Optimization and Innovation of the Operation Model of Mobile Social E-commerce under AI Empowerment:Taking the Female Community Platform“Little Red Book”as an Example

This article takes the female community platform“Little Red Book”as an example to explore the optimization and innovation of mobile community e-commerce operation mode under Artificial Intelligence(AI)empowerment.Firstly,the relevant concepts were defined,and then the unique attributes of mobile community e-commerce were analyzed.As a typical representative of mobile community e-commerce,Little Red Book introduces the background and characteristics of its platform,analyzes its mobile community operation mode,and focuses on exploring how to establish a mobile community e-commerce platform and effective operation mode under the empowerment of AI technology,to provide some reference and inspiration for the development and operation of Little Red Book and other e-commerce platform enterprises.

Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.

An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

Maximal operators of pseudo-differential operators with rough symbols

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

Impacts of agri-food e-commerce on traditional wholesale industry:Evidence from China

Rapidly expanding studies investigate the effects of e-commerce on company operations in the retail market.However,the interaction between agri-food e-commerce(AEC)and the traditional agri-food wholesale industry(AWI)has not received enough attention in the existing literature.Based on the provincial panel data from 2013 to 2020 in China,this paper examines the effect of AEC on AWI,comprising three dimensions:digitalization(DIGITAL),agrifood e-commerce infrastructure and supporting services(AECI),and agri-food e-commerce economy(AECE).First,AWI and AEC are measured using an entropy-based combination of indicators.The results indicate that for China as a whole,AWI has remained practically unchanged,whereas AEC exhibits a significant rising trend.Second,the findings of the fixed-effect regression reveal that DIGITAL and AECE tend to raise AWI,whereas AECI negatively affects AWI.Third,threshold regression results indicate that AECI tends to diminish AWI with three-stage inhibitory intensity,which manifests as a first increase and then a drop in the inhibition degree.These results suggest that with the introduction of e-commerce for agricultural product circulation,digital development will have catfish effects that tend to stimulate the vitality of the conventional wholesale industry and promote technical progress.Furthermore,the traditional wholesale industry benefits financially from e-commerce even while it diverts part of the traditional wholesale circulation for agricultural products.

Impact of BRICS Trade Facilitation on China's Exports Using Cross-Border E-Commerce

With the rapid growth of the global digital economy, cross-border e-commerce, as an emerging form of trade, has gradually become a powerful engine to promote the development of global trade. BRICS is an important force in the global economy, and the progress of the BRICS countries' trade facilitation level has an important impact on the global trade environment. This paper conducts an in-depth study of the dynamic changes in BRICS trade facilitation from 2013 to 2022, and uses an extended gravity model to analyze the specific impact of this change on China's exports using cross-border e-commerce. The results show that although the BRICS countries have made some progress in trade facilitation, the overall level still needs to be improved, and there are obvious differences among member countries. However, the improvement of trade facilitation among BRICS countries has undoubtedly brought significant positive effects to China's exports using cross-border e-commerce.

THE SCHUR TEST OF COMPACT OPERATORS

Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).

BIG HANKEL OPERATORS ON HARDY SPACES OF STRONGLY PSEUDOCONVEX DOMAINS

In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.

SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).

Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

Predicting Purchasing Behavior on E-Commerce Platforms: A Regression Model Approach for Understanding User Features that Lead to Purchasing

This research introduces a novel approach to improve and optimize the predictive capacity of consumer purchase behaviors on e-commerce platforms. This study presented an introduction to the fundamental concepts of the logistic regression algorithm. In addition, it analyzed user data obtained from an e-commerce platform. The original data were preprocessed, and a consumer purchase prediction model was developed for the e-commerce platform using the logistic regression method. The comparison study used the classic random forest approach, further enhanced by including the K-fold cross-validation method. Evaluation of the accuracy of the model’s classification was conducted using performance indicators that included the accuracy rate, the precision rate, the recall rate, and the F1 score. A visual examination determined the significance of the findings. The findings suggest that employing the logistic regression algorithm to forecast customer purchase behaviors on e-commerce platforms can improve the efficacy of the approach and yield more accurate predictions. This study serves as a valuable resource for improving the precision of forecasting customers’ purchase behaviors on e-commerce platforms. It has significant practical implications for optimizing the operational efficiency of e-commerce platforms.

Research on Current Situation and Legal Regulation of Cosmetics Live Streaming E-commerce in China

Analyze the compatibility between cosmetics and live streaming e-commerce from its own nature,marketing means and supply chain characteristics.According to the prominent problems,sort out the relationship between all parties in the cosmetics live e-commerce industry chain.Combined with the latest regulatory policies of live streaming e-commerce and cosmetics,the responsibilities of different subjects in cosmetics live streaming e-commerce are summarized,and relevant suggestions and countermeasures are put forward for the standardization and development of live streaming e-commerce.Cosmetics brand owners are the first responsible persons for product quality.Anchors,as a mixed identity between intermediary,advertising spokesperson and operator,should bear stricter joint and several liability when recommending products related to consumers’health.If anchors fail to clearly identify themselves in the recommendation process,thus causing consumers to mistake them for the operator of the cosmetics,they should assume the obligations of the operator.

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

How Does E-Commerce Policy Affect Consumption Disparities of Rural Households?-Evidence from China

In the context of China’s ongoing efforts to promote countryside revitalization and facilitate domestic economic circulation,it is of great significance to reduce the consumption disparity among rural households and unleash the consumption potential in the countryside.Based on data from China Family Panel Studies,this paper adopts a staggered difference-in-differences method to assess the impact of the e-commerce to enter rural areas on the consumption disparity among rural households.Findings:the comprehensive demonstration work of promoting e-commerce to enter rural areas has reduced the consumption disparity among rural households through the following mechanisms.Firstly,this policy initiative has mitigated the consumption-inhibiting effect on rural household consumption due to the local market size and external market accessibility by promoting the distribution of consumer goods to villages.Secondly,this policy initiative has also increased the agricultural income of rural households and reduced their consumption disparity by distributing farm produce to cities and enhancing the agricultural income of rural households.Moreover,the work is characterized by inclusive growth and is not susceptible to the“elite capture”phenomenon.