An environmentally friendly sodium dodecyl sulfate‐synergistic microwave‐assisted extraction followed by ultra‐high‐performance liquid chromatography with photodiode array method for the simultaneous extraction and determination of iridoids,phenylpropanoids, and lignans from Eucommiae Cortex

A simple and green sodium dodecyl sulfate‐synergistic microwave‐assisted extraction method was developed to extract and determine the iridoids, phenylpropanoids, and lignans in Eucommiae Cortex followed by ultra‐high‐performance liquid chromatography with photodiode array detection. The biodegradable solution (sodium dodecyl sulfate) was used as a promising alternative to organic solvents. The response surface methodology provided the optimum extraction conditions (2 mg/mL sodium dodecyl sulfate, 1100 W microwave power, and 6 min extraction time). The recoveries of three types of components ranged from 95.0 to 105% (RSDs < 5%). The intra‐ and inter‐day precision and accuracy were less than 3.40% and within the range of 97.1‐105%, respectively. Compared with other extraction methods, this newly established method was more efficient and environmental friendly. The results demonstrated that sodium dodecyl sulfate‐synergistic microwave‐assisted extraction followed by ultra‐high‐performance liquid chromatography with photodiode array method was applicable for the simultaneous extraction and determination of these three types of compounds for quality evaluation of Eucommiae Cortex.     

Green and enhanced extraction of coumarins from Cortex Fraxini by ultrasound‐assisted deep eutectic solvent extraction

Green and enhanced extraction of bioactive ingredients from medicinal plants has become a hot research field, and deep eutectic solvents have been considered as a novel kind of sustainable solvents in the extraction process. In this study, hydrogen bond acceptor (choline chloride, etc.) and hydrogen bond donor (l ‐malic acid, etc.) were used to prepare different kinds of deep eutectic solvents to extract coumarins from Cortex Fraxini. The extraction conditions, including the composition and moisture content of deep eutectic solvents, extraction time, and liquid‐solid ratio, were systematically optimized basing on the extraction yield of coumarins. To further investigate the extraction mechanism, Fourier transform infrared spectroscopy was performed, and the microstructures of Cortex Fraxini powders were observed before and after extraction using scanning electron microscope. Results showed that the novel ultrasound‐assisted extraction with conditions of deep eutectic solvent containing betaine/glycerin (1:3), aqueous solution (20%), solid‐liquid ratio (15 mg/mL), and extraction time (30 min) exhibited the best extraction yields for the four target coumarins and much better extraction efficiency than with conventional solvent extractions. This suggests that the new ultrasound‐assisted deep eutectic solvent extraction could be used as a green and high‐efficient approach for extraction of the main coumarins from Cortex Fraxini.     

Quantification and identification of bioactive metabolites from Kalopanacis Cortex by HPLC with evaporative light scattering detection and ESI quadrupole TOF MS

A method based on HPLC coupled with an evaporative light scattering detection and ESI quadrupole TOF MS was established for the quantification and identification of phenolics and triterpene saponins in Kalopanacis Cortex using a gradient elution of acetonitrile with 0.1% formic acid and water with 0.1% formic acid on an RP C₁₈ column (4.6 × 250 mm, 5 μm). Diverse validation parameters, such as the linearity, LOD and LOQ, accuracy, precision, repeatability, and stability, were successfully obtained. Additionally, the efficiencies of different extraction methods were compared. The developed method was applied for the quantitative analysis of twelve representative metabolites in 61 Kalopanacis Cortex samples. The quantitation results showed that coniferin, kalopanaxsaponin C, septemlosides II, III, C, and D exhibited distinct regional patterns in Kalopanacis Cortex samples. These six compounds including one new triterpene saponin show potential as marker compounds for evaluating the quality of Kalopanacis Cortex and the geographical variation in its chemical composition.     

Selective extraction of berberine from Cortex Phellodendri using polydopamine‐coated magnetic nanoparticles

A new extraction agent featuring dopamine self‐polymerized on magnetic Fe₃O₄ nanoparticles has been successfully synthesized and evaluated for the SPE of berberine from the extract of the traditional Chinese medicinal plant, Cortex Phellodendri. The nanoparticles prepared possessed a core–shell structure and showed super‐paramagnetism. It was found that these polydopamine‐coated nanoparticles exhibited strong and selective adsorption for berberine. Among the chemical components present in C. Phellodendri, only berberine was adsorbed by the nanoparticles and extracted by a following SPE procedure. Various conditions such as the amount of polydopamine‐coated nanoparticles, desorption solvent, desorption time and equilibrium time were optimized for the SPE of berberine. The purity of berberine extracted from C. Phellodendri was determined to be as high as 91.3% compared with that of 9.5% in the extract. The established SPE protocol combined advantages of highly selective enrichment with easy magnetic separation, and proved to be a facile efficient procedure for the isolation of berberine. Further, the prepared polydopamine‐coated magnetic nanoparticles could be reused for multiple times, reducing operational cost. The applicability and reliability of the developed SPE method were demonstrated by isolating berberine from three different C. Phellodendri extracts. Recoveries of 85.4–111.2% were obtained with relative standard deviations ranging from 0.27–2.05%.     

