A Fixed Point Approach to the Fuzzy Stability of a Mixed Type Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.

Landslide prediction based on improved principal component analysis and mixed kernel function least squares support vector regression model

Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

Generalizations of mixed weighted power mean inequality

Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequslity was derived in this paper. As its applications, some separations of other inequalities were given.

More general results on mixed extreme value distributions

The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.

Recognizing mixed urban functions from human activities using representation learning methods

When various urban functions are integrated into one location,they form a mixture of functions.The emerging big data promote an alternative way to identify mixed functions.However,current methods are largely unable to extract deep features in these data,resulting in low accuracy.In this study,we focused on recognizing mixed urban functions from the perspective of human activities,which are essential indicators of functional areas in a city.We proposed a framework to comprehensively extract deep features of human activities in big data,including activity dynamics,mobility interactions,and activity semantics,through representation learning methods.Then,integrating these features,we employed fuzzy clustering to identify the mixture of urban functions.We conducted a case study using taxiflow and social media data in Beijing,China,in whichfive urban functions and their correlations with land use were recognized.The mixture degree of urban functions in each location was revealed,which had a negative correlation with taxi trip distance.The results confirmed the advantages of our method in understanding mixed urban functions by employing various representation learning methods to comprehensively depict human activities.This study has important implications for urban planners in understanding urban systems and developing better strategies.

Charge transfer and orbital reconstruction of non‐noble transition metal single‐atoms anchored on Ti_(2)CT_(x)‐MXenes for highly selective CO_(2) electrochemical reduction

Inspired by MXene nanosheets and their regulation of surface functional groups,a series of Ti_(2)C‐based single‐atom electrocatalysts(TM@Ti_(2)CT_(x),TM=V,Cr,Mn,Fe,Co,and Ni)with two dif‐ferent functional groups(T=–O and–S)was designed.The CO_(2)RR catalytic performance was stud‐ied using well‐defined ab initio calculations.Our results show that the CO_(2) molecule can be more readily activated on TM@Ti_(2)CO_(2) than the TM@Ti_(2)CS_(2) surface.Bader charge analysis reveals that the Ti_(2)CO_(2) substrate is involved in the adsorption reaction,and enough electrons are injected into the 2π*u orbital of CO_(2),leading to a V‐shaped CO_(2) molecular configuration and partial negative charge distribution.The V‐shaped CO_(2) further reduces the difficulty of the first hydrogenation reac‐tion step.The calculatedΔG of the first hydrogenation reaction on TM@Ti_(2)CO_(2) was significantly lower than that of the TM@Ti_(2)CS_(2) counterpart.However,the subsequent CO_(2) reduction pathways show that the UL of the potential determining step on TM@Ti_(2)CS_(2) is smaller than that of TM@Ti_(2)CO_(2).Combining the advantages of both TM@Ti_(2)CS_(2) and TM@Ti_(2)CO_(2),we designed a mixed functional group surface with–O and–S to anchor TM atoms.The results show that Cr atoms an‐chored on the surface of mixed functional groups exhibit high catalytic activity for the selective production of CH4.This study opens an exciting new avenue for the rational design of highly selec‐tive MXene‐based single‐atom CO_(2)RR electrocatalysts.

Transport Integrated Development(TID) and Practices in Chongqing Municipality

With the development of rail transit, transport integrated development(TID) has become a key issue in land development and utilization. This paper analyzed core theories and design principles of TID, analyzed the successful experience of Kowloon City in Hong Kong, compared success and failure of some TID projects in Chongqing Municipality, i.e. Nanping, Chaotianmen, Lianglukou and Guanyinqiao, and fully demonstrated that TID could promote the internal update and development of the city. TID concepts for Chongqing were proposed as "rail transit stations should ensure mixed high-benefit land uses with multiple functions, public open spaces with a certain ratio, a high-efficiency pedestrian system with comfortable environment, high-efficiency seamless transfer and connection modes.

Extreme value distributions of mixing two sequences with different MDA＇s

Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.

