ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE

Let X be a Banach space and be a sequence in X. The author shows that is a basic sequence if and only if converges for every j≥1 and holds for every choice of scalar variables {αnj} such that converges for each n≥ 1 and any choice of scalar variables {rn} such that converges. Moreover, some applications about the result are given.

SOME PROPERTIES OF MULTIPLE TAYLOR SERIES AND RANDOM TAYLOR SERIES

Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there

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.

THE LOWER ORDER AND LINEAR ORDER OF MULTIPLE DIRICHLET SERIES

The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.

CONVERGENCE OF LOGARITHMIC MEANS OF MULTIPLE WALSH-FOURIER SERIES

Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L （[0, 1）d）, d≥1 into space weak - LI（[0,1）^d） are studied. The maximal Orlicz space such that the Norlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found.

ON ORDER AND TYPE OF MULTIPLE DIRICHLET SERIES

This article investigates the growth of multiple Dirichlet series. The order and the type of n-tuple Dirichlet series in Cn are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained, which generalize some results about simple Dirichlet series of Lindelof and Pringsheim.

APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE

In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.

Heterogeneous information phase space reconstruction and stability prediction of filling body–surrounding rock combination

Traditional research believes that the filling body can effectively control stress concentration while ignoring the problems of unknown stability and the complex and changeable stress distribution of the filling body–surrounding rock combination under high-stress conditions.Current monitoring data processing methods cannot fully consider the complexity of monitoring objects,the diversity of monitoring methods,and the dynamics of monitoring data.To solve this problem,this paper proposes a phase space reconstruction and stability prediction method to process heterogeneous information of backfill–surrounding rock combinations.The three-dimensional monitoring system of a large-area filling body–surrounding rock combination in Longshou Mine was constructed by using drilling stress,multipoint displacement meter,and inclinometer.Varied information,such as the stress and displacement of the filling body–surrounding rock combination,was continuously obtained.Combined with the average mutual information method and the false nearest neighbor point method,the phase space of the heterogeneous information of the filling body–surrounding rock combination was then constructed.In this paper,the distance between the phase point and its nearest point was used as the index evaluation distance to evaluate the stability of the filling body–surrounding rock combination.The evaluated distances(ED)revealed a high sensitivity to the stability of the filling body–surrounding rock combination.The new method was then applied to calculate the time series of historically ED for 12 measuring points located at Longshou Mine.The moments of mutation in these time series were at least 3 months ahead of the roadway return dates.In the ED prediction experiments,the autoregressive integrated moving average model showed a higher prediction accuracy than the deep learning models(long short-term memory and Transformer).Furthermore,the root-mean-square error distribution of the prediction results peaked at 0.26,thus outperforming the no-prediction method in 70%of the cases.

Further-Adjusted Long-Term Temperature Series in China Based on MASH

A set of homogenized monthly mean surface air temperature （SAT） series at 32 stations in China back to the 19th century had previously been developed based on the RHtest method by Cao et al., but some inhomogeneities remained in the dataset. The present study produces a further-adjusted and updated dataset based on the Multiple Analysis of Series for Homogenization （MASH） method. The MASH procedure detects 33 monthly temperature records as erroneous outliers and 152 meaningful break points in the monthly SAT series since 1924 at 28 stations. The inhomogeneous parts are then adjusted relative to the latest homogeneous part of the series. The new data show significant warming trends during 1924-2016 at all the stations, ranging from 0.48 to 3.57℃ （100 yr）^-1, with a regional mean trend of 1.65℃ （100 yr）^-1 ; whereas, the previous results ranged from a slight cooling at two stations to considerable warming, up to 4.5℃ （100 yr）^-1. It is suggested that the further-adjusted data are a better representation of the large-scale pattern of climate change in the region for the past century. The new data axe available online at http：//www.dx.doi.org/10.11922/sciencedb.516.

THE DISTRIBUTION OF VALUES OF TAYLOR SERIES

Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.

