Analysis of pseudo-random number generators in QMC-SSE method

In the quantum Monte Carlo(QMC)method,the pseudo-random number generator(PRNG)plays a crucial role in determining the computation time.However,the hidden structure of the PRNG may lead to serious issues such as the breakdown of the Markov process.Here,we systematically analyze the performance of different PRNGs on the widely used QMC method known as the stochastic series expansion(SSE)algorithm.To quantitatively compare them,we introduce a quantity called QMC efficiency that can effectively reflect the efficiency of the algorithms.After testing several representative observables of the Heisenberg model in one and two dimensions,we recommend the linear congruential generator as the best choice of PRNG.Our work not only helps improve the performance of the SSE method but also sheds light on the other Markov-chain-based numerical algorithms.

Pythagoreans Figurative Numbers: The Beginning of Number Theory and Summation of Series

In this article we shall examine several different types of figurative numbers which have been studied extensively over the period of 2500 years, and currently scattered on hundreds of websites. We shall discuss their computation through simple recurrence relations, patterns and properties, and mutual relationships which have led to curious results in the field of elementary number theory. Further, for each type of figurative numbers we shall show that the addition of first finite numbers and infinite addition of their inverses often require new/strange techniques. We sincerely hope that besides experts, students and teachers of mathematics will also be benefited with this article.

Obtaining Simply Explicit Form and New Properties of Euler Polynomials by Differential Calculus

Utilization of the shift operator to represent Euler polynomials as polynomials of Appell type leads directly to its algebraic properties, its relations with powers sums;may be all its relations with Bernoulli polynomials, Bernoulli numbers;its recurrence formulae and a very simple formula for calculating simultaneously Euler numbers and Euler polynomials. The expansions of Euler polynomials into Fourier series are also obtained;the formulae for obtaining all πm as series on k-m and for expanding functions into series of Euler polynomials.

Series expansion feasibility of singular integral in method of moments

When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.

A METHOD OF SOLVING THE FUZZY FINITE ELEMENT EQUATIONS IN MONOSOURCE FUZZY NUMBERS

For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.

The Series of Reciprocals of Non-central Binomial Coefficients

Utilizing Gamma-Beta function, we can build one series involving reciprocal of non-central binomial coefficients, then We can structure several new series of reciprocals of non-central binomial coefficients by item splitting, these new created denominator of series contain 1 to 4 odd factors of binomial coefficients. As the result of splitting items, some identities of series of numbers values of reciprocals of binomial coefficients are given. The method of splitting terms offered in this paper is a new combinatorial analysis way and elementary method to create new series.

The Number of Representations of an Integer as a Sum of Eight Triangular Numbers

An infinite product is expanded to Laurent series by residue theorem.Applying this expansion, the formula for the number of representations of an integer as a sum of eight triangular numbers is easily obtained.

Determination of Polarity Terms of Some Nitrogen-Containing Surfactants and Simulated Hydrophobic Tail Models by Gas Chromatography

Some polarity terms of two groups of nitrogen-containing surfactants （six alkanolamides and nine polyoxyethylenated long chain amines） are measured through gas chromatography. The apparent methanol carbon number (CMeOH) and polarity index （IP） values are determined on the investigated surfactants as stationary phases in packed columns. Similarly, CMeOH and IP values are determined on simulated hydrophobic tail （SHT） models. The obtained results reveal that the introduction of SHT approach permits the distinction between the polarities of different surfactants and their head groups. The measured polarity terms are discussed as related to hydrophile-lipophile balance （HLB） number and the hydrophobic group carbon number （RCN）. Some equations relating the measured polarity values and these variable have been developed.

Prediction of Kappa Number in Eucalyptus Kraft Pulp Continuous Digester Using the Box &Jenkins Methodology

The quality of the resulting pulping continuous digesters is monitored by measuring the Kappa number, which is a reference of residual lignin. The control of the kappa number is carried out mainly in the top of the digester, therefore it is important to get some indication of this analysis beforehand. In this context, the aim of this work was to obtain a prediction model of the kappa number in advance to the laboratory results. This paper proposes a new approach using the Box & Jenkins methodology to develop a dynamic model for predicting the kappa number from a Kamyr continuous digester from an eucalyptus Kraft pulp mill in Brazil. With a database of 1500 observations over a period of 30 days of operation, some ARMA models were studied, leading to the choice of ARMA (1, 2) as the best forecasting model. After fitting the model, we performed validation with a new set of data from 30 days of operation, achieving a model of 2.7% mean absolute percent error.

Periodic, Irrational and Transcendental Numbers in the Factorial Series

The main aim of the article is to investigate the irrational and transcendental properties of certain real numbers by means of the factorial series and the factorial number system. The difference between the factorial series and the factorial system is that the factorial series does not set an upper bound at a given place after the radix point, while in the factorial system (i – 1) is the maximal possible value for ri after the radix point. I give an extended definition of periodic numbers, and show the relationship between periodic and irrational numbers. I prove the transcendence of e by means of the factorial series and the factorial number system.

