Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices

We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational f...     

Research on the Quantitative Analysis for In-Situ Detection of Acid Radical Ions Using Laser Raman SpectroscopySCIEI北大核心CSCD

Laser Raman spectroscopy as an in situ analytical technology can enable detailed investigation of the ocean environment. It is necessary to set up a quantitative analysis method based on laser Raman spectroscopy to understand the marine status in situ. In the laboratory investigations, varied concentration of HCO3-, SO r and coastal waters of Qingdao are taken as the samples, operating 532 nm of laser, using fiber optic probes to simulate detection mode in situ. Raman spectra are analyzed using the method of internal standard normalization, multiple linear regression(MLR), general Partial Least Squares(PLS) and PLS based on dominant factor respectively in data processing. It was found that correlation coefficients of calibration curves are not high in internal standard normalization method and predicted relative errors on the prepared samples are much high, so internal standard normalization method cannot be effectively used in the quantitative analysis of HCO3-, SO r in the water. And with the multiple linear regression, the analysis accuracy was improved effectively. The calibration curve of PLS based on dominant factor showed that the SOi- and HCO3- of pre-made solution with correlation coefficient R-2 of 0. 990 and 0. 916 respectively. The 30 mmol . L-1 of SO42- and 20 mmol . L-1 of HCO3- in two target samples were determined with the relative errors lower than 3. 262% and 5. 267% respectively. Sat in the coastal waters as the research object was analyzed by above-mentioned methods, comparing with 28. 01 mmol . L-1 by ion chromatography. It was demonstrated that PLS based on dominant factor method is superior to the rest of the three analysis methods, which can be used in situ calibration, with the mean relative error about 1. 128%. All the results show that analysis accuracy would be improved by the PLS based on dominant factor method to predict concentration of acid radical ions.     

Velocity-dependent symmetries and non-Noether conserved quantities of electromechanical systems

The theory of velocity-dependent symmetries(or Lie symmetry) and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invariance of Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained for continuous electromechanical systems;the Lie's theorem and ...