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Embeddings of potentials along the moment curve

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In this paper, let [Formula: see text] and [Formula: see text] be the potential along the moment curve [Formula: see text] ([Formula: see text]) defined by setting, for any suitable function [Formula: see text], [Formula: see text] The authors obtain some equivalent characterizations via capacities of the embedding [Formula: see text] from Lebesgue spaces [Formula: see text] associated with the [Formula: see text]-dimensional Lebesgue measure to [Formula: see text] endowed with the non-negative Radon measure [Formula: see text] in the form of [Formula: see text] for a weight [Formula: see text]. The main ingredient of this paper lies in the different approach to the estimate of the capacity of the anisotropic cubes [Formula: see text] along [Formula: see text].

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  • 10.1002/ame2.12550
Pharmacokinetic analysis on compatibility of Atractylodes macrocephala and Paeoniae radix herb pair ameliorates functional constipation model rats using microdialysis with ultra-performance liquid chromatography.
  • Jan 27, 2025
  • Animal models and experimental medicine
  • Xiaoting Wang + 4 more

In a previous study, we found that Atractylodes macrocephala and Paeoniae radix (AM-PR) was useful for the alleviation of functional constipation (FC). However, the precise mechanism underlying the compatibility between AM and PR in the treatment of FC remains uncertain. This study aims to analyze the pharmacokinetic differences in the active ingredients in the blood of rat models with FC when applied individually and in combination with AM-PR. It also seeks to compare the changes in the content of the active ingredient when applied individually and in combination with invitro AM-PR, further in-depth investigation into its material foundation in terms of pharmacokinetics, as well as the composition of the substance. Blood microdialysis samples were collected using microdialysis technology. These samples from rats with FC were compared after administration of AM, PR, and AM-PR. The concentration of the main active ingredients was determined using the Ultra Performance Liquid Chromatography-Tunable Ultraviolet (UPLC-TUV) method. The concentration of the main active ingredients of the decoction compatibility before and after combining AM-PR was also determined using the UPLC-TUV method. Our findings reveal that upon combination, the time to maximum concentration (Tmax) of isochlorogenic acid A (ICA-A) and ataridolide II (ATR-II) Tmax was prolonged, terminal elimination half-life (T1/2) was reduced, and maximum plasma concentrations (Cmax) increased. The Tmax of ataridolide III (ATR-III) remained consistent, whereas its T1/2 and Cmax were significantly reduced. Conversely, for peoniflorin (PAE), Tmax occurred sooner, T1/2 was shortened, and Cmax increased. The Tmax for albiflorin (ALB) remained consistent, whereas T1/2 and Cmax witnessed significant increases. The area under the moment curve (AUMC) (0-t) and AUMC (0-∞) of PAE, ALB, ICA-A, ATR-II experienced an increase after AM-PR administration in rats, attributable to the heightened Cmax. In comparison to individual herb administration, the Tmax of ALB was advanced in combination, the Tmax of PAE remained unchanged, and the Tmax of ICA-A and ART-II was delayed, with an increased area under the concentration-time curve (AUC) (0-t), indicating enhanced Cmax and bioavailability. Furthermore, the dissolution rates of PAE, ICA-A, and ATR-II significantly improved after compatibility. This study partially clarifies the rationale and compatibility of AM-PR in treating FC and offers a new perspective on the pharmacokinetic interactions of AM-PR in FC treatment.

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