To explore the effect and mechanism of bivalent ion doping on yttrium iron garnet (YIG), Zn-YIG (Zn-doped YIG) nanoparticles with a size of 60~70 nm were prepared by the sol-gel method. It was proven that Zn ion doping resulted in lattice expansion and internal stress due to crystallite size shrinkage. A Raman spectroscopic analysis proved the influence of Zn doping on the crystal structure and peak intensity by analyzing Raman vibration modes. The characteristics and chemical mechanism of mass loss and phase evolution in each temperature region were explored through TG-DSC measurements. Moreover, it was revealed that the antiferromagnetic coupling, pinning mechanisms and particle aggregation lead to coercivity, exhibiting different variation trends. A saturation magnetization (Ms) curve variation mechanism was further revealed, which was due to the thermal effects, super-exchange effect, and coupling effect between sub-lattices. Meanwhile, the influence of the thermal effect on Ms and its mechanism were explored by spin theory, and it was proven that it was mainly caused by the random arrangement of magnetic moments and thermal vibration. These results provide theoretical support for the wider application of YIG devices in microwave and high-temperature fields.

YIG (yttrium iron garnet) nanoparticles have been prepared by both solid-state reaction and sol–gel methods. XRD revealed that the particles are single phase. The average particle size calculated using XRD patterns is consistent with the size estimated through scanning electron microscopy. The size of the nanoparticles prepared by the solid-state method is higher than those prepared by the sol–gel method on account of the different annealing temperatures and synthesis processes. The two types of particles also have different magnetic parameters. The mechanisms leading to symmetry and asymmetry of the ferromagnetic resonance (FMR) curves were studied. The Landau-Lifshitz or Gilbert damping model (LLG model) and the Bastrukov theory were used to fit the FMR data, with the former providing the better fitting.

In the field of biological control, there are a large number of systems that gradually evolve over a certain period of time. However, due to some natural or human intervention behavior, the system state will be subjected to some relatively short time interference, so that the system state changes in an instant. This sudden change of state makes the system not simply described by continuous or discrete dynamical systems, but by means of impulse dynamical systems. In this paper, the multi-point boundary value problem of a class of second-order nonlinear impulsive integral differential equations is studied on the basis of impulsive differential equation theory. The main results of this kind of equation are obtained by using the fixed point theorem of strict set contraction operator. Under certain assumptions, the existence of the solution of the equation is proved by constructing the operator on the special cone. Finally, combined with the practical application, the theory was applied to the stability prediction of biological ecosystem, and the correctness of the conclusion was verified.

Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.