基于季节ARIMA模型对某三级综合性医院门诊量的预测研究

目的 通过建立季节ARIMA模型,对浙江省某三级综合性医院门诊量进行预测,为医院合理配备门诊人力资源提供依据。方法 以2013年1—6月浙江省某医院门诊量数据为基线,利用SPSS软件构建季节ARIMA模型,对2023年7—12月的门诊量进行预测,通过对比门诊量实测值,评价季节ARIMA模型预测门诊人次的精度。结果 该综合性医院门诊量呈现逐年上升趋势,并呈现周期性波动的特征。拟合的最优季节ARIMA模型为ARIMA(0,1,1)(1,0,1)12,BIC(贝叶斯信息准则)为5.273,MAPE(平均绝对百分误差)为14.265,R2(模块决定系数)为0.408,总体相对误差为1.83%,预测结果良好。结论 季节ARIMA模型较好地模拟了该三级综合性医院门诊量在时间序列上的变化趋势,为该院门诊量的短期预测提供理论依据。

基于时序InSAR监测的VMD-SSA-LSTM矿区地表形变预测模型研究

矿区地表形变引起的滑坡、塌陷等灾害对矿山安全生产造成了极大影响,因此对地表形变进行预测对于矿山安全开采和灾害预警预报具有重要的现实意义。采用时序InSAR技术获取矿区面域式地表形变数据,结合变分模态分解算法(VMD)对其进行分解,通过构建麻雀优化算法(SSA)与长短期记忆神经网络(LSTM)相结合的预测模型,对分解后的形变分量进行综合预测;以云南省玉溪市大红山矿区为例,利用该模型对其地表形变进行了预测,结果表明:VMD算法在一定程度上可以解决矿山地表形变数据时序特征复杂且难以直接分析判别的问题;SSA-LSTM预测模型通过智能搜索算法自动寻找预测网络模型超参数,有效减少了人为因素对模型预测效果的干扰,模型预测结果的决定系数R2均大于0.96;同时,该模型采用“多维输入”的方式训练模型,提高了训练效率;该模型在预测精度、训练效率等方面均取得了较好的效果。采用VMD-SSA-LSTM预测算法对时间序列InSAR监测下的形变数据进行分析能有效预测矿区地表形变,可为矿山安全生产管理提供参考。

基于Informer神经网络的锂离子电池容量退化轨迹预测

通过对锂离子电池容量退化轨迹的精确预测可以大幅提升电池材料的研究效率。针对Transformer网络在锂电池容量退化轨迹预测这种长时间序列预测任务中存在的问题,本工作采用滑动窗口策略,构建了一种基于Informer网络的锂离子电池容量退化轨迹预测方法。首先,利用滑动窗口对数据集进行划分和再拼接,便于神经网络挖掘数据序列内部的相关性;然后,根据Informer网络的周期性时间特征捕捉能力设计适用于锂电池数据的全局时间戳;最后,使用前10%容量数据通过多步滚动预测方法实现模型输出,缓解预测中的误差累积问题,进而得到完整的预测轨迹。通过选取不同的误差评价指标和训练过程中的时间开销,在美国马里兰大学提供的锂电池数据集上验证了所建立模型的准确性和训练效率,并在美国航空航天局提供的电池数据集上验证了模型的泛用性。本工作模型的预测结果与多层感知机神经网络、循环神经网络及Transformer网络模型对比,退化轨迹与真实轨迹最为拟合,且训练时间开销小,预测结果的平均绝对误差和均方根误差控制在2.57%和3.5%,验证了所提预测方法的有效性。

基于LSTM-WGAN的时间序列数据异常检测

在时序数据中发现隐藏的异常行为或事件,可以保障生产安全,具有重要意义。目前的异常检测模型存在训练不稳定、容易产生梯度消失的问题,影响异常检测效果,针对该问题,提出一种LSTM-WGAN模型,WGAN负责捕获变量之间的潜在关联,进一步提升了LSTM的检测能力。同时,以Wasserstein距离代替交叉熵损失训练判别器和生成器,结合重构损失以及判别损失实现异常检测。在NAB公开数据集上的实验结果表明LSTM-WGAN相较于基准模型在准确率、召回率以及F1得分上都有较大幅度的提升。

CONVERGENCE AND GROWTH OF MULTIPLE DIRICHLET SERIES

This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.

Halin图和Series-Parallel图的动态色数

图的动态着色是BruceMontgomery于2001年引入的一个新概念。本文分别证明了Halin图和非5圈的Series Parallel图的动态色数都不超过4。

Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages

This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks, and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employ- ing the Fourier-Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential func- tion and the modal coordinates of wave height. Based on the B ernoulli-Euler beam theory and the D＇Alembert＇s prin- ciple, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordi- nate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the cou- pling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange＇s equations in terms of quasi-coordinates. Lastly, the cou-piing dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.

A series solution for surface motion amplification due to underground group cavities:Incident P waves

A series solution for surface motion amplification due to underground group cavities for incident plane P waves is derived by Fourier-Bessel series expansion method. It is shown that underground group cavities significantly am-plify the surface ground motion nearby. It is suggested that the effect of subways on ground motion should be con-sidered when the subways are planned and designed.

基于变量选择与Transformer模型的中长期电力负荷预测方法

准确且有效的负荷预测对于电力系统的实时运行和调度非常重要。提出了一种融合变量选择与稀疏Transformer模型的预测方法,将静态变量和时序变量作为输入,充分发挥静态变量在全局时间范围内的信息增强作用,基于门控机制设计变量分权组件,根据变量与预测结果的相关性,赋予变量不同的权重。设计了双层编码结构,进行时序特征提取,对注意力进行稀疏处理,通过多变量输入对未来时刻负荷进行预测。基于真实电力负荷数据的实验表明,本文模型能够提高中长期负荷预测精度和效率。

Fast Converging Series for Riemann Zeta Function

Riemann zeta function has a key role in number theory and in its applications. In this paper we present a new fast converging series for . Applications of the series include the computation of the and recursive computation of , and generally . We discuss on the production of irrational number sequences e.g. for encryption coding and zeta function maps for analysis and synthesis of log-time sampled signals.