SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.

CHARACTERISTIC FUNCTIONS OF BILINEAR TIME SERIES MODEL

Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.

AN ASYMPTOTIC EXPANSION FORMULA OF KERNEL FUNCTION FOR QUASI FOURIER-LEGENDRE SERIES AND ITS APPLICATION

Is this paper we shall give cm asymptotic expansion formula of the kernel functim for the Quasi Faurier-Legendre series on an ellipse, whose error is 0(1/n2) and then applying it we shall sham an analogue of an exact result in trigonometric series.

Modeling Breast Cancer Incidence Rates: A Comparison between the Components of Functional Time Series (FTS) Model Applied on Karachi (Pakistan) and US Data

Several studies showed that the breast cancer incidence rates are higher in high-income (developed) countries, due to the link of breast cancer with several risk factors and the presence of systematic screening policies. Some of the authors suggest that lower breast cancer incidence rates in low-income (developing) countries probably reflect international variation in hormonal factors and accessibility to early detection facilities. Recent studies showed that the breast cancer increased rapidly among women in Pakistan (a developing country) and it became the first malignancy among females of Pakistan. Although, the incidence rates may contain important evidence for understanding and control of the disease;however in Pakistan, the breast cancer incidence data have never been available in the last five decades since independence;rather, only hospital-based data are available. In this study, we intend to apply Functional Time Series (FTS) models to the breast cancer incidence rates of United State (developed country), and to see the difference between various components (age and time) of Functional Time Series (FTS) models applied independently on the breast cancer incidence rates of Karachi (Pakistan) and US. Past studies have already suggested that the incidence of US breast cancer cases was expected to increase in the coming decades. A progressive increase in the number of new cases is already predetermined by the high birth rate that occurred during the middle part of the century, and it will lead to nearly a doubling in the number of cases in about 4 decades. We also obtain 15 years predictions of breast cancer incidence rates in United States and compare them with the forecasts of incidence curves for Karachi. Development of methods for cancer incidence trend forecasting can provide a sound and accurate foundation for planning a comprehensive national strategy for optimal partitioning of research resources between the need for development of new treatments and the need for new research directed toward primary preventive measures.

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.

Functional Causality between Oil Prices and GDP Based on Big Data

This paper examines the causal relationship between oil prices and the Gross Domestic Product(GDP)in the Kingdom of Saudi Arabia.The study is carried out by a data set collected quarterly,by Saudi Arabian Monetary Authority,over a period from 1974 to 2016.We seek how a change in real crude oil price affects the GDP of KSA.Based on a new technique,we treat this data in its continuous path.Precisely,we analyze the causality between these two variables,i.e.,oil prices and GDP,by using their yearly curves observed in the four quarters of each year.We discuss the causality in the sense of Granger,which requires the stationarity of the data.Thus,in the first Step,we test the stationarity by using the Monte Carlo test of a functional time series stationarity.Our main goal is treated in the second step,where we use the functional causality idea to model the co-variability between these variables.We show that the two series are not integrated;there is one causality between these two variables.All the statistical analyzes were performed using R software.

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier- Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.

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.

Modeling Distortion Signals of Power Grid Based on Wiener-G Functionals

The uniform mathematical model of distortion signals in power grid has been setup with the theory of Wiener-G Functional. Firstly,the Matlab simulation models were established. Secondly,the Wiener kernel of power load was found based on the Gaussian white noise as input. And then the uniform mathematical model of the power grid signal was established according to the homogeneous of the same order of Wiener functional series. Finally,taking three typical distortion sources which are semiconductor rectifier,electric locomotive and electric arc furnace in power grid as examples,we have validated the model through the Matlab simulation and analyzed the simulation errors. The results show that the uniform mathematical model of distortion signals in power grid can approximation the actual model by growing the items of the series under the condition of the enough storage space and computing speed.

The Proof of the Generalized Piemann’s Hypothesis

The article presents the proof of the validity of the generalized Riemann hypothesis on the basis of adjustment and correction of the proof of the Riemanns hypothesis in the work?[1], obtained by a finite exponential functional series and finite exponential functional progression.

FUZZY APPROACHING SET AND FUZZYAPPROACHING FUNCTIONAL MAPPING

By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

Three-dimensional Analysis of Functionally Graded Piezoelectric Plate with Arbitrarily Distributed Material Properties

An orthotropic functionally graded piezoelectric rectangular plate with arbitrarily distributed material properties was studied, which is simply supported and grounded（electrically） on its four lateral edges. The state equations of the functionally graded piezoelectric material were obtained using the state-space approach, and a Peano-Baker series solution was obtained for the coupled electroelastic fi elds of the functionally graded piezoelectric plate subjected to mechanical and electric loading on its upper and lower surfaces. The influence of different distributions of material properties on the structural response of the plate was studied using the obtained solutions.

