Study on the spread for modern mathematics in China is the most significant part when reviewing the history of modern mathematics.The propagation of Fourier series in China plays a vital role in this process and the school of functionalism of Zhejiang University was a pioneer. It is recognized that the famous Chen-Hardy-Littlewood theorem is the first sign that modern Chinese mathematics has reached the world-class level. This paper discusses the contribution of the school of functionalism in Zhejiang University to the development of modern mathematics in China from the following aspects: an overview of the research and education of Fourier series in China and the pedagogical context of Chinese Fourier mathematicians. Mathematicians such as Jiangong CHEN, Fuchun WANG, Qingjun LU, Ruiyun XU, Minde CHENG and Fuchen XIANG had published 84 academic papers abroad, 25 papers domestically and one monograph which is related with Fouries series from 1928 to 1950. During this period,the school of functionalism won four academic prizes from the government of the Republic of China.

Congruence in elementary number theory is favored by many scholars. In this paper, using the elementary method, the properties of trigonometric sums and the estimation of Kloosterman sums, we study the distribution of integers and their inverse on short intervals and solve a number theory conjecture problem proposed by professor CAI Tianxin from two different angles. Assume that p is an odd prime number except for 3,5,7, and 13, there is at least one set of integers 1<i,j<p2 which satisfy the congruence i?j≡1?mod?p. It not only shows that the congruence equation has a solution, but also gives a strong asymptotic formula, indicating that the number of solutions is less than M2p+Op12ln2p.

By using the critical point theory, variational methods and the theory of fractional variable exponent Sobolev space, this paper studies the solvability of the boundary value problem of fractional p(x)-Laplacian equation with nonlocal coefficient. When the nonlinearity item is sublinear near zero or local superlinear at infinity, some sufficient condition for the existence of multiple solutions are obtained.

Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H.We call T∈B(H) satisfies the Browder's theorem if σ(T)\σw(T)?π00(T) or σw(T)=σb(T); we call T satisfies the Weyl's theorem if σ(T)\σw(T)=π00(T), where σ(T),?σw(T),?σb(T) denote the spectrum, Weyl spectrum, and Browder spectrum of T, respectively, π00(T)={λ∈iso?σ(T):?0<dimN(T-λI)<∞}. In this note,we explore the Weyl's theorem for operator and its functional, and get a new judgement for the Weyl's theorem. In addition, we consider the spectrum mapping theorem for some new spectrum.

In this paper, we first introduce the notion of D^*-metric space and the related knowledge. Based on the D^*-metric space, we extend the generalized weakly contractive maps related to two kinds of distance control functions (ψ,?) from metric space to the D^*-metric space,and discuss the existence and uniqueness of fixed point under generalized weakly contractive conditions by constructing iterative sequences.We also present several new fixed point theorems. The results enrich the fixed point theory of D^*-metric space.

By introducing some parameters, we construct a non-homogeneous kernel function including hyperbolic functions on the whole plane. In addition, by using the rational fraction expansion of tangent function, a Hilbert-type integral inequality associated with the best possible constant factor and the higher derivatives of tangent function is presented. Furthermore, some meaningful and special results are presented by specializing the parameters with different values as on application.

In this paper, we investigate the moving average processes, which is generated by extended negatively dependent (END) random variables Sequence. By using the Rademacher-Menshov type inequality of END random variables sequence, the limit properties of moment complete convergence and almost everywhere convergence of the maximal partial sums for moving average processes are obtained. END random variables sequence are widely used dependent sequence, our results extend the corresponding results in previous papers.

The development of virtual scene requires a more natural paradigm to meet the needs of users, and the graphical paradigm can be an effective supplement to the natural paradigm. At present, there is little research on the use of graphical paradigm in virtual space, and there is still a depth conflict between the graphical interactive components and the subject of the scene in the application of virtual scene. This article proposes a new interactive paradigm ie. SOMRM paradigm, and takes virtual reality (VR) finding difference scene and augmented reality (AR) Tetris scene as examples. It studies two methods of reducing the depth conflict in virtual scenes by halo blur and changing the distance between components and participants. The accuracy and ease of two methods are compared by analyzing the data of time and deviation needed by the participants to perform interactive tasks such as viewing, grasping and sliding in the virtual scene.The results show that adding halo blur is a better way to reduce the depth conflict in virtual scene.