Statistical Analysis and Evaluation of Macroeconomic Policies: A Selective Review

In this paper,we highlight some recent developments of a new route to evaluate macroeconomic policy effects,which are investigated under the framework with potential outcomes.First,this paper begins with a brief introduction of the basic model setup in modern econometric analysis of program evaluation.Secondly,primary attention goes to the focus on causal effect estimation of macroeconomic policy with single time series data together with some extensions to multiple time series data.Furthermore,we examine the connection of this new approach to traditional macroeconomic models for policy analysis and evaluation.Finally,we conclude by addressing some possible future research directions in statistics and econometrics.

FURTHER APPLICATIONS OF POLAR COORDINATES IN C^n

Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.

On the Gauss-Weierstrass Summability of Multiple Trigonometric Series at μ-smoothness Points

The notion of μ-smoothness points of periodic functions of several variables is introduced and the rate of convergence of the Gauss-Weierstrass means of relevant Fourier series at these points is investigated.

Dominant Skyline Query Processing over Multiple Time Series

Multiple time series （MTS）, which describes an object in multi-dimensions, is based on single time series and has been proved to be useful. In this paper, a new analytical method called α/β-Dominant-Skyline on MTS and a formal definition of the α/β-dominant skyline MTS are given. Also, three algorithms, called NL, BC and MFB, are proposed to address the α/β-dominant skyline queries over MTS. Finally experimental results on both synthetic and real data verify the correctness and effectiveness of the proposed method and algorithms.

Multifractal modeling of the production of concentrated sugar syrup crystal

High quality, concentrated sugar syrup crystal is produced in a critical step in cane sugar production： the clarification process. It is characterized by two variables： the color of the produced sugar and its clarity degree. We show that the temporal variations of these variables follow power-law distributions and can be well modeled by multiplicative cascade multifractal processes. These interesting properties suggest that the degradation in color and clarity degree has a systemwide cause. In particular, the cascade multifractal model suggests that the degradation in color and clarity degree can be equivalently accounted for by the initial ＂impurities＂ in the sugarcane. Hence, more effective cleaning of the sugarcane before the clarification stage may lead to substantial improvement in the effect of clarification.

INDUSTRIAL PRODUCTION IN GERMANY AND AUSTRIA:A CASE STUDY IN STRUCTURAL TIME SERIES MODELLING

Industrial production series are volatile and often cyclical. Time series models can be used toestablish certain stylized facts, such as trends and cycles, which may be present in these series. Incertain situations, it is also possible that common factors, which may have an interesting interpretation,can be detected in production series. Series from two neighboring countries with close economicrelationships, such as Germany and Austria, are especially likely to exhibit such joint stylized facts.

IDENTIFICATION OF MULTIVARIATE ARMA MODELS

In this paper, we propose the estimates of orders and parameters in identifiable multivariate ARMA models. These estimates are direct and easy to be calculated, and can be proved to follow LIL (Law of iterated logarithm) and CLT (Central limit theorem) under some mild conditions.

A Novel Hybrid Model for Gasoline Prices Forecasting Based on Lasso and CNN

Gasoline is the lifeblood of the national economy.The forecasting of gasoline prices is difficult because of frequent price fluctuations,its complex nature,diverse influencing factors,and low accuracy of prediction results.Previous studies mainly focus on forecasting gasoline prices in a single region by single time series analysis which ignores the daily price co-movement of different series from multiple regions.Because price co-movement may contain useful information for price forecasting,this paper proposes the LassoCNN ensemble model that combines statistical models and deep neural networks to forecast gasoline prices.In this model,the Least Absolute Shrinkage and Selection Operator(Lasso)screens and chooses the correlated time series to enhance the performance of forecasting and avoid overfitting,while Convolutional Neural Network(CNN)takes the selected multiple series as its input and then forecasts the gasoline prices in a certain region.Forecasting results of gasoline prices at the national level and regional levels by using the new method demonstrate that the new approach provides more accurate results for the predictions of gasoline prices than those results generated by alternative methods.Thus,the relevant series can enhance the performance of forecasting and help to gain better results.