Pythagorean fuzzy set (PFS) is an extension of traditional intuitionistic fuzzy set (IFS). It can deal with decision-making problems with multi-attribute information in a wider area. In this paper, we first point out errors in the ranking criterion of Pythagorean fuzzy number (PFN) proposed in a paper, and analyze the reasons that cause these errors through the derivation of reliable information (accuracy function). Then, we propose a new score function through the curved trapezoidal area (CTA) corresponding to the reliable information, which provides a ranking criterion of PFN.The basic properties of the score function are discussed. Finally, we show an example indicating the effectiveness and advantage of the new ranking method.

In this paper, the asymptotic behavior of solutions for the abstract evolution equations with fading memory and nonlinear damping in the time-dependent space is discussed. As an application of theory of process on time-dependent space, the existence of time-dependent attractors in E_t^{\theta } is proved by using contractive function method and more detailed estimates.

We study the Liouville theorem for steady Q-tensor system of liquid crystal in R³. Assuming that u\in L^{\frac{\mathrm{9}}{\mathrm{2}},\mathrm{\infty }}({\mathrm{R}}^{\mathrm{3}})?\stackrel{·}{H^{\mathrm{1}}}({\mathrm{R}}^{\mathrm{3}}) and \mathit{Q}\in H^{\mathrm{2}}({\mathrm{R}}^{\mathrm{3}}), we show that the steady system admits only trivial solution u=0, Q =0.

By defining several parameters, a half-discrete kernel function including its homogeneous and non-homogeneous forms is constructed. With the help of infinite series representation of tangent function and some techniques of analysis, a half-discrete Hilbert-type inequality with the constant factor expressed by cotangent function is established, and to prove that |\alpha {|}^{-\frac{\mathrm{1}}{q}}|\beta {|}^{-\frac{\mathrm{1}}{p}}\frac{\mathrm{\pi }}{\gamma }\left[\mathrm{\Phi }\left(\frac{\gamma \mathrm{\pi }}{{\lambda }_{\mathrm{1}}}\right)-\mathrm{\Phi }\left(\frac{\gamma \mathrm{\pi }}{{\lambda }_{\mathrm{2}}}\right)\right] is the optimal constant factor. In addition, by assigning the parameters different values, some special homogeneous and non-homogeneous Hilbert-type inequalities are established.

The problem of testing the change point in trend for a class of fractional Brownian motion with Hurst exponent is studied, and a posterior testing method is proposed which firstly makes first-order difference to the observation sequence and then constructs Wilcoxon rank statistics based on the difference sequence for testing. Under the null hypothesis, it is proved that the limit distribution of the test statistic is a functional of the standard fractional Brownian motion and the critical values of the test statistic are given. The numerical simulation results show that the test method proposed in this paper can control the empirical size well except for the case where the Hurst value is too large, and the empirical power can almost be close to 1 following the increase of sample size. Moreover, the method is robust to the intercept change point and variance change point when the sample size is large. Finally, a set of monthly temperature data in the northern hemisphere is analyzed, it is found that there is no change point in trend.

Contradictory equations often appear in the predictions of housing price, the number of shared bike rentals, air pollution and other problems. It is of important theoretical significance and practical application value to conduct research on the related numerical method. When the number of contradictory equations is huge, it is too difficult to use the traditional least square method to solve the problem due to the accumulation of errors. In view of this, this paper adopts the least square support vector machine (LS-SVM) algorithm, which is suitable for machine learning of big data process, to solve the huge contradictory equations, and applies the algorithm to problems with practical application background. Experimental results show that the linear, nonlinear, univariate and multivariable contradictory equations can be solved numerically, the change of data type and data volume does not affect the results much, and the appropriate model can be built to obtain high accuracy results as long as the appropriate parameters are selected.

