单双齿啮合区交界处发生突变;齿廓磨损量在节圆附近接近零,在齿根和齿顶处的磨损量较大。在对非圆齿轮不同节曲线向径处的磨损量进行研究时发现,在最小节曲线向径处的齿根磨损量显著大于最大节曲线向径处。该研究结果为使用修形方法降低时变啮合力与磨损量,从而延长齿轮寿命提供了一定的理论依据。

基于圆形统计和时间序列的月相对两种拖网渔业CPUE的影响

为了解和掌握月相对渔业产量或单位捕捞努力量渔获量(catch per unit effort,CPUE)的影响规律,利用2016—2019年(每年3月2日—11月29日)马达加斯加西海岸底拖网独角新对虾(Metapenaeus monoceros)和2017—2020年(每年6月15日—10月9日)西白令海中层拖网狭鳕(Theragra chalcogramma)的渔业生产数据,结合基于圆形统计的广义线性模型(GLM)和基于时间序列的广义加性模型(GAM)2种不同的月相量化和统计的方法,分析月相对拖网渔业CPUE的影响。结果表明:月相对独角新对虾的CPUE具有显著性影响(P<0.05),2种方法得出的影响趋势较为一致,较高CPUE出现在上弦月;基于圆形统计的GLM显示,月相对狭鳕CPUE具有显著性影响(P<0.05),较高CPUE出现在新月期,而基于时间序列的GAM显示,月相对狭鳕CPUE的影响不显著(P>0.05);交叉验证显示,基于圆形统计的GLM平均绝对误差(E_(MA))和均方根误差(E_(RMS))均小于基于时间序列的GAM,而GLM分析的决定系数R~2则大于GAM,表明前者的拟合具有更好的准确性、稳定性和拟合优度。研究表明,当周期性循环变量(月份、月相和小时等)具有较弱的显著性时,使用基于圆形统计的GLM更能反映月相对拖网渔业CPUE的影响。

基于环视多通道图像采集的桥墩病害检测

针对传统桥墩病害检测过程中的局限性,通过对桥墩病害的采集机制进行研究,提出了一种基于环形攀爬机器人的桥墩病害检测方法。设计了一种能够适配环形攀爬机器人的环视多通道桥墩病害图像采集系统。采集时先驱动机器人爬行至目标区域,之后通过上位机对核心板进行寻址并发送相应的指令,控制指定的摄像头进行图像的采集工作。为了实现传输过程中的速度匹配,采集到的数据会先暂时存放到SDRAM中,之后按以太网的传输格式对数据进行打包处理,通过捕捉摄像头输出的帧同步信号来判断每一帧图像的开始,并为其添加相应的对齐帧头,由此建立严格的时序电路,来确保采集过程中图像数据的有序传输。该系统可以快速实现对桥墩表面病害信息的采集,病害的检测精度可以达到0.3 mm~0.4 mm,能够满足大部分病害的检测要求。

环状RNA hsa_circ_103809在结肠癌中的表达及其临床意义

目的探讨环状RNA(circRNA)hsa_circ_103809在结肠癌组织中的表达及与复发和预后的关系。方法对结肠癌HCT116、SW480、DLD-1、SW620细胞株及正常结肠上皮NCM460细胞株中hsa_circ_103809的表达进行检测,对既往实验结果进行验证。另选取2018年6月至2019年6月于金华市人民医院结直肠肛门外科且术后病理明确为结肠癌患者80例,术后取肿瘤组织及癌旁组织作为研究样本,检测样本中hsa_circ_103809表达差异,并分析hsa_circ_103809与结肠癌临床病理学的关系;受试者工作特征(receiver operating characteristic,ROC)曲线分析评估hsa_circ_103809对结肠的诊断效能;Cox风险回归模型对结肠癌预后的进行单、多因素分析;Kaplan-Meier生存曲线及Log rank检验对结肠癌进行生存分析。结果①与正常结肠上皮NCM460细胞株相比,结肠癌HCT116、SW480、DLD-1、SW620细胞株hsa_circ_103809表达均降低(P<0.05);②与癌旁组织相比,肿瘤组织中hsa_circ_103809表达降低(P<0.05);③肿瘤组织中hsa_circ_103809表达与结肠癌患者性别、年龄、病理分期无关(P>0.05),与分化程度、肿瘤类型、癌胚抗原(carcinoembryonic antigen,CEA)水平有关(P<0.05);hsa_ci④rc_103809对结肠癌诊断效能曲线下面积为0.736(95%CI:0.661~0.803),约登指数为0.375,截断值为0.726,敏感度为65.50%,特异性为70.80%;⑤经Cox风险回归模型分析显示肿瘤类型与hsa_circ_103809低表达是患者复发的独立危险因素;hsa_circ_103809低表达患者生存时间明显短于高表达患者(P<0.05)。结论hsa_circ_103809在结肠癌肿瘤组织中呈低表达,且对患者预后复发及生存周期具有一定评估价值。

圆轨道有限时间收敛导引律

运载器运送飞行器进入期望的飞行轨道,通常采用传统的闭路导引方法。导引方法仅仅能将飞行器导引到期望的目标点,也就是说到达期望的位置。但是由于速度矢量没有约束,导致到达期望的位置后速度矢量与期望的速度矢量之间有偏差,进而随着飞行器的运动,使得飞行轨道越来越偏离目标轨道。针对圆轨道入轨时的初始位置和速度误差修正和轨道精确导引问题,提出一种基于Lyapunov理论的圆轨道有限时间收敛导引律。上述导引律通过在导引律中引入轨道向径偏差和向径变化率进行反馈,来减小初始入轨位置和速度偏差并对轨道进行精确导引。通过数学仿真进行验证,结果表明圆轨道有限时间收敛导引律能有效减小初始位置和速度误差并对圆轨道进行精确导引。