The multi-attribute grey target decision method for attribute value within three-parameter interval grey number

Based on the grey system theory and methods, the grey-target decision-making problem is discussed, in which the attribute values are grey numbers and the maximum probability of the value of grey number is known. Firstly, the optimal effect vector is the positive bull’s-eye and positive bull’s-eye distance of each scheme is defined. Subjectively or objectively weighting method is integrated to determine the index weight and integrated optimization model of index weight is established. Finally, the critical effect vector is the negative bull’s-eye and negative bull’s-eye distance of each scheme is defined, then relative bull’s-eye distance and comprehensive the bull’s-eye distance of grey target decision-making are given. An example is also presented to illustrate the usefulness and effectiveness of the methods obtained in this paper and provides a new idea for grey target decision-making method research.     

A sharper uncertainty principle

The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. Examples are provided to show that the new uncertainty principle is truly sharper than the existing ones in literature.     

Two regularization methods for backward heat problems with new error estimates

We introduce two new methods for solving a backward heat conduction problem. For these two methods, we give a stability analysis with new error estimates. Meanwhile, we investigate the roles of the regularization parameters in these two methods. Numerical results show that our algorithm is effective.     

Highly Enantio- and Diastereoselective Hydrogenation of Cyclic Tetra-Substituted β-Enamido Phosphorus Derivatives

Catalytic asymmetric hydrogenation of enamido phosphorus derivatives is one of the most efficient methods for the construction of chiral amino phosphorus products, among which the congested tetra-substituted substrates remains an unaddressed challenge. In this study, we utilize a commercially available Rh-Josiphos system for the efficient and stereoselective hydrogenation of a wide set of tetra-substituted cyclic β-enamido phosphonates/phosphine oxides, thus enabling access to chiral β-amino phosphorus compounds featuring two vicinal stereocenters. This protocol was broadly applicable to different ring systems possessing various phosphonate/phosphine oxide groups and further applied in the preparation of amino-phosphine ligands. DFT mechanistic explorations indicate that the C=C migratory insertion into Rh^III−H bond could be the rate- and stereo-determining step. The origins of stereoselectivity are revealed through distortion/interaction analysis, which is primarily regulated by distinguished dispersion interactions and steric repulsions.     

Application of stable isotope technique to authenticate the geographical origin of imported apple products

Journal of Radioanalytical and Nuclear Chemistry - This research aimed to authenticate the geographical origin of imported fresh apples using isotopic techniques. The results show that the...     

Targeted isolation of 1,1-diphenyl-2-picrylhydrazyl inhibitors from Saxifraga atrata and their antioxidant activities

Saxifraga atrata is an important traditional Tibetan medicine used to treat cough and pneumonia, and has tremendous medicinal potential. In this study, we devised a technique to separate 1,1-diphenyl-2-picrylhydrazyl inhibitors from a methanol extract of S. atrata. The material was first processed using MCI GEL CHP20P medium-pressure liquid chromatography, yielding 1.1 g of the target fraction Fr2. Subsequently, online hydrophilic interaction liquid chromatography-1,1-diphenyl-2-picrylhydrazyl assay was used to identify prospective 1,1-diphenyl-2-picrylhydrazyl inhibitors, and two 1,1-diphenyl-2-picrylhydrazyl inhibitor fractions (Fr24 and Fr25) were identified from Fr2. Then, medium-pressure preparation was continued using an XIon column to separate two 1,1-diphenyl-2-picrylhydrazyl inhibitor fractions (Fr24 and Fr25). The target compound was concentrated in fractions Fr24 and Fr25 using reverse-phase liquid chromatography during further separation procedures. Finally, the purity, structure, and 1,1-diphenyl-2-picrylhydrazyl inhibitory activity of the isolated 1,1-diphenyl-2-picrylhydrazyl inhibitors were determined. Two 1,1-diphenyl-2-picrylhydrazyl inhibitors (adenosine with the half maximal inhibitory concentration of 66.87 ± 14.33 μM and (-)-4-O-(E)-caffeoyl-l -threonic acid with the half maximal inhibitory concentration of 59.06 ± 5.02 μM) were isolated with purities exceeding 95%. The results showed that this technology is effective in the targeted separation of antioxidants from natural products.     

Iterative method for solving a nonlinear boundary value problem

In this paper, a boundary value problem for a nonlinear second-order ordinary differential equation is studied. By means of the maximum principle we established the existence and the uniqueness of a solution of the problem. Then for finding the solution an iterative method is proposed. It is proved that this method converges much faster than the Picar successive approximations and in a particular case it gives two-sided monotone approximations to the exact solution of the problem. Finally, some illustrative examples are considered to confirm the efficiency of the method.     

Hybrid projection methods for equilibrium problems with non‐Lipschitz type bifunctions

Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz‐type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd.     

Tikhonov regularization method for a system of equilibrium problems in Banach spaces

The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.