As an important form of expressing the relationship among entities, graph networks have been widely used in data analysis, relational reasoning, and information services. For these applications, how to reasonably represent network characteristic information is the primary task of network analysis research. Graph embedding technology solves the problem of how to efficiently and reasonably map massive, heterogeneous, and complex high-dimensional graph data to low-dimensional vector space while still retaining the original data feature information. This paper aims to survey the algorithm and research progress of graph embedding in recent years, analyze the development status of this field, and explore the direction for subsequent research. First, it reviews the principle and basic theory of graph embedding technology, then systematically investigates the current mainstream graph embedding algorithms, including graph embedding approaches based respectively on dimensionality reduction, matrix decomposition,network topology,neural network, generative adversarial network, and hypergraph. Then we show the application scenarios of graph embedding technology and introduce the commonly used test data sets and evaluation criteria. Finally, we highlight the future research trends and directions of graph embedding, such as dynamic graph embedding, graph embedding scalability and interpretability.

In order to take prompt and effective response to environmental emergencies caused by benzene leakage, the method of generating emergency plan based on case-based reasoning and emergency response effect is studied. Firstly, based on the random forest algorithm and expert knowledge, a method of calculating weight is constructed to retrieve all the historical similar cases. The similar case set is then obtained. Secondly we develop a system to evaluate the emergency response effect of each similar case. Thirdly we introduce an adaptive group consensus adjustment algorithm to get the group evaluation opinions. The comprehensive evaluation value of each response plan is obtained by jointly accounting for the case similarity and disposal effect, based on which the optimal scheme can be generated. An example is used to illustrate the feasibility and effectiveness of the proposed method.

This paper presents a new algorithm for resource prediction based on machine learning model V-TGRU in private cloud computing environment. The algorithm makes statistics of historical records and combines the prior resource usage of different tasks under the current workload, at the same time, considering the workload characteristics, host characteristics, the affinity between tasks in the same resource pool and other factors. The multi factor data matrix is further standardized and coded. The standardized coded data are modeled by V-TGRU to dynamically predict the resource occupation of multi tasks, and carry out multi-objective task optimal scheduling. Experimental results show that this method can effectively complete the pre-judgment and selection of resources, reduce the scheduling time and times, save cloud resources and bandwidth, and ensure the stable operation of application tasks.

The resonant tunneling diode (RTD) programmable logic gate is a threshold logic circuit, which is composed of the monostable-bistable transition logic element (MOBILE) and positive and negative input branches. Since the three-layer network structure in the binary neuron model can be used to realize the threshold function, an realization algorithm of n-variable functions based on RTD programmable logic gate is proposed through the three-layer network structure. According to the order of the Hamming distance from large to small, the algorithm searches for the optimal input vector and uses the theorem 1 or theorem 2 to generate hidden layer functions. By judging the value of transformation times, the true and false of the input vector and the weight of the hidden layer function can be determined. The accuracy of the algorithm is improved by defining the optimal input vector and the transformation time. And due to the use of the theorem 2, the circuit designed by the algorithm is also more simple.

To solve the problems in the conventional thermal heating synthesis of isoquinoline-based ionic liquids, an ultrasound-assisted synthesis of isoquinoline-based ionic liquids was developed. The comparative study of the quaternization process of isoquinoline proved that the method has apparent advantages over conventional thermal heating, i.e., ecofriendly nature, higher yield, and shorter reaction time. The ultrasonic method was then extended to the anion exchange reaction. The results demonstrated that the use of ultrasound irradiation efficiently promoted the anion-exchange reaction of isoquinolinium bromides with simple anions [N(CF₃SO₂)₂]^- and [PF₆]^-. It was also found that the anion-exchange reactions of isoquinolinium bromides with complex 2,4-dichlorophenoxyacetic acid anion were realized under ultrasonic conditions, which could not be achieved under the conventional heating method. The structure characterization, thermal behavior, and solubility of the obtained ionic liquids were investigated and discussed. All ionic liquids exhibited good thermal stability. This article thus provides a rapid and efficient method for the establishment of a multifunctionalized ionic liquids library.

