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Soliton excitation is investigated for a coherently coupled nonlinear Schrodinger system, which describes soliton propagation in optical fibers with two orthogonally polarized components. Analytical soliton solutions, in which two free functions are involved, are constructed via the auxiliary function method. Special solitons can be excited by setting the free functions as some specific functions. S-type, V-type, W-type, periodic wave and doubly periodic wave solitons are excited and demonstrated graphically.

A thermophoretic motion system with a variable heat transmission factor is investigated, which describes wrinkling soliton propagation in a substrate-supported graphene sheet. Analytic multiple-lump wave solutions are constructed via the Hirota bilinear method and symbolic computation. A numerical simulation shows that the system exhibits breaking lump waves. The system parameters control the open width and number of breaking gaps. These results should contribute to a better understanding of the propagation characteristics of wrinkling solitons in a complex graphene thermophoretic motion system.

This paper puts forward an innovative theory and method to calculate the canonical labelings of graphs that are distinct to N a u t y &rsquo, s. It shows the correlation between the canonical labeling of a graph and the canonical labeling of its complement graph. It regularly examines the link between computing the canonical labeling of a graph and the canonical labeling of its o p e n k-n e i g h b o r h o o d s u b g r a p h. It defines d i f f u s i o n d e g r e e s e q u e n c e s and e n t i r e d i f f u s i o n d e g r e e s e q u e n c e. For each node of a graph G, it designs a characteristic m _ N e a r e s t N o d e to improve the precision for calculating canonical labeling. Two theorems established here display how to compute the first nodes of M a x Q ( G ) . Another theorem presents how to determine the second nodes of M a x Q ( G ) . When computing C m a x ( G ) , if M a x Q ( G ) already holds the first i nodes u 1 , u 2 , ⋯ , u i , Diffusion and Nearest Node theorems provide skill on how to pick the succeeding node of M a x Q ( G ) . Further, it also establishes two theorems to determine the C m a x ( G ) of disconnected graphs. Four algorithms implemented here demonstrate how to compute M a x Q ( G ) of a graph. From the results of the software experiment, the accuracy of our algorithms is preliminarily confirmed. Our method can be employed to mine the frequent subgraph. We also conjecture that if there is a node v &isin, S ( G ) meeting conditions C m a x ( G - v ) ⩽ C m a x ( G - w ) for each w &isin, S ( G ) &and, w &ne, v , then u 1 = v for M a x Q ( G ) .

Gentiana radix is used in traditional Chinese medicine and has functions of clearing heat and drying dampness, as well as purging liver and gallbladder fire. A highly sensitive and effective strategy for rapid screening and identification of target constituents has been developed by using ultra high-performance liquid chromatography coupled with linear ion trap-Orbitrap mass spectrometry (UHPLC-LTQ-Orbitrap) in crude and wine-processed . Based on the accurate mass measurement (&lt, 5 ppm), retention times, and MS fragmentation ions, 52 constituents were unambiguously or tentatively characterized from Gentiana radix, including 21 iridoids, 11 flavonoids, 19 xanthones, and a triterpenoid. This study demonstrated that the established method could be a rapid, effective analytical tool for screening and characterization of compounds in the complex systems of . By comparing the structure and peak areas of chemical constituents in crude and wine-processed Gentiana radix, we found that some compounds in crude and wine-processed Gentiana radix were significantly different.

Atractylodis Rhizoma is the dried rhizome of Atractylodes lancea (Thunb.) DC. or Atractylodes chinensis (DC.) Koidz and is often processed by stir-frying with wheat bran to reduce its dryness and increase its spleen tonifying activity. However, the mechanism by which the processing has this effect remains unknown. To explain the mechanism based on the pharmacokinetics of the active compounds, a rapid, sensitive ultra-performance liquid chromatography-tandem mass spectrometry method was developed to analyze atractylenolides I, II, and III, and atractyloside A simultaneously in rat plasma after oral administration of raw and processed Atractylodis Rhizoma. Acetaminophen was used as the internal standard and the plasma samples were pretreated with methanol. Positive ionization mode coupled with multiple reaction monitoring mode was used to analyze the four compounds. The method validation revealed that all the calibration curves displayed good linear regression over the concentration ranges of 3.2&ndash, 350, 4&ndash, 500, 4&ndash, 500, and 3.44&ndash, 430 ng/mL for atractylenolides I, II, and III, and atractyloside A, respectively. The relative standard deviations of the intra- and inter-day precisions of the four compounds were less than 6% with accuracies (relative error) below 2.38%, and the extraction recoveries were more than 71.90 &plusmn, 4.97%. The main pharmacokinetic parameters of the four compounds were estimated with Drug and Statistics 3.0 and the integral pharmacokinetics were determined based on an area under the curve weighting method. The results showed that the integral maximum plasma concentration and area under the curve increased after oral administration of processed Atractylodis Rhizoma.

Prussian Blue type Na2MnFe(CN)6 was prepared by direct precipitation method and a subsequent drying procedure as a cath-ode material for aqueous rechargeable sodium-ion batteries. XRD patterns showed that Na2MnFe(CN)6 has a typical Prussian Blue struc-ture with space group Fm3m. Na2MnFe(CN)6 presents good electrochemical behaviors at 10 mAg-1 discharge current density with specific capacity 73.1 mAhg-1 after 30 cycles. The results show that Na2MnFe(CN)6 could be a potential cathode material for aqueous Sodium-ion battery.

This paper provides a full theoretical and experimental analysis of a serial algorithm for the point-in-polygon test, which requires less running time than previous algorithms and can handle all degenerate cases. The serial algorithm can quickly determine whether a point is inside or outside a polygon and accurately determine the contours of input polygon. It describes all degenerate cases and simultaneously provides a corresponding solution to each degenerate case to ensure the stability and reliability. This also creates the prerequisites and basis for our novel boolean operations algorithm that inherits all the benefits of the serial algorithm. Using geometric probability and straight-line equation F ( P ) = ( y i &minus, y i + 1 ) ( x p &minus, x i ) &minus, ( y i &minus, y p ) ( x i + 1 &minus, x i ) , it optimizes our two algorithms that avoid the division operation and do not need to compute any intersection points. Our algorithms are applicable to any polygon that may be self-intersecting or with holes nested to any level of depth. They do not have to sort the vertices clockwise or counterclockwise beforehand. Consequently, they process all edges one by one in any order for input polygons. This allows a parallel implementation of each algorithm to be made very easily. We also prove several theorems guaranteeing the correctness of algorithms. To speed up the operations, we assign each vector a number code and derive two iterative formulas using differential calculus. However, the experimental results as well as the theoretical proof show that our serial algorithm for the point-in-polygon test is optimal and the time complexities of all algorithms are linear. Our methods can be extended to three-dimensional space, in particular, they can be applied to 3D printing to improve its performance.