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"Pneumonia Prevention No.1" belongs to 'traditional Chinese medicine prescription for prevention of viral pneumonia and influenza' was urgently formulated by Notice on Printing the Novel Coronavirus Diagnosis and Treatment Scheme for COVID-19 (Trial Version 3) and Traditional Chinese Medicine Prevention and Treatment Scheme for COVID-19 in Hubei Province (Trial). Because the prescription drug has the bidirectional regulation function of human immune function, moderate improvement of immune function can effectively resist virus invasion, while excessive immune function will produce immune overresponse. Excessive immune response will aggravate the condition of patients with COVID-19, resulting in the death of severe patients.Twenty medical workers aged 20-60 years old, who had no immune disease, no current disease and healthy physical examination, were selected as participants. The participants took Hubei "Pneumonia Prevention No.1" decoction, one dosage each day, twice a day, for 7 consecutive days. With the before-after control method, blood samples were collected from the median cubital veins before and after medication. Immunoglobulin IgA, IgG and IgM were measured by immunoturbidimetry, and T lymphocyte subsets CD3, CD4, CD8 and CD4/CD8 were measured by flow cytometry. The changes of indexes before and after medication were compared with SPPS 13.0 statistical software. The data were expressed by (mean ± standard deviation).The results of this study show that in healthy participants, the immunoglobulin and T lymphocyte subsets did not differ significantly before and after drug administration (P0.05).Under normal drug administration circumstances, "Pneumonia Prevention No. 1" had no significant regulating effect on the immune system in a healthy population and did not increase the immune system capacity beyond a reasonable range. It is safe to be used as a prophylactic measure in healthy populations.

We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their relationship with weak random periodic solutions. In particular, we establish the existence of invariant measures of random dynamical systems by virtue of their weak random periodic solutions. Finally, we use concrete examples to illustrate the weak random periodic phenomena of dynamical systems induced by random and stochastic differential equations.

In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition of random almost periodic measure. Finally, we discuss the relationship between random almost periodic solutions and almost periodic measures.

In this paper, a necessary and sufficient condition for an invariant subset of a flow to be an attractor is given. At the same time a criterion for the existence of strongly gradient-like flows is also given.

In this paper, several results involving m-chain are proved. At the same time, a criterion for the existence of trajectories joining singular points is given.

Some properties of attractivity, strong repellors and uniform persistence for continuous maps in metric spaces are presented. A result in [J. Dynam. Differential Equations 13 (2001) 107] on uniform persistence is improved.

For the continuous flows defined on a topological space, we have discussed some properties for the invariant sets and their domains of influence. We have proved the following open problem posed by C. Conley: an attractor in a locally connected compact Hausdorff invariant set has finitely many components. In the meantime, two necessary and sufficient conditions for a set to be an attractor have been given.

Some definitions such as m-chain recurrent set, weakly gradient flow and generalized Morse decomposition for a flow defined on a topological space are introduced in this paper. Some conclusions, include the chain recurrent set contain the m-chain recurrent set; the m-chain recurrent set contain the non-wandering set, are proved. In some flows the non-wandering set is proper subset of the m-chain recurrent set; in the meantime the m-chain recurrent set is proper subset of the chain recurrent set. Moreover some criterions for the existence of trajectories joining singular points and a necessary and sufficient condition of the weakly gradient flow are also given here. At last the generalized Morse decomposition of the invariant set are discussed in the paper.

In this paper, we discuss the autonomous differential systems in higher dimensional spaces R n (n ⩾ 3) . By using the index of vector field and fixed point theorem, we prove the existence of periodic solutions for these kind of systems.

We investigated the moving law of the scroll wave filament by perturbation arguments,and obtained that, when the normal direction of scroll wave front curve surface is similar to that of its filament, the normal speed (noted by α ) of the filament is relative not only to the curvature of the filament, but also to that of scroll wave front curve surface,i.e., (where D is diffusional coefficient), and irrelative to the characteristic speed of excitable media. Besides, we also investigated the moving law of the filament along the axis direction, and obtained the similar result to that of Keener's (J.P. Keener, Physica D31 (1988) 269).

In this paper, we studied the periodic solution, connecting orbits between singular points and global structure in Oregonator.

The researches on traveling wave solution and dispersive relation in Tyson's model were only confined to numerical simulation and theoretically formal expression in the past, because of lack of the analytic representation of speed of the traveling wave. In this paper we give its analytic expression by Painleve analysis, and so we can obtain the explicit representation of traveling wave solution and dispersive relation.

We consider the Lienard equation x+f(x)x˙+g(x)=0, and the generalized Lienard equation x+f(x,x˙)x˙+g(x)=0. Results of nonexistence of periodic solutions for Lienard equations have seldom appeared. To deal with this problem, the Dulac function method is usually employed. We give new results based on some distinct ideas. We shall prove that a trajectory of system exists such that one side of it tends to the origin and the other side approaches to infinity, hence implying the nonexistence of periodic solutions