The calculation of the spatial autocorrelation weight based on spatial distance is the core of the classical spatial interpolation method. However, due to the complex nonlinear relationship between spatial distance and the autocorrelation weight, traditional spatial interpolation methods such as inverse distance weighting (IDW) and the Kriging method have limitations on the accurate weight calculation. In this paper,based on the strong nonlinear fitting ability of neural network, we establish a spatial auto-regressive neural network (SARNN) model by combining neural network and spatial autoregressive method, and realize the accurate calculation of spatial autocorrelation weights. In order to verify the validity and feasibility of the SARNN model, we use two types of simulation data and marine environment data for cross-validation, and compare the accuracy with that of the IDW and Kriging. The results show that the performance SARNN is significantly better than IDW and Kriging, regarding all the statistical indicators such as R², RMSE, MAE and MAPE. At the same time, SARNN predicts the mutation data and extremum more accurately and improves the problems in traditional interpolation method such as low spatial smooth transition, “bull's eye” and sawtooth phenomenon. Therefore, SARNN provides a new idea of spatial interpolation and has a wider application potential.

In this study, the impact analysis of five Fujian-landfall and northward-moving typhoons on Hangzhou are examined based on automatic weather stations data, sounding data and the global forecast system (GFS) data with statistical analysis, composite analysis, comparative analysis and physical diagnostic analysis. The results are summarized as follows. (1) These five typhoons could be divided into two types after landfall. One is northward-moving typhoons that after landing on Fujian province keeps moving over 30°N. The other is the typhoon Meranti (1010) which weakened to low pressure as soon as it arrived southern Zhejiang province. The northward-moving type brought both gale and heavy rainfall to Hangzhou while typhoon Meranti (1010) mainly produced heavy rainfall. (2) It will have significant impact on Hangzhou when the center of northward-moving typhoon is located in the central part of Fujian province ,as the south-westerly and southerly low-level jets are significant and Hangzhou is located within the first quadrant of the typhoon circulation which is the junction of these two jets, it is beneficial for the formation of the gale and heavy rainfall. On the contrast, it will cause great influence on Hangzhou when typhoon Meranti (1010) has weakened into a tropical low. The typhoon inverted trough has an obvious combination with the cold air of the westerly belt. A southerly jet forms between the circulation of the tropical low and the subtropical high, which is favorable for the formation of the heavy rainfall. (3) These two types of typhoons have some similar indexes and structure. However, the northward-moving type contains richer saturated water vapor and more suitable dynamic condition than typhoon Meranti (1010). Besides, typhoon Meranti (1010) reserves more available potential energy owing to cold air enhancing the baroclinicity.

The consistency of horizontal wind fields based on the data from the two observation devices,namely the wind profile radar of Xiaoshan station in Zhejiang province from 2015 to 2018, and the L-band up-air meteorological sounding data of Hangzhou station was evaluated . The influence of the different data source and location of the two devices and the non-directional drift of the sounding balloon on the evaluation result is reduced by selecting the profile of the drift of the balloon to the wind profile radar. The results show that there is no significant difference between the wind profile radar and L-band radar sounding in the absence of precipitation at the height of 1~55 km. The correlation coefficient of the two observed u component in the height range is 0.95, the mean absolute bias and root mean square error are 1.47 and 2.29 m·s^-1 respectively, and the three statistics of the v component are 0.87, 1.52 and 2.12 m·s^-1 respectively. However, the correlation coefficient of the two observed u component and v component under 1 km is about 0.5, and the root mean square error reaches 2~8 m·s^-1. Considering the instability of the near-stratigraphic wind and the sampling scheme, these results are less reliable. Besides, there is no significant difference between the statistical results with or without precipitation.

Studies about natural gravels are significant for understanding of regional tectonics and climate change, and especially the gravel size is an important parameter in geology. To provide users with a more comprehensive understanding and application background of gravel statistical methods, we summarize two types of gravel statistical methods (surface gravel statistics methods and stratigraphic gravel statistics methods) with the operation of gravel statistical methods, sampling process, sample size, error analysis, and applicable conditions. The surface gravel statistics methods usually include the Wolman pebble count and area sampling. The Wolman pebble count emphasizes random sampling and is more suitable for gravel diameter larger than 2 mm to study the downstream fining of sediment in gravel-bed rivers. The area sampling is mostly used to explore natural phenomena of the gravel-sand transition in rivers and the characteristic of aquatic habitats due to its suitable gravel size range up to fine-grained sand. In contrast, the stratigraphic gravel statistics methods emphasize the stratification of gravel and apply the volumetric sampling. Previous researchers developed several kinds of mesh sieves based on corresponding research purposes. And the gravel size range can also reach to fine sand, which is most suitable for studying the response of gravel grain sizes to climate and tectonics, streambed monitoring and sediment transport analysis. This comprehensive study of the gravel statistical methods indicates that the choice of different methods largely depends on the research purpose and field working conditions which suggests us to make flexible selection based on specific situations.