Computing Voronoi skeletons of a 3-D polyhedron by space subdivision

We tackle the problem of computing the Voronoi diagram of a 3-D polyhedron whose faces are planar. The main difficulty with the computation is that the diagram's edges and vertices are of relatively high algebraic degrees. As a result, previous approaches to the problem have been non-robust, difficult to implement, or not provenly correct.

We introduce three new proximity skeletons related to the Voronoi diagram: (1) the Voronoi graph (VG), which contains the complete symbolic information of the Voronoi diagram without containing any geometry; (2) the approximate Voronoi graph (AVG), which deals with degenerate diagrams by collapsing sub-graphs of the VG into single nodes; and (3) the proximity structure diagram (PSD), which enhances the VG with a geometric approximation of Voronoi elements to any desired accuracy. The new skeletons are important for both theoretical and practical reasons. Many applications that extract the proximity information of the object from its Voronoi diagram can use the Voronoi graphs or the proximity structure diagram instead. In addition, the skeletons can be used as initial structures for a robust and efficient global or local computation of the Voronoi diagram.

We present a space subdivision algorithm to construct the new skeletons, having three main advantages. First, it solves at most uni-variate quartic polynomials. This stands in sharp contrast to previous approaches, which require the solution of a non-linear tri-variate system of equations. Second, the algorithm enables purely local computation of the skeletons in any limited region of interest. Third, the algorithm is simple to implement.     

Quality assessment of cortex cinnamomi by HPLC chemical fingerprint, principle component analysis and cluster analysis

HPLC fingerprint analysis, principle component analysis (PCA), and cluster analysis were introduced for quality assessment of Cortex cinnamomi (CC). The fingerprint of CC was developed and validated by analyzing 30 samples of CC from different species and geographic locations. Seventeen chromatographic peaks were selected as characteristic peaks and their relative peak areas (RPA) were calculated for quantitative expression of the HPLC fingerprints. The correlation coefficients of similarity in chromatograms were higher than 0.95 for the same species while much lower than 0.6 for different species. Besides, two principal components (PCs) have been extracted by PCA. PC1 separated Cinnamomum cassia from other species, capturing 56.75% of variance while PC2 contributed for their further separation, capturing 19.08% variance. The scores of the samples showed that the samples could be clustered reasonably into different groups corresponding to different species and different regions. The scores and loading plots together revealed different chemical properties of each group clearly. The cluster analysis confirmed the results of PCA analysis. Therefore, HPLC fingerprint in combination with chemometric techniques provide a very flexible and reliable method for quality assessment of traditional Chinese medicines.     

Selective and sensitive determination of protoberberines by capillary electrophoresis coupled with molecularly imprinted microextraction

In this work, we developed a novel molecularly imprinted solid‐phase microextraction with capillary electrophoresis method for the selective extraction and determination of protoberberines in complicated samples. The imprinted monolith was prepared in a micropipette tip‐based device by using acrylamide as the functional monomer, ethyleneglyoldimethacrylate as the cross‐linker and dimethylsulfoxide as the porogen, and exhibited an imprinting factor of 2.41 to berberine, 2.36 to palmatine and 2.38 to jatrorrhizine. Good capillary electrophoresis separation was achieved by using 20 mM phosphate buffer at pH 7 as running buffer with the addition of organic modifier of 10% methanol. Parameters such as sample pH value, sample flow rate and sample volume were investigated for imprinted monolith‐based solid‐phase microextraction. An imprinted solid‐phase microextraction with capillary electrophoresis method was developed, the method showed a wide linear range (0.3–50 μg/mL), good linearity (R² ≥ 0.9947) and good reproducibility (relative standard deviations ≤ 0.73%), the limit of detection was as low as 0.1 μg/mL, which was lower than some reported methods based on capillary electrophoresis for protoberberines. The method has been applied for determination of three common protoberberines in Cortex Phellodendri Chinensis, by using a molecularly imprinted monolith as the selective sorbent, most of the matrices in the Cortex Phellodendri Chinensis sample were removed and three protoberberines were selectively enriched and well determined.     

A unified Pythagorean hodograph approach to the medial axis transform and offset approximation

Algorithms based on Pythagorean hodographs (PH) in the Euclidean plane and in Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. In this paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. On the basis of this approach we design a new, simple interpolation algorithm. The main advantage of the unifying method presented lies in the fact that it uses, after only some simple additional computations, an arbitrary algorithm for interpolation using planar PH curves also for interpolation using spatial MPH curves. We present the functionality of our method for G¹ Hermite data; however, one could also obtain higher order algorithms.     

On Some Monogenic Semigroups with an Associate Subgroup

Let S be any semigroup and a, s ∈ S. If a = asa, then s is an associate of a. A subgroup G of S is an associate subgroup of S if every a ∈ S has a unique associate a* in G. It turns out that G = H _z for some idempotent z, the zenith of S. The mapping a → a* is a unary operation on S. We say that S is monogenic if S is generated, as a unary semigroup, by a single element.

We embark upon the problem of the structure of monogenic semigroups in this sense by characterizing monogenic ones belonging to completely simple semigroups, normal cryptogroups, orthogroups, combinatorial semigroups, cryptic medial semigroups, cryptic orthodox semigroups, and orthodox monoids. In each of these cases, except one, we construct a free object. The general problem remains open.