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.

SHARP MORREY REGULARITY THEORY FOR A FOURTH ORDER GEOMETRICAL EQUATION

This paper is a continuation of recent work by Guo-Xiang-Zheng[10].We deduce the sharp Morrey regularity theory for weak solutions to the fourth order nonhomogeneous Lamm-Rivière equation △^{2}u=△(V▽u)+div(w▽u)+(▽ω+F)·▽u+f in B^(4),under the smallest regularity assumptions of V,ω,ω,F,where f belongs to some Morrey spaces.This work was motivated by many geometrical problems such as the flow of biharmonic mappings.Our results deepens the Lp type regularity theory of[10],and generalizes the work of Du,Kang and Wang[4]on a second order problem to our fourth order problems.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network

The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model(FDTM)in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network(LM-NN)technique.The fractional dengue transmission model(FDTM)consists of 12 compartments.The human population is divided into four compartments;susceptible humans(S_(h)),exposed humans(E_(h)),infectious humans(I_(h)),and recovered humans(R_(h)).Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments:aquatic(eggs,larvae,pupae),susceptible,exposed,and infectious.We investigated three different cases of vertical transmission probability(η),namely when Wolbachia-free mosquitoes persist only(η=0.6),when both types of mosquitoes persist(η=0.8),and when Wolbachia-carrying mosquitoes persist only(η=1).The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives(α=0.4,0.6,0.8).LM-NN approach includes a training,validation,and testing procedure to minimize the mean square error(MSE)values using the reference dataset(obtained by solving the model using the Adams-Bashforth-Moulton method(ABM).The distribution of data is 80% data for training,10% for validation,and,10% for testing purpose)results.A comprehensive investigation is accessible to observe the competence,precision,capacity,and efficiency of the suggested LM-NN approach by executing the MSE,state transitions findings,and regression analysis.The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures,which achieves a precision of up to 10^(-4).

Image Splicing Forgery Detection Using Feature-Based of Sonine Functions and Deep Features

The growing prevalence of fake images on the Internet and social media makes image integrity verification a crucial research topic.One of the most popular methods for manipulating digital images is image splicing,which involves copying a specific area from one image and pasting it into another.Attempts were made to mitigate the effects of image splicing,which continues to be a significant research challenge.This study proposes a new splicing detectionmodel,combining Sonine functions-derived convex-based features and deep features.Two stages make up the proposed method.The first step entails feature extraction,then classification using the“support vector machine”(SVM)to differentiate authentic and spliced images.The proposed Sonine functions-based feature extraction model reveals the spliced texture details by extracting some clues about the probability of image pixels.The proposed model achieved an accuracy of 98.93% when tested with the CASIA V2.0 dataset“Chinese Academy of Sciences,Institute of Automation”which is a publicly available dataset for forgery classification.The experimental results show that,for image splicing forgery detection,the proposed Sonine functions-derived convex-based features and deep features outperform state-of-the-art techniques in terms of accuracy,precision,and recall.Overall,the obtained detection accuracy attests to the benefit of using the Sonine functions alongside deep feature representations.Finding the regions or locations where image tampering has taken place is limited by the study.Future research will need to look into advanced image analysis techniques that can offer a higher degree of accuracy in identifying and localizing tampering regions.

UNIQUENESS OF INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION BY PHASELESS FAR FIELD PATTERN

In this paper,we establish the unique determination result for inverse acoustic scattering of a penetrable obstacle with a general conductive boundary condition by using phaseless far field data at a fixed frequency.It is well-known that the modulus of the far field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field,so it is impossible to reconstruct the location of the underlying scatterers.Based on some new research results on the impenetrable obstacle and inhomogeneous isotropic medium,we consider different types of superpositions of incident waves to break the translation invariance property.

Image Splicing Detection Using Generalized Whittaker Function Descriptor

Image forgery is a crucial part of the transmission of misinformation,which may be illegal in some jurisdictions.The powerful image editing software has made it nearly impossible to detect altered images with the naked eye.Images must be protected against attempts to manipulate them.Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications.Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images.Because image tampering detection targets processing techniques such as object removal or addition,identifying altered images remains a major challenge in research.In this study,a novel image texture feature extraction model based on the generalized k-symbolWhittaker function(GKSWF)is proposed for better image forgery detection.The proposed method is divided into two stages.The first stage involves feature extraction using the proposed GKSWF model,followed by classification using the“support vector machine”(SVM)to distinguish between authentic and manipulated images.Each extracted feature from an input image is saved in the features database for use in image splicing detection.The proposed GKSWF as a feature extraction model is intended to extract clues of tampering texture details based on the probability of image pixel.When tested on publicly available image dataset“CASIA”v2.0(ChineseAcademy of Sciences,Institute of Automation),the proposed model had a 98.60%accuracy rate on the YCbCr(luminance(Y),chroma blue(Cb)and chroma red(Cr))color spaces in image block size of 8×8 pixels.The proposed image authentication model shows great accuracy with a relatively modest dimension feature size,supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand,foot and mouth disease(HFMD),primarily caused by enterovirus 71,was reported in Taiwan in 1998.HFMD surveillance is needed to assess the spread of HFMD.The parameters we use in mathematical models are usually classical mathematical parameters,called crisp parameters,which are taken for granted.But any biological or physical phenomenon is best explained by uncertainty.To represent a realistic situation in any mathematical model,fuzzy parameters can be very useful.Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling.However,few works use fuzzy theory in building models to simulateHFMDdynamics.In this context,we examined anHFMD model with fuzzy parameters.A Non Standard Finite Difference(NSFD)scheme is developed to solve the model.The developed technique retains essential properties such as positivity and dynamic consistency.Numerical simulations are presented to support the analytical results.The convergence and consistency of the proposed method are also discussed.The proposed method converges unconditionally while the many classical methods in the literature do not possess this property.In this regard,our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Computational Analysis for Computer Network Model with Fuzziness

