THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

For p ∈ R, the generalized logarithmic mean Lp（a, b） and Seiffert＇s mean T（a, b） of two positive real numbers a and b are defined in （1.1） and （1.2） below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp（a, b） 〈 T（a,b） 〈 Lq（a,b） holds for all a,b 〉 0 and a ≠ b.

Refinement of an Inequality for the Generalized Logarithmic Mean

In this article, we show that the generalized logarithmic mean is strictly Schurconvex function for p 〉 2 and strictly Schur-concave function for p 〈 2 on R_＋^2. And then we give a refinement of an inequality for the generalized logarithmic mean inequality using a simple majoricotion relation of the vector.

Generalized weighted functional proportional mean combining forecasting model and its method of parameter estimation

A new kind of combining forecasting model based on the generalized weighted functional proportional mean is proposed and the parameter estimation method of its weighting coefficients by means of the algorithm of quadratic programming is given. This model has extensive representation. It is a new kind of aggregative method of group forecasting. By taking the suitable combining form of the forecasting models and seeking the optimal parameter, the optimal combining form can be obtained and the forecasting accuracy can be improved. The effectiveness of this model is demonstrated by an example.

APPROXIMATION OF CONTINUOUS FUNCTIONS BY GENERALIZED KARAMATA MEANS

A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order is obtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums of their Fourier series to be of Jackson order. The error estimate is shown to be the best possible.

EXISTENCE OF AREA MINIMIZING TANGENT CONES OF INTEGRAL CURRENTS WITH PRESCRIBED MEAN CURVATURE

Given an integral M-currrent To in Rm+k and a tensor H of type(m.l)on Rn+k with values orthogonal to each of its arguments we proved in a previous peper[3]the sxistence of anintegral m-current T =γ(M,θ.ζ)with boundary T0 and mean curvature vector H by minimizing an appropriate functional on suitable subclasses of the set of all integral currents.In thes paperwe discuss the existence and structure of oriented tangent cones C of T at points x∈spt(T) spt(T),especially we show that C is locally mass minimizing.

Application of Multiple Mean Generational Function Method to Typhoon Prediction over the Western North Pacific

[ Objective] The multiple mean generational function （MMGF） method was applied to forecast the annual number of typhoons （TYs） over the Western North Pacific （WNP）. [Method]The method yields a number of predictors by mean generational function based on the rolling 50- year data of TYs frequency and sunspot number, and was repeated to generate forecasts year after year by optimal subset regression. [ Result] The results showed a reasonably high predictive ability dudng period 2000 -2010, with an average root mean square （RMSE） value of 1.92 and a mean absolute error （MAE） value of 1.64. [ Conclusion] Although the MMGF method needs further validation in the practical operation, it already has strong potential for the improvement of skill at forecasting annual frequency of TYs in the WNP.

Spectrum Deviation Method of Identification of Foreshocks or Generalized Foreshocks and Its Applications

Based on previous research work,we present a spectrum deviation method to recognize a foreshock or generalized foreshock in this paper. The criterion to determine whether an event is a foreshock is a wide spectrum for an ordinary event,however,a moderate earthquake with foreshock or generalized foreshock has the characteristics of a narrow frequency band,and it deviates to the low frequency. It may be explained by metastable extension in the rupture source or related area of the main shock or regional fragmentation damage and crack nucleation process. The calculation results of two foreshocks,the M_S4. 7 event which occurred before the Yushu M_S7. 1 earthquake on April 14,2010 and the M_S5. 3 event which occurred before the Yutian M_S7. 3 earthquake on February 12,2014,show that the spectra of foreshocks shift,and they are quite different from the nonforeshock seismic spectrum of equivalent size. Therefore,this result can verify the validity of the spectrum deviation method.

Generalization of the linguistic aggregation operator and its application in decision making

A generalization of the linguistic aggregation functions （or operators） is presented by using generalized and quasiarithmetic means. Firstly, the linguistic weighted generalized mean （LWGM） and the linguistic generalized ordered weighted averaging （LGOWA） operator are introduced. These aggregation functions use linguistic information and generalized means in the weighted average （WA） and in the ordered weighted averaging （OWA） function. They are very useful for uncertain situations where the available information cannot be assessed with numerical values but it is possible to use linguistic assessments. These aggregation operators generalize a wide range of aggregation operators that use linguistic information such as the linguistic generalized mean （LGM）, the linguistic OWA （LOWA） operator and the linguistic or- dered weighted quadratic averaging （LOWQA） operator. We also introduce a further generalization by using quasi-arithmetic means instead of generalized means obtaining the quasi-LWA and the quasi-LOWA operator. Finally, we develop an application of the new approach where we analyze a decision making problem regarding the selection of strategies.

CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS

In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially. convexity of functions, are described by subdifferentials.

Study on Ann-Based Multi-Step Prediction Model of Short-Term Climatic Variation

In the context of 1905–1995 series from Nanjing and Hangzhou, study is undertaken of estab-lishing a predictive model of annual mean temperature in 1996–2005 to come over the Changjiang (Yangtze River) delta region through mean generating function and artificial neural network in combination. Results show that the established model yields mean error of 0.45°C for their abso-lute values of annual mean temperature from 10 yearly independent samples (1986–1995) and the difference between the mean predictions and related measurements is 0.156°C. The developed model is found superior to a mean generating function regression model both in historical data fit-ting and independent sample prediction. Key words Climate trend prediction. Mean generating function (MGF) - Artificial neural network (ANN) - Annual mean temperature (AMT)

Generalized Weighted Mean Combining Forecasting and Its Application in the Forecasting of Air Materials Consumption

This paper presents the parameter estimation methods of weighting coefficients in generalized weighted mean combining forecasting, and uses this forecasting model to forecast air materials consumption. Finially, the efficiency of generalized weighted mean combining forecasting has been demonstrated by an example.

