非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

用相位调制方法测量光盘盘基应力双折射的精度分析

偏振相位调制方法是测量微小双折射的一种高精度检测方法。本文系统全面地分析了以ＰＭＣＳＡ结构形式测量光盘盘基应力双折射的相位调制方法中，由各种误差源造成的对测试结果的影响。     

Runge–Kutta interpolants for high precision computations

Runge–Kutta (RK) pairs furnish approximations of the solution of an initial value problem at discrete points in the interval of integration. Many techniques for enriching these methods with continuous approximations have been proposed. Here we construct C ¹ continuous, eighth and ninth order interpolation methods for a recently appeared RK pair of orders 9(8). These interpolants share a very small leading truncation error making them suitable for use at quadruple precision, i.e. 32–33 decimal digits of accuracy. Extended numerical results justify our effort.     

Game of two cars: Case of variable speed

A stochastic version of Isaacs's (Ref. 1) game of two cars is dealt with here. In this version, the pursuer, owing to thrust and drag forces, has a variable speed, whereas the evader's speed is constant. Also, the pursuer can maneuver as long as his speed is bounded by some lower and upper limits. The probability of interception, corresponding to optimal (saddle-point) feedback strategies, is computed and serves as a reference for evaluating the performance of four different versions of the proportional navigation pursuit law as well as two other strategies.     

A high-current electron beam ion trap as an on-line charge breeder for the high precision mass measurement TITAN experiment

The precision of atomic mass measurements in a Penning trap is directly proportional to the charge state q of the ion and, hence, can be increased by using highly charged ions (HCI). For this reason, charge breeding with an electron beam ion trap (EBIT) is employed at TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) on-line facility in Vancouver, Canada. By bombarding the injected and trapped singly charged ions with an intense beam of electrons, the charge state of the ions is rapidly increased inside the EBIT. To be compatible with the on-line requirements of short-lived isotopes, very high electron beam current densities are needed. The TITAN EBIT includes a 6 Tesla superconducting magnet and is designed to have electron beam currents and energies of up to 5 A and 60 keV, respectively. Once operational at full capacity, most species can be bred into a He-like configuration within tens of ms. Subsequently, the HCI are extracted, pass a Wien filter to reduce isobaric contamination, are cooled, and injected into a precision Penning trap for mass measurement. We will present the first results and current status of the TITAN EBIT, which has recently been moved to TRIUMF after assembly and commissioning at the Max-Planck-Institute (MPI) for Nuclear Physics in Heidelberg, Germany.     

Quality assurance and statistical control

In scientific research laboratories it is rarely possible to use quality assurance schemes, developed for large-scale analysis. Instead methods have been developed to control the quality of modest numbers of analytical results by relying on statistical control: Analysis of precision serves to detect analytical errors by comparing thea priori precision of the analytical results with the actual variability observed among replicates or duplicates. The method relies on the chi-square distribution to detect excess variability and is quite sensitive even for 5–10 results. Interference control serves to detect analytical bias by comparing results obtained by two different analytical methods, each relying on a different detection principle and therefore exhibiting different influence from matrix elements; only 5–10 sets of results are required to establish whether a regression line passes through the origo. Calibration control is an essential link in the traceability of results. Only one or two samples of pure solid or aqueous standards with accurately known content need to be analyzed. Verification is carried out by analyzing certified reference materials from BCR, NIST, or others; their limited accuracy of 5–10% make them less suitable for calibration purposes.     

Determination of Low Contents of Fenpiverine Bromide by Extraction Spectrophotometry

An ion-pair extraction spectrophotometry method was developed for the determination of fenpiverine bromide in tablets. To determine this substance it was necessary to find experimental conditions that would allow eliminating the influence of other components of the tablets. Attention was paid to the fact that a suitable pH of water phase was necessary to achieve high selectivity.Received December 11, 2002; accepted April 24, 2003 Published online July 28, 2003     

腔长失调对光腔衰荡法测量精度的影响

 只考虑腔长失调因素下建立了反射率模拟测量的理论模型。根据高斯光束传输规律分析了腔长失调对衰荡腔模式耦合的影响，推导了腔长失调与谐振腔输出脉冲信号、衰荡信号与反射率之间的关系，模拟了腔长失调在±10mm范围内的光脉冲衰荡现象。结果表明：对于光敏面直径为0.2mm的高速探测器，为了保证10^-6的测量精度，腔长的失调量应控制在±1mm之间。在光路调节中采用具有对数变换功能的示波器和动态范围较大的探测器，可以提高测量精度。     

Predicting Bitcoin (BTC) Price in the Context of Economic Theories: A Machine Learning Approach

Bitcoin (BTC)—the first cryptocurrency—is a decentralized network used to make private, anonymous, peer-to-peer transactions worldwide, yet there are numerous issues in its pricing due to its arbitrary nature, thus limiting its use due to skepticism among businesses and households. However, there is a vast scope of machine learning approaches to predict future prices precisely. One of the major problems with previous research on BTC price predictions is that they are primarily empirical research lacking sufficient analytical support to back up the claims. Therefore, this study aims to solve the BTC price prediction problem in the context of both macroeconomic and microeconomic theories by applying new machine learning methods. Previous work, however, shows mixed evidence of the superiority of machine learning over statistical analysis and vice versa, so more research is needed. This paper applies comparative approaches, including ordinary least squares (OLS), Ensemble learning, support vector regression (SVR), and multilayer perceptron (MLP), to investigate whether the macroeconomic, microeconomic, technical, and blockchain indicators based on economic theories predict the BTC price or not. The findings point out that some technical indicators are significant short-run BTC price predictors, thus confirming the validity of technical analysis. Moreover, macroeconomic and blockchain indicators are found to be significant long-term predictors, implying that supply, demand, and cost-based pricing theories are the underlying theories of BTC price prediction. Likewise, SVR is found to be superior to other machine learning and traditional models. This research’s innovation is looking at BTC price prediction through theoretical aspects. The overall findings show that SVR is superior to other machine learning models and traditional models. This paper has several contributions. It can contribute to international finance to be used as a reference for setting asset pricing and improved investment decision-making. It also contributes to the economics of BTC price prediction by introducing its theoretical background. Moreover, as the authors still doubt whether machine learning can beat the traditional methods in BTC price prediction, this research contributes to machine learning configuration and helping developers use it as a benchmark.