1000 resultados para Trace Functionals


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We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

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Laser-induced breakdown spectroscopy (LIBS) as a powerful analytical technique is applied to analyze trace-elements in fresh plant samples. We investigate the LIBS spectra of fresh holly leaves and observe more than 430 lines emitted from 25 elements and molecules in the region 230-438 nm. The influence of laser wavelength on LIBS applied to semi-quantitative analysis of trace-element contents in plant samples is studied. The results show that the UV laser has lower relative standard deviations and better repeatability for semi-quantitative analysis of trace-element contents in plant samples. This work may be helpful for improving the quantitative analysis power of LIBS applied to plant samples.

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A plasticized Cr3+ ion sensor by incorporating 2,3,8,9-tetraphenyl-1,4,7,10-tetraazacyclododeca-1,3,7,9-tetraene (TTCT) ionophore exhibits a good potentiometric response for Cr3+ over a wide concentration range (1.0×10-6-1.0×10-1 M) with a slope of 19.5 mV per decade. The sensor response is stable for at least three months. Good selectivity for Cr3+ in comparison with alkali, alkaline earth, transition and heavy metal ions, and minimal interference are caused by Li+, Na+, K+, Co2+, Hg2+, Ca2+, Pb2+ and Zn2+ ions, which are known to interfere with other chromium membrane sensors. The TTCT-based electrode shows a fast response time (15 s), and can be used in aqueous solutions of pH 3 - 5.5. The proposed sensor was used for the potentiometric titration of Cr3+ with EDTA and for a direct potentiometric determination of Cr3+ content in environmental samples.