In this work, a non-isospectral and variable-coefficient Kadomtsev–Petviashvili equation is considered using Hirota’s bilinear form and a direct assumption with arbitrary functions. Analytical ...rational solutions in light of positive quadratic functions and lump solutions of the variable-coefficient Kadomtsev–Petviashvili equation are obtained. These lump solutions describe two types of characters by some three-dimensional graphs and contour plots, which contain bright lump wave and bright–dark lump wave. Meanwhile, periodic structure of the lump wave is also shown.
•Flaxseed protein hydrolysates were prepared using immobilized Alcalase and Flavourzyme.•Peptides with molecular weight higher than 1,000 Da enhanced the mouthfulness and continuity in umami ...soup.•Low molecular weight (128–1,000 Da) peptides improved the flavor of MRPs.•The hydrolysates can be used as a template for the preparation of flaxseed Maillard reaction products.
We aimed to simplify the enzymolysis process for flaxseed protein hydrolysates production as Maillard reaction products (MRPs) to generate different flavor characteristics. More than 50% activity of immobilized enzymes (Alcalase and Flavourzyme) was retained after repeated use. Subsequently, after five weeks, the activities of the immobilized enzymes were also observed to be higher after storage at 4 °C. The optimum conditions for production of flaxseed protein hydrolysates using sequential enzymatic hydrolysis were as follow: 3,000 U/g of Alcalase at 60 °C and pH 8.0 for 2 h and 120 U/g of Flavourzyme at 50 °C and pH 6.5 for 2 h. Partial least squares regression analysis revealed that resulting peptides with the molecular weight (MW) higher than 1,000 Da could improve the mouthfulness and stability in umami soup; whereas, peptides with MW of 128–1,000 Da mainly contributed to the generation of meat-like flavor compounds with a significant effect on umami taste and bitterness.
In this paper, a variable-coefficient symbolic computation approach is proposed to solve the multiple rogue wave solutions of nonlinear equation with variable coefficients. As an application, a (
2
+
...1
)-dimensional variable-coefficient Kadomtsev–Petviashvili equation is investigated. The multiple rogue wave solutions are obtained and their dynamic features are shown in some 3D and contour plots.
The multiple exp-function method is utilized for solving the multiple soliton solutions for the new (2+1)-dimensional Korteweg–de Vries equation, which include one-soliton, two-soliton, and ...three-soliton type solutions. The physical phenomena of these obtained multiple soliton solutions are analyzed and illustrated in figures by selecting appropriate parameters.
We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. We show ...that, this new scheme is stable as long as the initial condition does not exceed certain threshold, and it asymptotically preserves the quasi-static limit in the transient regime. Furthermore, we show that the fully discrete scheme is conservative and positivity preserving, which makes it ideal for simulations. The analogical schemes for the radial symmetric cases and the subcritical degenerate cases are also presented and analyzed. With extensive numerical tests, we verify the claimed properties of the methods and demonstrate their superiority in various challenging applications.
Asymmetric insertion of an arylvinylcarbenoid into the C–H bond for direct enantioselective C(sp2)-H functionalization of aniline derivatives catalyzed by a rhodium(I)-diene complex was developed ...for the first time. The reaction occurred exclusively at the uncommon vinyl terminus site with excellent E selectivity and enantioselectivities, providing various chiral γ,γ-gem-diarylsubstituted α,β-unsaturated esters with broad functional group compatibility under simple and mild conditions. It provides a rare example of the asymmetric C–H insertion of arenes with selective vinylogous reactivity. Synthesis applications of this protocol were featured by several versatile product transformations. Systematic DFT calculations were also performed to elucidate the reaction mechanism and origin of the uncommon enantio- and regioselectivity of the Rh(I)-catalyzed C(sp2)-H functionalization reaction. The measured and computed inverse deuterium kinetic isotope effect supports the C–C bond-formation step as the rate-determining step. Attractive interactions between the chiral ligand and substrates were also proposed to control the enantioselectivity.
Under investigation is the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in the incompressible fluid in this paper. The extended homoclinic test technique, ansätz functions and the bilinear ...form are used to construct double periodic-soliton solutions of the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Some entirely new double periodic-soliton solutions are presented. The properties and physical structure for these obtained solutions are discussed with some figures. The ansätz functions are first used in (3+1)-dimensional higher order differential equation.
An enantioselective Si−H insertion between α‐arylvinyldiazoesters and silanes has been developed by employing rhodium(I)/chiral diene complex as the catalyst. This protocol offers a catalytic ...asymmetric approach to various chiral silanes containing α‐arylvinyl functionality at room temperature with good enantiocontrol (89–99% ee). Transformation of the resulting enantiomerically enriched α‐arylvinyl‐α‐silyl esters led to a variety of other valuable building blocks. The deuterium kinetic isotope effect experiments revealed a rhodium(I)‐mediated concerted Si−H insertion mechanism.
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