In this paper, we apply the theory of soft sets to partially ordered semigroup. First, several new notions such as left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup, whole filter soft partially ordered semigroup, prime left (right) ideal soft partially ordered semigroup, prime ideal soft partially ordered semigroup over partially ordered semigroups S are introduced. Further, with prime left (right) ideal soft partially ordered semigroup and prime ideal soft partially ordered semigroup over S, the necessary and sufficient conditions that the non-null soft set over S is a right (left) filter soft partially ordered semigroup and filter soft partially ordered semigroup over S are given separately. Finally, quotient ordered homomorphic images and inverse images under partially ordered homomorphic on left (right) filter soft partially ordered semigroup, filter soft partially ordered semigroup, whole left (right) filter soft partially ordered semigroup and whole filter soft partially ordered semigroup are studied,and some related conclusions are obtained.

The number of homomorphisms between finite 2-groups M_{\mathrm{2}}(\mathrm{2},m) and generalized quaternion groups Q_{\mathrm{4}n} a kind of maximal class 2-groups, is obtained by studying the structure of M_{\mathrm{2}}(\mathrm{2},m). Further, it is verified that the above groups satisfy the conjecture of ASAI and YOSHIDA.

We construct a q-type Lupas-Kantorovich operators based on the q-type integer and q-type calculus, investigate the rate of convergence of q-type Lupas-Kantorovich operators by modulus continuity as well as the properties of statistical convergence and weighted statistical convergence of the operators.

In order to study the impact of cooperative behaviors between predators on the dynamic behavior of the food chain system, a top-level predator (which only feeds on the predator population) on the basis of the original cooperative hunting model is introduced, and a food chain model with cooperative hunting is established. The local stability of the equilibrium point is discussed by using the linearization method. By establishing an appropriate Lyapunov function, a sufficient condition for the global stability of the system at the equilibrium point is given. In addition, by using the central manifold reduction theorem, the explicit formulas of the branch periodic solution is studied. Numerical simulations are conducted to verify our theoretical analysis. The results show that when there is no cooperative relationship between predators, the positive equilibrium point is stable. With the increase of cooperative predation parameter \alpha, the system will have a stable limit cycle, and the limit cycle will continue to expand following the increase of cooperative predation parameter \alpha. Moreover, if the predator population density is too large, the system will produce continuous periodic oscillation, that is, the three species i.e. diet, mid-level predator, top-level predator, either coexist in the form of periodic oscillation, or the number of species eventually tends to be stable. Therefore, cooperative hunting is more conducive to maintaining ecological balance.

Let H be an infinite dimensional complex separable Hilbert space and B(H) be the algebra of all bounded linear operators on H. We call property (W_E) holds for T\in B(H) if \sigma (T)\backslash {\sigma }_{\mathrm{w}}(T)=E(T), where \sigma (T) and {\sigma }_{\mathrm{w}}(T) denote the spectrum and Weyl spectrum of T respectively, and E(T)=\{\lambda \in \mathrm{i}\mathrm{s}\mathrm{o}\text{?}\sigma (T):\text{?}\mathrm{d}\mathrm{i}\mathrm{m}N(T-\lambda I)>\mathrm{0}\}. By using the property of topological uniform descent of operators in this paper, the necessary and sufficient conditions for which the property (W_E) holds for bounded linear operators and its functions are given. Furthermore, we show the applications of the main results, and explore the relationship of property (W_E) between the Drazin invertible operator and its Drazin inverse.

Reliability is the primary topic in the theoretical research of reliability models, especially the premise for discussing other indicators in the δ shock model. In this paper, three methods including multiple integration method, independent convolution method and memoryless method are used to prove the system reliability of Yule-Furry classical δ shock model, and the similarities and differences between the three methods are analyzed. Based on the proof process of the memoryless method, the distribution function of the lifetime T is obtained, and a simple proof of reliability is derived.

The fractional-order permanent magnet synchronization motor chaotic systems were studied based on sliding mode control theory and fractional-order calculus, using two self-adaptive sliding mode methods. Self-adaptive sliding mode synchronization of system was researched, by constructing sliding mode function, controllers and adaptive rules. Two sufficient conditions were established to ensure self-adaptive sliding mode synchronization of the systems. Numerical simulations verify the feasibility of the proposed method.

Due to the increasing complexity of data form, multi-view clustering algorithms emerge one after another. The main disadvantages of existing methods include: the computational complexity of these methods is high; the final clustering involves additional processing steps; the similarity graph constructed may not be the optimal graph. In order to solve the above problems, a clustering algorithm based on sparse consensus graph decomposition is proposed. The algorithm is first tested on single-view data, and then extends from single-view data to multi-view data. The algorithm takes into account different contributions of different views to the final result by giving each view appropriate weight, at the same time, makes use of the L_{\mathrm{2,1}} norm to obtain the consensus graph with better performance, learns the non-negative representation matrix on the basis of the consensus graph, and reveals the cluster result directly after alternation iteration. Finally, an update iterative algorithm is proposed and tested on a large number of data sets to verify the effectiveness of the algorithm.

