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1.
J. J. EGOZCUE J. L. DIAZ-BARRERO V. PAWLOWSKY-GLAHN 《数学学报(英文版)》2006,22(4):1175-1182
The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison's ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space. 相似文献
2.
A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded.
Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem
and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed.
Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function
theorem.
Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311. 相似文献
3.
Miguel A. Arcones 《Annals of the Institute of Statistical Mathematics》1998,50(1):87-117
We consider exact weak and strong Bahadur-Kiefer representations of the least absolute deviation estimator for the linear regression model. The precise behavior of these representations is obtained under minimal conditions. 相似文献
4.
A new method is introduced to solve potential flow problems around axisymmetric bodies. The approach relies on expressing the infinite series expansion of the Laplace equation solution in terms of a finite sum which preserves the Laplace solution for the potential function under a Neumann-type boundary condition. Then the coefficients of the finite sum are calculated in a least squares approximation sense using the Gram-Schmidt orthonormalization method. Sample benchmark problems are presented and discussed in some detail. The solutions are accurate and converged faster when a rather small number of terms were used. The method is simple and can be easily programmed. 相似文献
5.
最小一乘稳健多元分析校正 总被引:1,自引:3,他引:1
本文论述最小一乘求解的多元分析校正算法,探讨了最小一乘较常规最小二乘法及其他隐健算法的优点。用计算机数值模拟及实际多组分光谱体系对方法进行了检验,展示了最小一乘法在分析化学计量学中实际应用的可行性。 相似文献
6.
Simultaneous measurement of glucose and glutamine in aqueous solutions by near infrared spectroscopy 总被引:1,自引:0,他引:1
Hoeil Chung Mark A. Arnold Martin Rhiel David W. Murhammer 《Applied biochemistry and biotechnology》1995,50(2):109-125
A method is described for measuring the concentrations of both glucose and glutamine in binary mixtures from near infrared
(NIR) absorption spectra. Spectra are collected over the range from 5000–4000/cm (2.0–2.5μm) with a 1-mm optical path length.
Glucose absorbance features at 4710, 4400, and 4300/cm and glutamine features at 4700, 4580, and 4390/cm provide the analytical
information required for the measurement. Multivariate calibration models are generated by using partial least squares (PLS)
regression alone and PLS regression combined with a preprocessing digital Fourier filtering step. The ideal number of PLS
factors and spectral range are identified separately for each analyte. In addition, the optimum Fourier filter parameters
are established for both compounds. The best overall analytical performance is obtained by combining Fourier filtering and
PLS regression. Glucose measurements are established over the concentration range from 1.66–59.91 mM, with a standard error of prediction (SEP) of 0.32 mM and a mean percent error of 1.84%. Glutamine can be measured over the
concentration range from 1.10–30.65 mM with a SEP of 0.75 mM and a mean percent error of 6.67%. These results demonstrate
the analytical utility of NIR spectroscopy for monitoring glucose and glutamine levels in mammalian and insect cell cultures. 相似文献
7.
Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037. 相似文献
8.
偏最小二乘法在原子吸收光谱分析中的应用——钴和铟的同时测定 总被引:4,自引:1,他引:3
本文用偏最小二乘法(PLS)校正了火焰原子吸收分析In252.137nm对Co252.136nm的吸收线重叠干扰,对混合样中Co和In的含量进行了测定,结果令人满意。 相似文献
9.
Using statistically designed experiments, 12,500 observations are generated from a 4-pieced Cobb-Douglas function exhibiting increasing and decreasing returns to scale in its different pieces. Performances of DEA and frontier regressions represented by COLS (Corrected Ordinary Least Squares) are compared at sample sizes ofn=50, 100, 150 and 200. Statistical consistency is exhibited, with performances improving as sample sizes increase. Both DEA and COLS generally give good results at all sample sizes. In evaluating efficiency, DEA generally shows superior performance, with BCC models being best (except at corner points), followed by the CCR model and then by COLS, with log-linear regressions performing better than their translog counterparts at almost all sample sizes. Because of the need to consider locally varying behavior, only the CCR and translog models are used for returns to scale, with CCR being the better performer. An additional set of 7,500 observations were generated under conditions that made it possible to compare efficiency evaluations in the presence of collinearity and with model misspecification in the form of added and omitted variables. Results were similar to the larger experiment: the BCC model is the best performer. However, COLS exhibited surprisingly good performances — which suggests that COLS may have previously unidentified robustness properties — while the CCR model is the poorest performer when one of the variables used to generate the observations is omitted. 相似文献
10.
Min Hsien Liu 《中国化学会会志》2007,54(1):141-148
Density functional theory (DFT) calculations are made and least squares calibration performed for various halohydrocabons, which were 27 straight‐chain alkyl halides, 20 branch‐chain alkyl halides and 19 aromatic halides, to determine their enthalpies of formation (ΔHf). The mean absolute error (M. |A.E.|) in ΔHf across 66 molecular computations was only 7.8 kJ/mol (1.9 kcal/mol). Grouping the molecules by their structural characteristics improved M. |A.E.| of ΔHf by 0.2–2.2 kJ/mol over that obtained using corresponding modified data for the same 66 unclassified molecules. 相似文献