In order to explore the impact of land use degree on ecosystem service value (ESV) and its change due to Guanzhong plain urban agglomeration,ESV assessment and spatial-temporal analysis of Guanzhong plain urban agglomeration are conducted by equivalent factor method, hot spot analysis method and sensitivity index method, based on land use data of five periods from 1995 to 2015. The results show that the ESV in Guanzhong plain urban agglomeration area has dropped by 4.959 billion yuan in the past 20 years; among the types of ecosystem services, regulation services play a prominent role,in particular hydrological regulation plays a dominant role; the distribution of cold spots and hot spots of ESV has obvious regional characteristics. The main urban area of the city is mainly the ESV cold point cluster area, while Qinba mountain area, forest land in the east of Shanxi province and main rivers such as the Yellow River and Wei River are the ESV hot spot cluster area.The forest land, water area and cropland are of great significance for the change of ESV in the studied area. The long-term macro-rule of ESV in the concerned area is obtained, which are expected to provide theoretical support for regional ecological environment protection, compensation and urban development planning in Guanzhong plain urban agglomeration in the future.

This study focuses on analysing the effect of different combinations of mangrove plants on soil restoration using field investigation,sampling,and laboratory analysis methods.Quanzhou bay degraded coastal wetland are examined. Results show that the enzyme activity of phosphatase and urease before restoration at degraded wetland are in the range of 8.78~17.72 μg/(g?24 h) and 45.86~80.12 μg/(g?24 h) ,respectively,these numbers increase to 10.21~14.22 μg/(g?24 h) and 85.83~102.22 μg/(g?24 h) after restoration.Concretely on different plant combinations restoration,Kandelia obovata+Aegiceras corniculatum+Rhizophora stylosa result in the most substantial boost in soil enzyme activity.Kandelia obovata+Aegiceras corniculatum+Avicennia marina makes the phosphatase less active,while enhancing urease activity.Kandelia obovata+Aegiceras corniculatum+Bruguiera gymnorrhiza does not make a significant difference in enzyme activity.

The catalysis of water molecules and the chiral transition of two stable configurations of alanine (Ala) and Ca²⁺ complexes in gas phase have been studied using the M06 method based on density functional theory. The study shows that the Ala_1·Ca²⁺ chiral transition has two pathways a and b. In pathway a, α-H is transferred merely using carbonyl O atom as a bridge. In pathway b, the proton on the amino group transfers to α-C from inside paper after α-H is transferred to carbonyl O atom. The Ala_2·Ca²⁺ chiral transition has four pathways a, b, c and d. In pathway a, α-H is transferred merely using carbonyl O atom as a bridge after the transition of proton on the carboxyl group. In pathway b, α-H is transferred to carbonyl O atom and then proton transfers from the amino group N atom to α-C after the transition of proton on the carboxyl group. In pathway c, α-H is transferred to the amino group N atom after the coordination bond between calcium and nitrogen is broken. In pathway d, the coordination bond between calcium and nitrogen is broken and Ala_2·Ca²⁺ is isomerized to Ala_1·Ca²⁺, then Ala_1·Ca²⁺ achieves the chiral transition. The potential energy surface calculation shows that the dominant pathway of the chiral transition of Ala_1·Ca²⁺ is pathway a, and the total energy barrier is 134.8 kJ·mol^－1. The dominant pathway of the chiral transition of Ala_2·Ca²⁺ is pathway d, and the total energy barrier is 235.3 kJ·mol^－1. The catalysis of water molecules then reduces them to 40.8 kJ·mol^－1 and 141.3 kJ·mol^－1 respectively. The results show that Ca²⁺ has a catalytic effect on the chiral transition of Ala, and water molecule has an excellent catalytic effect on the chiral transition of Ala and Ca²⁺ complexes.

In order to improve the accuracy of pure premium rate making of quality insurance for large-scale public building on the basis of literature analysis, this paper studies the influencing factors of quality loss of large-scale public building projects, and extracts 11 insurance premium rate factors. Based on the frequency-severity method and the distribution assumptions of Poisson distribution, Negative Binomial distribution, Gamma distribution and Inverse Gauss distribution, 8 quality insurance pure premium rate-making models are established by using generalized linear model and generalized additive model on the basis of 46 large-scale public buildings data sets completed in 1993—2016 in China, then the best model is selected and its rationality is verified. The results show that the model is suitable for the pure premium rate making of quality insurance for large-scale public building projects.