The configurational transition of polyelectrolyte chain confined in a cylinder was studied by means of coarse-grained molecular dynamics simulation. Specifically, the effects on the size and configuration transition of polyelectrolyte chain under the parameters of counterion valence, chain stiffness and confinement radius were studied by calculating the average radius of gyration, average persistence length, and average shape factor. It has been found that there are stable rod-like, globular, folded-chain and ring structures in confined space. In the case of trivalent counterions, the polyelectrolyte chain with moderate stiffness forms a stable ring structure, which can be well characterized by a tangent correlation function. The mechanism of condensation of polyelectrolyte chain and counterion is further explored by statistical analysis of polyelectrolyte chain and counterions distribution. Finally, the kinetic characteristics of the nucleation and growth of the ring structure are discussed, and the results agree with the experimental results. The results can provide a deep insight about the configurational behaviors of biological macromolecules in confined spaces.

This paper discusses the effect of ex-situ ecological combined remediation (ESECR) system on the purification of phosphorus of different forms in the polluted water of Pulin Creek, a tributary of Jiulong River, and each unit of ESECR treatment system is analyzed on the correlation between different phosphorus forms and environmental factors. Results showed that the average total removal rate of TP, DTP, DP and PP of ESECR treatment system were 84.3%, 84.4%, 90.8% and 78.9% respectively, among them the DP purification effect was the best. In each unit of ESECR treatment system, when the phosphorus content in the raw water was low, the sludge-membrane symbiotic (SSM) high efficiency coagulation water purification system had good TP, DTP and DP purification effect, the average removal rate were 81.4%, 76.0% and 84.8% respectively, the average removal rate of PP was 66.7%; when the content of phosphorus in the raw water was high, the average removal rate of TP, DTP and DP of the SSM high efficiency coagulation water purification system were 37.8%, 44.6% and 45.8%, nevertheless, the purification effect of PP was significant, and the average removal rate was 93.2%. When the processed water of the SSM high efficiency coagulation water purification system with low phosphorus content, the purification effect of ecological pond Ⅱ on TP and DTP was better than that of ecological pond Ⅰ, but the results on DP was opposite. For PP, the purification effect in ecological pond Ⅱ was better than that in ecological pond Ⅰ regardless of the impact of phosphorus content. The purification effect of ecological pond Ⅲ fluctuated, the purification effect on DP is relatively significant, and the average removal rate was 94.1%. In addition to the SSM high efficiency coagulation water purification system, the form of phosphorus in the polluted water of Pulin Creek and purified water by ESECR technology was mainly PP, and the percentage of each form in total phosphorus appeared as PP>DTP>DP. Pearson correlation analysis showed that different phosphorus forms were correlated with pH, water temperature and dissolved oxygen (DO) in ESECR treatment system.

During the burial process of fine-grained sedimentary rocks, with the increase of burial depth, a series of changes will occur in their mineral composition, organic matter morphology, pore type and content. In order to deeply reveal the characteristics of these changes, we tested the residual samples of organic matter thermal simulation by scanning electron microscopy, whole rock X-ray diffraction, vitrinite reflectance (R_o), rock pyrolysis and organic carbon content. It was found that the forms of organic matter changed from lump-banded to lump-like when the temperature increased from room temperature to 550 ℃. Clay minerals gradually transformed from lamellar to flocculent; the dissolution of carbonate minerals was dramatic, and the dissolution-precipitation phenomenon occured when the temperature was higher than 500 ℃. With the increase of temperature, the area of organic pores produced by thermal evolution of organic matter increased continuously. At 450-475 ℃, the organic pores reached the maximum, but when the temperature is higher than 475 ℃, the number and pore size of organic pores will decrease. As the clay minerals transformed from montmorillonite to illite-montmorillonite mixed layer and then to illite following the increase of temperature, the intergranular pores of clay minerals increase slowly at first, then increased rapidly and finally tended to be stable. The dissolution pores were mainly produced by feldspar and carbonate minerals, which were closely related to the organic acids produced by the thermal evolution of organic matter. Therefore, the change trend of dissolution pores is basically the same as that of organic matter pores, which increases slowly first and then increases rapidly, and then decreases slowly and tends to be stable. So the temperature range of 450-475 ℃, during which the number of pores and pore size are the largest, is a good reservoir.

