A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

A second-order boundary value problem with nonlinear and mixed two-point boundary conditions is considered, Lx=f(t,x,x′), t∈(a,b), g(x(a),x(b),x′(a),x′(b))=0, x(b)=x(a) in which L is a formally self-adjoint second-order differential operator. Under appropriate assumptions on L, f, and g, existence and uniqueness of solutions is established by the method of upper and lower solutions and Leray-Schauder degree theory. The general quasilinearization method is then applied to this problem. Two monotone sequences converging quadratically to the unique solution are constructed

A double-layer Huygens’ metasurface with complete phase coverage and its dual-polarized meta-lens antenna application

A novel double-layer Huygens’ unit with dual-polarized response and complete phase coverage has been proposed for highly efficient meta-lens antenna application. The designed unit is a symmetric structure in which the double-layer metallic patterns not only act as the electric dipoles but also induce the magnetic dipoles. The balance between the initial electric dipole and the induced magnetic dipole makes the impedance of the metasurface match with that of free space, thus allowing efficient transmission of electromagnetic waves. Moreover, full transmission phase shift and near-unit transmission amplitude can be achieved simultaneously by change the structural parameters of the unit. Utilizing such electromagnetic properties, a dual-polarized meta-lens consisting of 35 × 35 units with size of 161 × 161 mm2 is designed, fabricated and measured. The results exhibit its good radiation performance. The maximum gain at a frequency of 28 GHz reaches 30.8 dBi, with an aperture efficiency of 42.3%. The 3-dB gain bandwidth reaches 12.5%, covering the frequency range of 26.7–30.2 GHz. The simple structure of the designed dual-polarized metasurface, high gain and high antenna efficiency make it an important antenna engineering role

Numerical simulation of multiphysics coupling for magnetic fluid grinding of germanium wafer by rotating magnetic field

In order to improve the surface quality of germanium wafer, the material removal behavior of germanium wafer under the action of solid-liquid two-phase flow was studied by means of rotating magnetic field magnetic fluid grinding and numerical simulation. Firstly, the grinding principle of magnetic fluid was introduced. Secondly, a simulation model was established. Starting from the process parameters of magnetic fluid grinding and combined with finite element analysis, the surface mechanical properties are taken as the breakthrough point. The effects of processing parameters such as different excitation gaps, magnetic pole rotation speeds, and particle phase volume fractions on the surface quality of the germanium wafer were analyzed. The optimal processing parameters were determined. Finally, the magnetic fluid grinding test was carried out. The results show that when the excitation gap is 5 mm, the magnetic pole rotation speed is 1000 r/min, and the volume fraction of the particle phase is 25%. After grinding for 60 minutes, the surface quality of germanium wafer was improved effectively, and the surface roughness Ra decreased from 500 nm to 47 nm, which realized the removal of small plastic materials on the surface of germanium wafer

FPGA-Based Image Acquisition System Designed for Wireless

Part 12: Pattern RecognitionInternational audienceIntroduced micro-wireless transmission system image acquisition the overall structure, each part of the overall design ideas and works theory. Designed SBBC camera interface and data cache control module, analysis of the TCP / IP communication protocol standard structure and characteristics, and on this basis, the design of a non-standard short-range wireless communication protocol. System which controlled by the input and output module is based on FPGA, the system collected data alternately to the outer SDRAM, this realized the image data collection; Ethernet interface controller also designed in FPGA to achieve the image data transmit through wireless. The results show that: under normal conditions, the wireless communication module can be complete, accurate, stable wireless data transceiver functions

Relaxation Oscillations in Singularly Perturbed Generalized Lienard Systems with Non-Generic Turning Points

Based on the asymptotic analysis technique developed by Eckhaus [Lecture Notes in Math., vol. 985, pp 449-494. Springer, Berlin, 1983], this paper aims to study the existence and the asymptotic behaviors of relaxation oscillations of regular and canard types in a singularly perturbed generalized Lionard system with a non-generic turning point. The singularly perturbed Lionard system considered in this paper is very general and numerous real world models like some biological ones can be rewritten in the form of this system after a series of transformations. Under certain conditions, we rigorously prove the existence of regular relaxation oscillations and canard relaxation oscillations under the specific parameter conditions. As an application, two biological models, namely, a FitzHugh-Nagumo model and a twodimensional predator-prey model with Holling-II response are studied, in which, the existence of regular relaxation oscillations and canard relaxation oscillations as well as the bifurcation curves are obtained

Integrated metabolomics and transcriptomics analysis of roots of Bupleurum chinense and B. scorzonerifolium, two sources of medicinal Chaihu

Abstract Radix Bupleuri (Chaihu in Chinese) is a traditional Chinese medicine commonly used to treat colds and fevers. The root metabolome and transcriptome of two cultivars of B. chinense (BCYC and BCZC) and one of B. scorzonerifolium (BSHC) were determined and analyzed. Compared with BSHC, 135 and 194 differential metabolites were identified in BCYC and BCZC, respectively, which were mainly fatty acyls, organooxygen metabolites. A total of 163 differential metabolites were obtained between BCYC and BCZC, including phenolic acids and lipids. Compared with BSHC, 6557 and 5621 differential expression genes (DEGs) were found in BCYC and BSHC, respectively, which were annotated into biosynthesis of unsaturated fatty acid and fatty acid metabolism. A total of 4,880 DEGs existed between the two cultivars of B. chinense. The abundance of flavonoids in B. scorzonerifolium was higher than that of B. chinense, with the latter having higher saikosaponin A and saikosaponin D than the former. Pinobanksin was the most major flavonoid which differ between the two cultivars of B. chinense. The expression of chalcone synthase gene was dramatically differential, which had a positive correlation with the biosynthesis of pinobanksin. The present study laid a foundation for further research on biosynthesis of flavonoids and terpenoids of Bupleurum L

Enhanced Ozone Aging Resistance of Natural Rubber with 2-Mercaptobenzothiazole as the Constant-Viscosity Agent

For the actual storage and serving, a phenomenon of hardening and cracking always occurs in the natural rubber (NR), which sharply reduces the mechanical performance and hinders the further application of NR. Recently, some type of constant-viscosity agent has played a key role to be used for the treatment of NR, especially for the effect of ozone aging resistance. In this study, 2-mercaptobenzothiazole (MBT) was introduced into NR, and the constant viscosity and ozone aging resistance of NR with different contents of MBT were investigated using an accelerated storage experiment and an ozone aging experiment, respectively. The results indicated that the addition of MBT could improve the constant viscosity of NR in a certain degree. With the MBT content of 0.15%, NR/MBT-0.15 obtained a best ozone aging resistance and maintained the original high tensile strength. Therefore, it provided a promising route to design and prepare NR with high-quality ozone aging resistance