Stable and Unstable Eigensolutions of Laplace’s Tidal Equations for Zonal Wavenumber Zero

Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.     

DETERMINATION OF A MULTIVARIATE DETECTION LIMIT AND LOCAL CHEMICAL RANK BY DESIGNING A NON-PARAMETRIC TEST FROM THE ZERO-COMPONENT REGIONS

In this paper we redefine the term detection limit to embrace the inherent multivariate nature of samples,instrumental measurements and chemometrics resolution procedures. The so-called zero-componentregions, i.e. parts with no chemical components eluting, are used as repeated analytical blanks to estimatea statistical multivariate detection limit for determining the number of chemical species in local regionsof a single two-way chromatogram or a collection of synchronized one-way chromatograms. For two-waychromatography the detection limit is determined from the distribution of the first eigenvalues obtainedfrom all possible combinations of spectra in the zero-component regions. The number of spectra in eachcalculation should correspond to the number included in the later examination of the local retention timeregions. For one-way chromatography on a collection of samples with similar chemical components atvarying concentrations the same procedure is used, with the samples taking the role of the spectra intwo-way chromatography. The detection limit can be chosen at various confidence levels depending onwhether false positive or negative detection of minor components is most critical. The results obtainedfrom the zero-eigenvalue distribution are more robust than those obtained by a previously developedF-test.     

THE GEOMETRY OF MULTIVARIATE OBJECT PREPROCESSING

The geometric properties of three common object-preprocessing transformations(constant sum,orclosure;constant length,or normalization;and maximum value,or ratioing)are investigated.Anargument is made for using absolute values in the constant sum and maximum value transformations.In general,each transformation distorts the shape and dimensionality of patterns in the data:transformed data lie on(C-l)-dimensional surfaces in the original C-dimensional space.A data set thathas been closed by one of these transformations can be reopened if a vector containing the constant sums,constant lengths or maximum values of the original objects was retained.Transformed data sets may befreely interconverted among these three transformations without the loss of information.     

1984世界大地测量系统（WGS84）

自１９６０年以来，美国国防制图局（ＤＭＡ）已建立了四个世界大地测量系统（ＷＧＳ）；ＷＧＳ６０，ＷＧＳ６６，ＷＧＳ７２和ＷＧＳ８４。最新的ＷＧＳ８４与前三者相比，是最为精确的大地参考框架，它是利用了广泛的，最新的大地测量数据全球确定的。ＷＧＳ８４提供了精确的参照框架，地球重力场模型，正常重力公式，大地水准面和包括全部大陆和主要海洋岛屿在内的１０５个局部（和区域）大地测量基准的转换参数。这些成果使测绘     

Water Resources of the South Asian Region in a Warmer Atmosphere

The global mean surface temperature may rise by about 0.3oC per decade during the next Few decades as a result of anthropogenic greenhouse gas emissions in the earth’s atmosphere. The data generated in the greenhouse warming simulations (Business-as-Usual scenario of IPCC) with the climate models developed at Max Planck Institute for Meteorology, Hamburg have been used to assess future plausible hydrological scenario for the South Asian region. The model results indicate enhanced surface warming (2.7oC for summer and 3.6oC for winter) over the land regions of South Asia during the next hundred years. While there is no significant change in the precipitation over most of the land regions during winter, substantial increase in precipitation is likely to occur during summer. As a result, an increase in soil moisture is likely over central India, Bangladesh and South China during summer but a statistically sig-nificant decline in soil moisture is expected over central China in winter. A moderate decrease in surface runoff may occur over large areas of central China during winter while the flood prone areas of NE-India. Bangladesh and South China are likely to have an increase in surface runoff during summer by the end of next century.     

Estimation of Winds at Different Isobaric Levels Based on the Observed Winds at 850 hPa Level Using Double Fourier Series

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