Parameter Estimation of a Mixed Production Function Model Based on Improved Firefly Algorithm and Model Application

In the analysis on economic growth factors, researchers usually use the production function model to calculate and measure influencing factors’ contribution rates to economic growth. Common production functions include the CD(Cobb-Douglas) production function, the CES(Constant Elasticity of Substitution) production function, the VES(Variable Elasticity of Substitution) production function,and so on. In consideration of the diversity and complementarity of models, the paper combines the CD production function with the CES production function and then proposes a mixed production function.With regard to the parameter estimation of model, the paper gives an improved firefly algorithm with the high precision and a fast rate of convergence. With regard to the calculation of factors’ contribution rates, traditional methods generally have big errors and are not applicable to complicated models, so the paper offers a new method which can calculate contribution rates scientifically. Finally, the paper calculates the contribution rates of factors affecting Chinese economic growth and gets a good result.

Photon statistics of pulse-pumped four-wave mixing in fiber with weak signal injection

We study the photon statistics of pulse-pumped four-wave mixing in fibers with weak coherent signal injection by measuring the intensity correlation functions of individual signal and idler fields. The experimental results show that the intensity correlation function of individual signal（idler） field g_（s（i））^（2） decreases with the intensity of signal injection. After applying narrow band filter in signal（idler） band, the value of g_（s（i））^（2） decreases from 1.9 ± 0.02（1.9 ± 0.02） to 1.03 ± 0.02（1.05 ± 0.02） when the intensity of signal injection varies from 0 to 120 photons/pulse. The results indicate that the photon statistics changes from Bose–Einstein distribution to Poisson distribution. We calculate the intensity correlation functions by using the multi-mode theory of four-wave mixing in fibers. The theoretical curves well fit the experimental results.Our investigation will be useful for mitigating the crosstalk between quantum and classical channels in a dense wavelength division multiplexing network.

A class of not max-stable extreme value distributions

The sequences {Zi , 1≤i≤n}, n≥1 have multi-nomial distribution among i.i.d. random variables {X1, , i≥1}, {X2, , ,n i i i≥1}, …, {Xm , i≥1}. The extreme value distribution GZ(x) of this particular triangular array of i.i.d. random variables Z1, , Z2, , …, ,i n n r ?1 Zn is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) GZ (x) = ,n ∏Φα Ai(x)×Φαr (x); i i=1 r ?1 r?1 ii) GZ (x) = ∏Ψα Ai(x)×Ψαr (x); iii) GZ (x) = ∏Λ Ai(λix)×Λ(x), r≥2, 0<α1≤α2≤…≤αr and λi∈(0,1] for i, 1≤i≤r?1 which occur if i i=1 i=1 Fj, …, Fm belong to the same MDA.

Optimal Recovery on the Classes of Functions with Bounded Mixed Derivative

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.

Prediction of a maximum pull-out load of anchor bolts using an optimal combination model

The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.

Improved deep mixed kernel randomized network for wind speed prediction

Forecasting wind speed is an extremely complicated and challenging problem due to its chaotic nature and its dependence on several atmospheric conditions.Although there are several intelligent techniques in the literature for wind speed prediction,their accuracies are not yet very reliable.Therefore,in this paper,a new hybrid intelligent technique named the deep mixed kernel random vector functional-link network auto-encoder(AE)is proposed for wind speed prediction.The proposed method eliminates manual tuning of hidden nodes with random weights and biases,providing prediction model generalization and representation learning.This reduces reconstruction error due to the exact inversion of the kernel matrix,unlike the pseudo-inverse in a random vector functional-link network,and short-ens the execution time.Furthermore,the presence of a direct link from the input to the output reduces the complexity of the prediction model and improves the prediction accuracy.The kernel parameters and coefficients of the mixed kernel system are optimized using a new chaotic sine–cosine Levy flight optimization technique.The lowest errors in terms of mean absolute error(0.4139),mean absolute percentage error(4.0081),root mean square error(0.4843),standard deviation error(1.1431)and index of agreement(0.9733)prove the efficiency of the proposed model in comparison with other deep learning models such as deep AEs,deep kernel extreme learning ma-chine AEs,deep kernel random vector functional-link network AEs,benchmark models such as least square support vector machine,autoregressive integrated moving average,extreme learning machines and their hybrid models along with different state-of-the-art methods.

