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 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.

Computational Experiments for Complex Social Systems:Integrated Design of Experiment System

Powered by advanced information industry and intelligent technology,more and more complex systems are exhibiting characteristics of the cyber-physical-social systems(CPSS).And human factors have become crucial in the operations of complex social systems.Traditional mechanical analysis and social simulations alone are powerless for analyzing complex social systems.Against this backdrop,computational experiments have emerged as a new method for quantitative analysis of complex social systems by combining social simulation(e.g.,ABM),complexity science,and domain knowledge.However,in the process of applying computational experiments,the construction of experiment system not only considers a large number of artificial society models,but also involves a large amount of data and knowledge.As a result,how to integrate various data,model and knowledge to achieve a running experiment system has become a key challenge.This paper proposes an integrated design framework of computational experiment system,which is composed of four parts:generation of digital subject,generation of digital object,design of operation engine,and construction of experiment system.Finally,this paper outlines a typical case study of coal mine emergency management to verify the validity of the proposed framework.

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.

Optimal scheduling of a township integrated-energy system using the adjustable heat-electricity ratio model

With the expansion and implementation of rural revitalization strategies,there is a constant need for new energy sources for the construction of new townships.Consequently,integrated energy systems with the interconnection and interaction of multiple energy sources are developing rapidly.Biomass energy,a renewable green energy source with low pollution and wide distribution,has significant application potential in integrated energy systems.Considering the application of biomass energy in townships,this study established an integrated biomass energy system and proposed a model to optimize its operation.Lowest economic cost and highest clean energy utilization rate were considered as the objective functions.In addition,a plan was suggested to adjust the heat-electricity ratio based on the characteristics of the combined heat and power of the biomass.Finally,a simulation analysis conducted for a town in China was discussed,demonstrating that the construction of a township integrated-energy system and the use of biomass can significantly reduce operating costs and improve the energy utilization rate.Moreover,by adjusting the heat-electricity ratio,the economic cost was further reduced by 6.70%,whereas the clean energy utilization rate was increased by 5.14%.

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.

A lightweight symmetric image encryption cryptosystem in wavelet domain based on an improved sine map

In the era of big data,the number of images transmitted over the public channel increases exponentially.As a result,it is crucial to devise the efficient and highly secure encryption method to safeguard the sensitive image.In this paper,an improved sine map(ISM)possessing a larger chaotic region,more complex chaotic behavior and greater unpredictability is proposed and extensively tested.Drawing upon the strengths of ISM,we introduce a lightweight symmetric image encryption cryptosystem in wavelet domain(WDLIC).The WDLIC employs selective encryption to strike a satisfactory balance between security and speed.Initially,only the low-frequency-low-frequency component is chosen to encrypt utilizing classic permutation and diffusion.Then leveraging the statistical properties in wavelet domain,Gaussianization operation which opens the minds of encrypting image information in wavelet domain is first proposed and employed to all sub-bands.Simulations and theoretical analysis demonstrate the high speed and the remarkable effectiveness of WDLIC.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.

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).

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.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Market Operation of Energy Storage System in Smart Grid:A Review

As a flexible resource,energy storage plays an increasingly significant role in stabilizing and supporting the power system,while providing auxiliary services.Still,the current high demand for energy storage contrasts with the fuzzy lack of market-oriented mechanisms for energy storage,the principle of market-oriented operation has not been embodied,and there is no unified and systematic analytical framework for the business model.However,the dispatch management model of energy storage in actual power system operation is not clear.Still,the specific scheduling process and energy storage strategy on the source-load-network side could be more specific,and there needs to be a greater understanding of the collaborative scheduling process of the multilevel scheduling center.On this basis,this paper reviews the energy storage operation model and market-based incentive mechanism,For different functional types and installation locations of energy storage within the power system,the operational models and existing policies for energy storage participation in the market that are adapted to multiple operating states are summarized.From the point of view of the actual scheduling and operation management of energy storage in China,an energy storage regulation and operation management model based on“national,provincial,and local”multilevel coordination is proposed,as well as key technologies in the interactive scenarios of source-load,network and storage.

Distributional Chaoticity of the Minimal Subshift of Shift Operators

This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.

Research on a Comprehensive Monitoring System for Tunnel Operation based on the Internet of Things and Artificial Intelligence Identification Technology

This article proposes a comprehensive monitoring system for tunnel operation to address the risks associated with tunnel operations.These risks include safety control risks,increased traffic flow,extreme weather events,and movement of tectonic plates.The proposed system is based on the Internet of Things and artificial intelligence identification technology.The monitoring system will cover various aspects of tunnel operations,such as the slope of the entrance,the structural safety of the cave body,toxic and harmful gases that may appear during operation,excessively high and low-temperature humidity,poor illumination,water leakage or road water accumulation caused by extreme weather,combustion and smoke caused by fires,and more.The system will enable comprehensive monitoring and early warning of fire protection systems,accident vehicles,and overheating vehicles.This will effectively improve safety during tunnel operation.

Study of Axisymmetric Infinite Guide Lined with Locally Reacting Material without Flow Using DtN Operators

The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.

Noether symmetry method for Birkhoffian systems in terms of generalized fractional operators

Compared with the Hamiltonian mechanics and the Lagrangian mechanics,the Birkhoffian mechanics is more general.The Birkhoffian mechanics is discussed on the basis of the generalized fractional operators,which are proposed recently.Therefore,differential equations of motion within generalized fractional operators are established.Then,in order to find the solutions to the differential equations,Noether symmetry,conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated.In the end,two applications are given to illustrate the methods and results.

Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Process Is Described by Integrals with Degenerate Kernels

We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.

Business Ecosystem Strategies of Mobile Network Operators in the 3G Era

This paper applies the perspective of business ecosystem to mobile communications industry,trying to help mobile network operators improve their strategies in the era of the third generation mobile communications(3G).According to the definition of the business ecosystem,the ecosystem structure of mobile network operators is analyzed.As an important hub in the ecosystem,mobile network operators are advised to take a keystone strategy.The key points of the strategy are summarized.Finally,suggestions for Chinese mobile network operators are given based on the analysis.

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.