To control the amount of trihalomethane (THMs) in drinking water, this study employs activated carbon as adsorbent to adsorb THMs. Experimental results show that coconut shell activated carbon ACL₁ has higher equilibrium adsorption capacity for THMs. The static adsorption test showed that activated carbon ACL₁ presented higher adsorption efficiency for THMs within 1 hour, and reached adsorption equilibrium within 4 h. It was found that, the temperature had little effect on the adsorption of THMs by activated carbon within the range of 27?36 ℃; When the initial concentration of THMs was twice the limit value of national standard, the removal rate of THMs was higher than 90%. The best adsorption effect of coconut shell activated carbon ACL₁ was on CHCl₃, followed by CHCl₂Br, CHClBr₂ and CHBr₃. The results of dynamic adsorption test showed that when the influent concentration of THMs were 200 μg·L^-1, the removal efficiency of THMs by the advanced treatment process meet the requirements of sanitary standard for drinking water (GB5749-2006). The adsorption effect of CHCl₃, CHCl₂Br, CHClBr₂ and CHBr₃ was consistent with the static adsorption test. The maximum adsorption time was 8.1, 15.3, 15.6 and 16.5 h, respectively.

The Shaanxi-Gansu-Ningxia Revolutionary Region is a key ecological management area in the Loess Plateau and the upper and middle reaches of the Yellow River. As an important ecological barrier area, its ecological governance is of great significance. Based on the improved equivalent factor method, geographic detectors and geographically weighted regression (GWR) models, this research choose Shaanxi-Gansu-Ningxia Revolutionary Region as the research area and analyzed the ESV changes, influencing factors and dominant factors of ESV of each county from 1995 to 2018. The main conclusions are as follows: (1) From 1995 to 2018, the ecosystem service value (ESV) of this region showed a characteristics of first decreasing and then rising, but the overall trend is increasing. Among them, the forest land and grassland contributed more to the ESV of the region; (2) The spatial feature of ESV level conversion presents obvious two extremes, low-level and high-level ESV regions are significantly expanding and the area of sub-high regions is significantly reduced; (3) The main factors leading to the spatial differentiation of ESV are land cover, population density and reclamation coefficient, and their spatial explanatory power exceed to 0.378 0. The interaction and synergy among natural, social and economic factors has enhanced the effects on ESV in the region; (4) The impact of each dominant factor on ESV shows spatial heterogeneity. Among them, the impact of land cover degree and reclamation coefficient decreases from east to west, while the impact of per capita GDP and population density decreases from west to east.

Based on the land use data in Zhejiang province of 8 periods from 1980 to 2020, this study analyzed the water system spatiotemporal pattern, water surface ratio, transformation trend, landscape pattern and other characteristics in different periods of Zhejiang province, trying to reveal the driving factors of these changes. The results show that: (1) the total water area of Zhejiang province tends to rise, the area of rivers and beaches tend to decrease, while the area of lakes, reservoirs, ponds and tidal flats tend to increase. The transfer of water system was concentrated in rivers, lakes and coastal side. (2) The water landscape pattern index of Zhejiang province increase by MPS, NP, LST, FRA, CCONTAG, and decrease by PD, ED, LPI, COHESION and AI, reflecting the fragmentation, dispersion and complexity of water landscape. (3) The area of water system shows different pattern in different cities, in particular, the area of rivers, reservoirs ponds in Hangzhou is the largest, the area of lakes in Jiaxing and Huzhou is the largest, the area of tidal flats in Ningbo is the largest, the area of beaches in Shaoxing is the largest. The water system of each basin mainly consists of reservoirs and ponds, and their area were increased during these periods, while the area of other land types changed little. (4) The water area system of Zhejiang province was closely related to human activities (GDP, total output value of agriculture, forestry, animal husbandry and fishery, population density), while the influence of natural factors on water area was relatively stable with the influence of annual precipitation greater than that of annual temperature.