Group LASSO for Change-points in Functional Time Series

Multiple change-points estimation for functional time series is studied in this paper.The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions.Group least absolute shrinkage and selection operator(LASSO)is then applied to estimate the number and the locations of possible change points.However,the group LASSO(GLASSO)always overestimate the true points.To circumvent this problem,a further Information Criterion(IC)is applied to eliminate the redundant estimated points.It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently.Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method.

Inventory Management and Demand Forecasting Improvement of a Forecasting Model Based on Artificial Neural Networks

Forecasting is predicting or estimating a future event or trend.Supply chains have been constantly growing in most countries ever since the industrial revolution of the 18th century.As the competitiveness between supply chains intensifies day by day,companies are shifting their focus to predictive analytics techniques to minimize costs and boost productivity and profits.Excessive inventory(overstock)and stock outs are very significant issues for suppliers.Excessive inventory levels can lead to loss of revenue because the company's capital is tied up in excess inventory.Excess inventory can also lead to increased storage,insurance costs and labor as well as lower and degraded quality based on the nature of the product.Shortages or out of stock can lead to lost sales and a decline in customer contentment and loyalty to the store.If clients are unable to find the right products on the shelves,they may switch to another vendor or purchase alternative items.Demand forecasting is valuable for planning,scheduling and improving the coordination of all supply chain activities.This paper discusses the use of neural networks for seasonal time series forecasting.Our objective is to evaluate the contribution of the correct choice of the transfer function by proposing a new form of the transfer function to improve the quality of the forecast.

Performance evaluation for PCC-OFDM systems impaired by carrier frequency offset over AWGN channels

Orthogonal frequency division multiplexing （OFDM） is sensitive to carrier frequency offset （CFO）, which destroys the orthogonality and causes inter-carrier interference （ICI）. ICI self-cancellation schemes based on polynomial cancellation coding （PCC-OFDM） can evidently reduce the sensitivity to CFO. In this paper, we analyze the performance of PCC-OFDM systems impaired by CFO over additive white gaussian noise （AWGN） channels. Two criteria are used to evaluate the effect of CFO on performance degradations. Firstly, the closed-form expressions of the average carrier-to-interference power ratio （CIR） and the statistical average ICI power, both of which reflect the desired power loss, are presented. Simulation and analytical results show that the theoretical expressions depend crucially on the normalized frequency offset and are hardly relevant to the number of subcarriers. Secondly, by exploiting the properties of the Beaulieu series, the effect of CFO on symbol error rate （SER） and bit error rate （BER） performance for PCC-OFDM systems are exactly expressed as the sum of an infinite series in terms of the charac- teristic function （CHF） of ICI. We consider the systems modulated with binary phase shift keying （BPSK）, quadrature PSK （QPSK）, 8-ary PSK （8-PSK）, and 16-ary quadrature amplitude modulation （16-QAM）, and all above modulation schemes are mapped with Gray codes for the evaluations of BER.

Functional data analysis: An application to COVID-19 data in the United States in 2020

Background: In this paper, we conduct an analysis of the COVID-19 data in the United States in 2020 via functional data analysis methods. Through this research, we investigate the effectiveness of the practice of public health measures, and assess the correlation between infections and deaths caused by the COVID-19. Additionally, we look into the relationship between COVID-19 spread and geographical locations, and propose a forecasting method to predict the total number of confirmed cases nationwide.Methods: The functional data analysis methods include functional principal analysis methods, functional canonical correlation analysis methods, an expectation-maximization (EM) based clustering algorithm and a functional time series model used for forecasting.Results: It is evident that the practice of public health measures helps to reduce the growth rate of the epidemic outbreak over the nation. We have observed a high canonical correlation between confirmed and death cases. States that are geographically close to the hot spots are likely to be clustered together, and population density appears to be a critical factor affecting the cluster structure. The proposed functional time series model gives more reliable and accurate predictions of the total number of confirmed cases than standard time series methods.Conclusions: The results obtained by applying the functional data analysis methods provide new insights into the COVID-19 data in the United States. With our results and recommendations, the health professionals can make better decisions to reduce the spread of the epidemic, and mitigate its negative effects to the national public health.