Identically conserved currents and their charges

We examine, at a classical level, the features that distinguish dynamically conserved currents from identically conserved ones. Then we prove that, in four spacetime dimensions, the quantum charges corresponding to identically conserved currents always annihilate the vacuum state. We illustrate our discussion with several examples.     

Characterization of metal glycinate complexes by electrospray Q-TOF-MS/MS and their determination by capillary electrophoresis–ICP-MS: application to premix samples

A method was developed for the determination of metal complexes with glycine (glycinates, [M(Gly)_x(H₂O)_y(SO₄)_z]_n, where M denotes Zn, Cu, Mn and Fe) in premix samples used for the preparation of animal feeds enriched in essential trace elements. The method was based on the extraction of the glycinates with 10 mM ammonium acetate (pH 7.4) followed by their determination using capillary electrophoresis with ICP MS detection. The stability of the glycinates in solution was verified by electrospray TOF-MS. Each supplement was shown to be a mixture of complexes, with polymerization degrees ranging from n = 1 to n = 4 (depending on the metal), that were fully or partially dehydrated. The metal glycine complex moiety was found to be preserved during capillary electrophoresis. The detection limits, calculated as three times the standard deviation of the blank plus the blank, were between 0.05 and 0.2 μg mL⁻¹ (as the metal), and the calibration curves were linear, allowing the analysis of premix samples. Repeatability for glycinate standards was below 12%, and analytical precision was typically within 15%.     

Heterostructural coaxial nanotubes of CNT@Fe<Subscript>2</Subscript>O<Subscript>3</Subscript> via atomic layer deposition: effects of surface functionalization and nitrogen-doping

This study attempted to synthesize one-dimensional (1D) coaxial nanotubes of Fe₂O₃ based on carbon nanotubes (CNT@Fe₂O₃) via atomic layer deposition (ALD) using ferrocene and oxygen as precursors. Results disclosed that undoped CNTs were suitable for the ALD of Fe₂O₃ (ALD-Fe₂O₃) only if they were chemically functionalized, due to their inert surface nature. It was further demonstrated that the effects of both covalent and non-covalent methodologies were limited in functionalizing undoped CNTs, leading to random and non-uniform deposition of Fe₂O₃. In sharp contrast, it was found that, as an alternative, nitrogen-doped CNTs (N-CNTs) contributed uniform and tunable ALD-Fe₂O₃, due to their active surface nature induced by incorporated N atoms. Consequently, various 1D heterostructural coaxial nanotubes were obtained with well-controlled growth of Fe₂O₃ on N-CNTs. For a better understanding, the underlying mechanisms were explored based on different N-doping configurations. In addition, high-resolution transmission electron microscopy and X-ray diffraction jointly demonstrated that as-deposited Fe₂O₃ is single-phase crystalline α-Fe₂O₃ (hematite). The as-synthesized heterostructural coaxial nanotubes of CNT@Fe₂O₃ may find great potential applications in photocatalysis, gas-sensing, and magnetic fields.     

Exponential dichotomies of evolution operators in Banach spaces

This paper considers three dichotomy concepts (exponential dichotomy, uniform exponential dichotomy and strong exponential dichotomy) in the general context of non-invertible evolution operators in Banach spaces. Connections between these concepts are illustrated. Using the notion of Green function, we give necessary conditions and sufficient ones for strong exponential dichotomy. Some illustrative examples are presented to prove that the converse of some implication type theorems are not valid.     

Manometer

Ohne Zusammenfassung