Dynamic behavior and stability analysis of nonlinear modes in the fourth-order generalized Ginzburg–Landau model with near $$\mathcal{PT}$$ PT -symmetric potentials

Nonlinear Dynamics - Parametrically excited oscillators are used in several domains, in particular to improve the dynamical behaviour of systems like in the case of the parametric amplification or...     

IVDAS: an interactive visual design and analysis system for image data symmetry detection of CNN models

Journal of Visualization - Convolutional neural networks (CNNs) have achieved breakthrough performance in image recognition and classification. However, it is still a challenge for CNNs to classify...     

Langevin dynamic for the 2D Yang–Mills measure

Publications mathématiques de l'IHÉS - It is well known that a real analytic symplectic diffeomorphism of the $2d$ -dimensional disk ( $d\geq 1$ ) admitting the origin as a...     

A Note about Multi-Hilbert Transform on D(ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)

In this paper, we first prove that, for a non-zero function f∈D(? ⁿ ), its multi-Hilbert transform Hnf is bounded and does not have compact support. In addition, a new distribution space D' _H (? ⁿ ) is constructed and the definition of the multi-Hilbert transform is extended to it. It is shown that D' _H (? ⁿ ) is the biggest subspace of D'(? ⁿ ) on which the extended multi-Hilbert transform is a homeomorphism.     

On local spectral properties of Hamilton type operators

In this paper, we introduce the class of Hamilton type operators and study various properties of this class. We show that every Hamilton type operator with property (β) or (δ) is decomposable. In addition, we prove that a Hamilton type operator T satisfies property (β), Dunford’s property (C) and Weyl’s theorem if and only if its adjoint does.     

A practicable strategy for enrichment and separation of four minor flavonoids including two isomers from barley seedlings by macroporous resin column chromatography,medium‐pressure LC,and high‐speed countercurrent chromatography

Separation of minor compounds especially with similar polarities and structures from complex samples is a challenging work. In the present study, an efficient method was successfully established by macroporous resin column chromatography, medium‐pressure liquid chromatography, and high‐speed countercurrent chromatography for separation of four minor flavonoids from barley seedlings. Macroporous resin column chromatography and medium‐pressure liquid chromatography were used for enrichment of these four flavonoids. High‐pressure liquid chromatography analysis showed the total content of these four flavonoids increased from 2.2% in the crude extract to 95.3% in the medium‐pressure liquid chromatography fraction. It was indicated that the combination of macroporous resin column chromatography and medium‐pressure liquid chromatography could be a practicable strategy for enrichment of minor compounds from complex sample. Then, high‐speed countercurrent chromatography was employed for separation of these four flavonoids using ethyl acetate/n‐butanol/water (0.1% glacial acetic acid) (4:1:5, v/v/v) as solvent system. As a result, four flavonoids including two isomers with purities higher than 98% were obtained. Interestingly, two flavonoids existing in one high‐pressure liquid chromatography peak were also successfully separated. All these indicated high‐speed countercurrent chromatography had great potential for separation of compounds with similar structures and polarities. This study provides a reference for efficient enrichment and separation of minor compounds from complex sample.     

Establishing the chromatographic fingerprint of traditional Chinese medicine standard decoction based on quality by design approach: A case study of Licorice

A novel analytical quality by design approach for developing a chromatographic fingerprint was established for analyzing complex traditional Chinese medicine, using a licorice standard decoction as an example. Considering the characteristics of integrity and ambiguity, the resolution of eight common peaks, total peak number, capacity factor distributions, and peak purity were selected as potential critical method attributes for assessing the quality of the chromatographic fingerprint. A central composite design was used to evaluate the relationship between critical method attributes and critical method parameters, including column temperature, wavelength, flow rate, formic‐acid concentration, and gradient parameters. A standard probability method was employed to calculate the design space of the fingerprint analysis parameters and evaluate the robustness of the methodology. The optimized high‐performance liquid chromatography fingerprint conditions were acetonitrile and 0.1% formic acid water gradient elution (0‐5 min, 5–19% A; 5–10 min, 19% A; 10–50 min, 19–42% A; 50–54 min, 42–100% A; 54–60 min, 100% A), column temperature 25±5°C, detection wavelength 265 nm. The design space of fingerprint analytical method based on the analytical quality by design approach not only met the requirements of the fingerprint analysis, but also improved the robustness and applicability of the fingerprint method.     

Copper‐Catalyzed Remote C(sp3)−H Trifluoromethylation of Carboxamides and Sulfonamides

Reported herein is an unprecedented protocol for trifluoromethylation of unactivated aliphatic C(sp³)?H bonds. With Cu(OTf)₂ as the catalyst, the reaction of N‐fluoro‐substituted carboxamides (or sulfonamides) with Zn(CF₃)₂ complexes provides the corresponding δ‐trifluoromethylated carboxamides (or sulfonamides) in satisfactory yields under mild reaction conditions. A radical mechanism involving 1,5‐hydrogen atom transfer of N‐radicals followed by CF₃‐transfer from Cu^II?CF₃ complexes to the thus formed alkyl radicals is proposed.     

Insight into shear‐induced modification for improving processability of polymers: Effect of shear rate on the evolution of entanglement state

Many experimental results have revealed that the re‐entanglement kinetics of disentangled polymers is much slower than that predicted by tube theory. This retarded recovery of fully entangled state is of practical significance that shear‐induced modification may offer a way to improve processability for a polymer by reducing viscosity. This work tried to figure out the shear‐rate dependence variation of viscosity in the view of evolution of entanglement state through disentanglement and re‐entanglement, aiming to provide fundamental insights into application prospect of shear‐induced modification in preparing “in‐pellet” disentangled polymers prior to final processing. High‐density polyethylene was sheared on a parallel‐plate rotational rheometer with a linearly increased shear rate. Results showed that higher shear rate could induce further disentanglement, resulting in a lower viscosity with a reduction rate up to 93.7%, larger molecular weight between entanglements M_e , and longer re‐entanglement time. Additionally, less entanglement would give a larger lamellar thickness of sheared samples after nonisothermal crystallization. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 598–606