An ecological vulnerability evaluation index system based on the evaluation model of "sensitivity-recovery-pressure" (SRP) is constructed. By using spatial geographical data and spatial principal component analysis (SPAC), the ecological vulnerability status, its spatial-temporal distribution characteristics and change trend of Fenhe River Basin in recent 20 years are analyzed, the driving factors of ecological vulnerability change are also discussed by using geodetector. First, The results show that: (1) The overall ecological vulnerability of Fenhe River Basin was at a moderate level, and the vulnerability level in southern area is higher than that in the northern area. The ecological vulnerability first increased then decreased in the time period, indicating that the quality of ecological environment has changed better from 2000 to 2020. (2) The ecological vulnerability level of these zones, such as the plain, hilly and low mountain, was higher than that of the middle mountain zone, and it was at the lowest level in the high-middle mountain zones. During the past 20 years, the ecological vulnerability level of plain, hilly, low mountain and high-middle mountain zones has decreased, while it has rised on middle-middle mountain zones. (3) The driving factors affecting the ecological vulnerability of Fenhe River Basin are of diversity. Among these factors such as nature environment, human activities and landscape pattern, soil organic carbon contents, land use degree and Shannon's evenness index (SHEI) are the main factors contributing to the spatial differentiation of ecological vulnerability. Under a relatively stable policy of ecological protection, the impact of climate change factors on ecological vulnerability has increased gradually.

The unbalanced economic development is a normal state of regional economy, and moderate regional economic differences are conducive to exerting regional comparative advantages. In recent years, the research work on regional economic differences are mostly concentrated in the developed areas such as the central coastal areas, the Yangtze River Delta and the Pearl River Delta, and there are few research results concerning the underdeveloped areas such as Guangxi. Taking 92 counties in Guangxi Zhuang Autonomous Region as the basic research objects, this paper uses the coefficient of variation, theil index and exploratory spatial data analysis to study the spatial and temporal evolution pattern of county agglomeration differences in Guangxi from 2005 to 2020, and explores the causes of this difference by constructing the spatial Durbin model. The results show that: (1) the absolute difference of county economy in Guangxi increased in this period, while the relative difference decreased slightly, and the intra-regional difference was always greater than the inter-regional difference; (2) the economic development of most counties was in an isolated state, low-level counties are clustered, the correlation of economic factors among regions was weak, which presented globally is a low-level equilibrium state; (3) the urbanization level, market scale, fiscal expenditure and investment level promote the county economic differences, while the industrial structure had a negative effect on the economic differences. Therefore, Guangxi needs to persist in agglomeration development to promote the common development of regional economy.

Taking 614 national intangible cultural heritages in Southwest China as the research object, the spatial distribution characteristics and influencing factors of these heritages were analyzed by using the methods of nearest proximity index, kernel density, geographical concentration index,geographical detector and buffer zone analysis. The results show that: (1) There are significant differences in the spatial distribution of intangible cultural heritage types in Southwest China, specifically, more traditional skills and dances, and least traditional sports, recreational arts and acrobatics; The spatial distribution of types show obvious condensation characteristics, among which the heritages of traditional skills and medicine show obvious condensation characteristics, while the heritages of traditional sports, recreational arts and acrobatics tend to be uniform; (2) Southwest intangible cultural heritages presents global feature of "more in the east and less in the west", forming a spatial distribution pattern of "two cores and one belt"; (3) The influencing factors are mainly divided into natural factors, socio-economic factors and historical and cultural factors. Among the natural factors, river system laid the initial pattern, among the socio-economic factors, urbanization had the greatest impact, among the historical and cultural factors, ethnic minorities and historical origins were of great significance.

Studying the level and difference of multi-functional land use from the perspective of different livelihood types is an important way to further promote the integrated development of tourism and land and coordinate the contradiction of land use for peri-urban tourism development. Taking Changsha peri-urban rural tourism destination for case study, based on participatory rural appraisal (PRA), the entropy weight method (EWM), location entropy(LE) ,etc., this paper explores the level of multifunctional land use, dominance and difference characteristics of different livelihood types of farmers in the area of suburban rural tourism destination. The results are as follows: (1) There are significant differences in the level of multifunctional land use for different types of farmers. The level of economic function and ecological function of land use for non-tourism type (NTT) farmers is the highest, and the level of social function of land use for tourism monopoly type(TMT) farmers is the highest. However, the land economic development level and the social security level of NTT farmers is seriously insufficient. (2) Different types of farmers' multifunctional land use have significant difference in synergy and trade-offs of internal function. For NTT: the trade-off conflict between economic function and social function of their land use is the most obvious. For part-time tourism type (PTT),tourism part-time type (TPT): the trade-off conflict between economic function and ecological function of their land use is the most obvious. For TMT: the internal trade-off conflict of tourism land function of their land use is the smallest and the synergy is the best. (3) The dominant functions of land use for different types of farmers are significantly different, which is related to the dominant uses and functional needs of land use. NTT is dominated by resource supply function (1.69), PTT is dominated by economic development function (1.19), TPT is dominated by ecological conservation function (1.06), and TMT is dominated by social security function (2.05). At the end, the paper puts forward specific policy suggestions on the transformation of farmers' multi-functional land use to TMT model and the complementary and coordinated development of land use functions of different livelihood types.