THE DOWNSCALING FORECASTING OF SEASONAL PRECIPITATION IN GUANGDONG BASED ON CLIMATE FORECAST SYSTEMS PRODUCTS

The Climate Forecast Systems(CFS) datasets provided by National Centers for Environmental Prediction(NCEP), which cover the time from 1981 to 2008, can be used to forecast atmospheric circulation nine months ahead. Compared with the NCEP datasets, CFS datasets successfully simulate many major features of the Asian monsoon circulation systems and exhibit reasonably high skill in simulating and predicting ENSO events. Based on the CFS forecasting results, a downscaling method of Optimal Subset Regression(OSR) and mean generational function model of multiple variables are used to forecast seasonal precipitation in Guangdong. After statistical analysis tests, sea level pressure, wind and geopotential height field are made predictors. Although the results are unstable in some individual seasons, both the OSR and multivariate mean generational function model can provide good forecasting as operational tests score more than sixty points. CFS datasets are available and updated in real time, as compared with the NCEP dataset. The downscaling forecast method based on the CFS datasets can predict three seasons of seasonal precipitation in Guangdong, enriching traditional statistical methods. However, its forecasting stability needs to be improved.

THE INEFFICIENCY OF THE LEAST SQUARES ESTIMATOR AND ITS BOUND

It was suggested by Pantanen that the mean squared error may be used to measure the inefficiency of the least squares estimator. Styan[2] and Rao[3] et al. discussed this inefficiency and it's bound later. In this paper we propose a new inefficiency of the least squares estimator with the measure of generalized variance and obtain its bound.

Research on Precipitation Prediction Model Based on Extreme Learning Machine Ensemble

Precipitation is a significant index to measure the degree of drought and flood in a region,which directly reflects the local natural changes and ecological environment.It is very important to grasp the change characteristics and law of precipitation accurately for effectively reducing disaster loss and maintaining the stable development of a social economy.In order to accurately predict precipitation,a new precipitation prediction model based on extreme learning machine ensemble(ELME)is proposed.The integrated model is based on the extreme learning machine(ELM)with different kernel functions and supporting parameters,and the submodel with the minimum root mean square error(RMSE)is found to fit the test data.Due to the complex mechanism and factors affecting precipitation change,the data have strong uncertainty and significant nonlinear variation characteristics.The mean generating function(MGF)is used to generate the continuation factor matrix,and the principal component analysis technique is employed to reduce the dimension of the continuation matrix,and the effective data features are extracted.Finally,the ELME prediction model is established by using the precipitation data of Liuzhou city from 1951 to 2021 in June,July and August,and a comparative experiment is carried out by using ELM,long-term and short-term memory neural network(LSTM)and back propagation neural network based on genetic algorithm(GA-BP).The experimental results show that the prediction accuracy of the proposed method is significantly higher than that of other models,and it has high stability and reliability,which provides a reliable method for precipitation prediction.

Generalized Markov interacting branching processes

We consider a very general interacting branching process which includes most of the important interacting branching models considered so far. After obtaining some key preliminary results, we first obtain some elegant conditions regarding regularity and uniqueness, Then the extinction vector is obtained which is very easy to be calculated. The mean extinction time and the conditional mean extinction time are revealed.The mean explosion time and the total mean life time of th, processes are also investigated and resolved.

Ensemble Prediction of Monsoon Index with a Genetic Neural Network Model

After the consideration of the nonlinear nature changes of monsoon index,and the subjective determination of network structure in traditional artificial neural network prediction modeling,monthly and seasonal monsoon intensity index prediction is studied in this paper by using nonlinear genetic neural network ensemble prediction（GNNEP）modeling.It differs from traditional prediction modeling in the following aspects： （1）Input factors of the GNNEP model of monsoon index were selected from a large quantity of preceding period high correlation factors,such as monthly sea temperature fields,monthly 500-hPa air temperature fields,monthly 200-hPa geopotential height fields,etc.,and they were also highly information-condensed and system dimensionality-reduced by using the empirical orthogonal function（EOF）method,which effectively condensed the useful information of predictors and therefore controlled the size of network structure of the GNNEP model.（2）In the input design of the GNNEP model,a mean generating function（MGF）series of predictand（monsoon index）was added as an input factor;the contrast analysis of results of predic- tion experiments by a physical variable predictor-predictand MGF GNNEP model and a physical variable predictor GNNEP model shows that the incorporation of the periodical variation of predictand（monsoon index）is very effective in improving the prediction of monsoon index.（3）Different from the traditional neural network modeling,the GNNEP modeling is able to objectively determine the network structure of the GNNNEP model,and the model constructed has a better generalization capability.In the case of identical predictors,prediction modeling samples,and independent prediction samples,the prediction accuracy of our GNNEP model combined with the system dimensionality reduction technique of predictors is clearly higher than that of the traditional stepwise regression model using the traditional treatment technique of predictors,suggesting that the GNNEP model opens up a vast range of possibilities for operational weather prediction.