On a Jensen-cubic Functional Equation and Its Hyers-Ulam Stability

In this paper,we obtain the general solution and stability of the Jensen-cubic functional equation f（（x1＋x2）/2,2y1＋y2）＋f（（x1＋x2）/2,2（y1-y2）） = f（x1,y1 ＋y2）＋f（x1,y1-y2）＋6f（x1,y1＋ f（x2,y1y2）＋f（x2,y1-y2）＋6f（x2,y1）.

Critical assessment of three kinds of activity coefficients of carbon and related mixing thermodynamic functions of Fe-C binary melts based on atom-molecule coexistence theory

Raoultian activity coefficients γ0c of C in infinitely dilute Fe-C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations Nc of C in Fe-C binary melts by the developed AMCT-Ni model based on the atom-molecule coexistence theory （AMCT）. The obtained expression of γ0c by the developed AMCT-Ni model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients γc,f%,c, andfH,c of C coupled with activity aR,C or a%,c or aH,c have been obtained by the developed AMCT-Ni model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients ec, ec, and hcc related to γc f%,c, and fH,c are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as AmixHm,Fe-C, △mix-Sm,Fe-C, and △mixGm,Fe-C of Fe-C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.

A Comparative Study on the Measurement Methods of Urban Mixed Land Use

The study aims at exploring the applicability and limitations of domestic and foreign methods for measuring the function mixing of urban land use,and sorting out various classic measurement methods according to the logic of “conceptual reflection–characteristics comparison–limitation analysis.” The study shows that:① the connotation and types of mixed land use functions are still controversial at home and abroad;② there is a lack of research on measurement methods in China;③ for medium and micro-scale planning,current measurement methods cannot fully reflect the differences in the degree of mixing caused by the planar and three-dimensional layout of building functions within the grid;④ the measurement methods for refined planning governance should improve the measurement model in terms of the number of functional types and the mixed layout of various functions in the horizontal and vertical directions at the medium and micro-scales,and improve its accuracy of the measurement results of a single grid and the whole area.

On the Mixed Minus Domination in Graphs

Let G=(V,E)be a graph,for an element x∈V∪E,the open total neighborhood of x is denoted by N_(t)(x)={y|y is adjacent to x or y is incident with x,y∈V∪E},and Nt[x]=Nt(x)∪{x}is the closed one.A function f:V(G)∪E(G)→{−1,0,1}is said to be a mixed minus domination function(TMDF)of G if∑_(y∈Nt[x])f(y)≥1 holds for all x∈V(G)∪E(G).The mixed minus domination numberγ′_(tm)(G)of G is defined as γ′_(tm)(G)=min{∑x∈V∪E f(x)|f is a TMDF of G.In this paper,we obtain some lower bounds of the mixed minus domination number of G and give the exact values ofγ′_(tm)(G)when G is a cycle or a path.

Establishing the role of detoxifying enzymes in field-evolved resistance to various insecticides in the brown planthopper （Nilaparvata lugens） in South India

The brown planthopper （BPH）, Nilaparvata lugens （Stal）, is one of the major pests of rice throughout Asia. Extensive use of insecticides for suppressing N. lugens has resulted in the development of insecticide resistance leading to frequent control failures in the field. The aim of the present study was to evaluate resistance in the field populations of N. lugens from major rice growing states of South India to various insecticides. We also determined the activity of detoxifying enzymes （esterases [ESTs], glutathione S- transferases [GSTs], and mixed-fimction oxidases [MFOs]）. Moderate levels of resistance were detected in the field populations to acephate, thiamethoxam and buprofezin （resistance factors 1.05-20.92 fold, 4.52-14.99 fold, and 1.00-18.09 fold, respectively） as compared with susceptible strain while there were low levels of resistance to imidacloprid （resistance factor 1.23-6.70 fold） and complete sensitivity to etofenoprox （resistance factor 1.05- 1.66 fold）. EST activities in the field populations were 1.06 to 3.09 times higher than the susceptible strain while for GST and MFO the ratios varied from 1.29 to 3.41 and 1.03 to 1.76, respectively. The EST activity was found to be correlated to acephate resistance （r = 0.999, P ≥ 0.001）. The high selection pressure of organophosphate, neonicotinoid, and insect growth regulator （IGR） in the field is likely to be contributing for resistance in BPH to multiple insecticides, leading to control failures. The results obtained will be beneficial to IPM recommendations for the use of effective insecticides against BPH.