The aim is to find a reduced-order 2-D regular Roesser model for a given 2-DSRM such that the associated model reduction error meets a prescribed Hx norm bound constraint.

Also considered is the case of the original curve and the degree reduction curve when they are continuous on(r,s) degree respectively on two end points(r≥0,s≥0). Besides, the estimation of the degree reduction error bound is presented. Finally,a numerical example is given.

Proposes a new kind of data reduction method based on the thinking o f second-scan ,get the relationship between reduction error and parameter of ar ithmetic, presents the flowchart of it finally.

The proposed Microscale Reduction Error (MRE) estimators and indicators are based on estimating the uniform validity properties of the double scale asymptotic expansion.

Microscale reduction error indicators and estimators for a periodic heterogeneous medium

To get a reasonably low-order compensator, frequency-weighted reduced-order models are exploited, with the reduction error treated as an uncertainty.

The second way is to construct the adjacency graph by using the given reduction error directly and performing the graph reduction just once.

The reduction error represents the relative error introduced in the graph reduction.

The purpose of this paper is to find an accurate and reliable reduction method for the synchro-reduction domain including nine to fifteen virtual height data above the minimal appreciable frequency fmin. For this domain three higher ionization mo-dels with two variables are given, whereas six or eight lower ionization models with two variables are given for the ionization below fmin. At most twenty different reduc-tion results may be obtained for each h'-f curve by the least square method. It is...

The purpose of this paper is to find an accurate and reliable reduction method for the synchro-reduction domain including nine to fifteen virtual height data above the minimal appreciable frequency fmin. For this domain three higher ionization mo-dels with two variables are given, whereas six or eight lower ionization models with two variables are given for the ionization below fmin. At most twenty different reduc-tion results may be obtained for each h'-f curve by the least square method. It is possible to select an accurate result from the above calculations. 468 theoretical noc-turnal h'-f curves have been reduced. They possess different shapes, critical fre-quencies fc, semi-thicknesses H and fmin's, and these theoretical virtual heights have an accuracy of about 0.1 km. The maximal reduction errors of 462 h'-f curves are less than 5 km, whereas those of 6 curves are between 5-9 km.

he average annual temperature and annual precipitation were reconstructed for past 116 years(1874～ 1990)under the nonlinear response function of Pinus massoniana to climate by the metheds of dendrochronology.The effect of reconstructed temperature was better than that of the precipitation,the reduction errors(RE) and percentage average of residuals for temperature and precipitation were 0.12,0.10,2.3%and 20%respectively. The reconstruction could be verified by the observed data and other historical records...

he average annual temperature and annual precipitation were reconstructed for past 116 years(1874～ 1990)under the nonlinear response function of Pinus massoniana to climate by the metheds of dendrochronology.The effect of reconstructed temperature was better than that of the precipitation,the reduction errors(RE) and percentage average of residuals for temperature and precipitation were 0.12,0.10,2.3%and 20%respectively. The reconstruction could be verified by the observed data and other historical records for most years,while in the several years with higher temperature and precipitation,the residuals between estimated and observed values too large to be accepted.

Tree--ring data were sampled from the north slope of Changbai Mountain, Northeast China. Three spedes from five sites growing along altitudinal gradient were coiled. For each site the tree cores were cross--dated using skeleton plot and measured to the nearest 0.01 mm using standard techniques. The dating and measurement were validated using an improved version of the COFECHA program. Final chronologies were developed using the program ARSTND. The age trend of trees was modeled by a cubic spline. Using a bi--weight...

Tree--ring data were sampled from the north slope of Changbai Mountain, Northeast China. Three spedes from five sites growing along altitudinal gradient were coiled. For each site the tree cores were cross--dated using skeleton plot and measured to the nearest 0.01 mm using standard techniques. The dating and measurement were validated using an improved version of the COFECHA program. Final chronologies were developed using the program ARSTND. The age trend of trees was modeled by a cubic spline. Using a bi--weight robust mean method, de--trend indias were averaged to form standard chronologies (STD). To minimize the variations that reflect competitive interactions between trees, further standardization was done by fitting an autoregression model to the de--trend index and residual chronologies (RES) were calculated using the same average method.Common interval analysis indicates that RES chronologies are with more common yearto --year variations and express more population signal. Therefore, RES chronologies are suitable for dendroclimatic research in this study. Comparisons of climatic quality among five RES chronologies indicate that trees growing near their upper elevational hot are more suitable for dendroclimatic study than those growing at the upper elevational limit and at the center of the distribution. Climatic data for Tianchi, Antu and Changbai meteorological stations were employed and four climatic elements, monthly mean minimum temperatUre, monthly mean temperature, monthly mean maximum temperature and monthly total precipitation, were involved in this study. All data were tested for homogeneity.Response function, correlation function, scatter diagram and single--year analysis were utilized to stUdy the response of tree radial growth to climatic elements. The results showed that ma studied were mainly affected by climatic elements. From 63% to 78% percent of growth variance can be accounted for by monthly mean air temperature and monthly total precipitation. And the response to temperature is stronger than to precipitation. While,for three temperature elements, the response to monthly mean maximum temperature is the strongest, especially, in winter and spring seasons. As a result, monthly mean maximum temperature was selected to reconstruct.Multiple linear regression analyses were used to perform calibration analysis.Regression equations were developed by regressing monthly mean maximum temperature for various combinations of blocks of month against ring-width data from all sites. To reconstruct a seasonal series of climate, January to April was selected as the reconstructing season, and an average record of January to April mean maximum temperature was formed from the three stations providing a regional record. This regional record allows to reconstruct past climate of Changbai Mountain.Regressions were calculated between January ~ April mean maximum temperature and ring --width data for various combinations of tree- ring sites. Band on the equation statistics such as the percentage of variance expressed by the equation, two regression equations were selected, one is for reconstruction before 1833, and the other for after. house a chrOnology from ANPK site was included in the second equation, the statistics of the equation were improved. The stability of there two equations was tested by cross--validation procedure using verification statistics including sign test, product mean and reduction error. All of these statistics indicated that the selected equations were of the predicative capability,and that they can be used as the transfer functions.According to the transfer functions, January ~ April mean maximum temperatures of Changbai Mountain were reconstructed year by year, and the reconstruction was smoothed by applying a resistant smoother. It was found that the reconstructed low--frequency variations were more reliable than the year--to--year variations. Therefore, only the low--frequency variations were discussed. From the 339 years' low--frequency variations, it was found that the departures oscill