A susceptible,exposed,infectious,quarantined and recovered(SEIQR)model with fuzzy parameters is studied in this work.Fuzziness in the model arises due to the different degrees of susceptibility,exposure,infectivity,quarantine and recovery among the computers under consideration due to the different sizes,models,spare parts,the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus,etc.Each individual PC has a different degree of infectivity and resis-tance against infection.In this scenario,the fuzzy model has richer dynamics than its classical counterpart in epidemiology.The reproduction number of the developed model is studied and the equilibrium analysis is performed.Two different techniques are employed to solve the model numerically.Numerical simulations are performed and the obtained results are compared.Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.

he adaptive chirplet transform and its application in GPR target detection

探地雷达不仅能够探测金属目标体,而且能够探测非金属目标体,而成为UX0和地雷探测的一种重要的浅部地球物理方法。但是在地雷和UX0探测中,目标体埋藏深度浅,在探地雷达数据信噪比较低情况下,地表和土壤层的反射严重干扰对目标体的拾取。本文采用自适用Chirplet变换来消除地表层和土壤层变化的干扰,并在Radon—Wigner分布的基础上,采用自适用Chirplet变换来拾取目标体的信号。通过对实际探测实验数据应用证明,本方法处理结果比传统的偏移方法具有较高的信噪比,并能清晰地提取目标体信号。

Convergence and stability of the Newton-Like algorithm with estimation error in optimization flow control

The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed.The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory,a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained.Furthermore,even when this sufficient condition doesn't hold,this algorithm can also converge,provided a modified step size,and an attraction region is obtained.Based on Lasalle's invariance principle applied to a suitable Lyapunov function,the dynamic system described by this algorithm is proved to be global stability if the error is zero.And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence.All trajectories ultimately converge to the equilibrium point.

MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects

Combined effects of Soret(thermal-diffusion) and Dufour(diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained.Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.

Volume Difference Inequalities for the Polars of Mixed Complex Projection Bodies

In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.

The Shephard Type Problems for General L_p-Centroid Bodies

In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.

Reducing the Range of Cancer Risk on BI-RADS 4 Subcategories via Mathematical Modelling

Breast Imaging Reporting and Data System,also known as BI-RADS is a universal system used by radiologists and doctors.It constructs a comprehensive language for the diagnosis of breast cancer.BI-RADS 4 category has a wide range of cancer risk since it is divided into 3 categories.Mathematicalmodels play an important role in the diagnosis and treatment of cancer.In this study,data of 42 BI-RADS 4 patients taken fromthe Center for Breast Health,Near East University Hospital is utilized.Regarding the analysis,a mathematical model is constructed by dividing the population into 4 compartments.Sensitivity analysis is applied to the parameters with the desired outcome of a reduced range of cancer risk.Numerical simulations of the parameters are demonstrated.The results of the model have revealed that an increase in the lactation rate and earlymenopause have a negative correlation with the chance of being diagnosed with BI-RADS 4 whereas a positive correlation increase in age,the palpable mass,and family history is distinctive.Furthermore,the negative effects of smoking and late menopause on BI-RADS 4C diagnosis are vehemently outlined.Consequently,the model showed that the percentages of parameters play an important role in the diagnosis of BI-RADS 4 subcategories.All things considered,with the assistance of the most effective parameters,the range of cancer risks in BI-RADS 4 subcategories will decrease.

GLOBAL OPTIMIZATION OF THE DIFFERENCE OF TWO INCREASING PLUS-CONVEX-ALONG-RAYS FUNCTIONS

The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.

Sensitivity Analysis of COVID-19 in Mediterranean Island

The aim of this study is to examine the progress of the worldwide pandemic Covid-19.As authors,we have decided to analyze the situation of COVID-19 onMediterranean islandwith accurate data.For this purpose,amathematical model is constructed and proposed by dividing the whole population into sensible and suitable compartments.The study captures the dates February 01 till May 15,2021.For the control of the spread of disease,vaccination and infection rates are compared and calculated.During calculations and comparison,MatLab software is used.All of the data that are used are taken from the Ministry of Health.The effect of parameters is examined with sensitivity analysis.Furthermore,with this analysis,values of parameters are obtained.Afterwards,by using the constructed model,the effect of vaccine on infected individuals is analyzed separately.As a result,it is concluded that the studied part of the island is late for the control of the disease via vaccine.This can be explained by two main reasons;vaccinating the people that are not inmobilitymost of the time(aged people and people with chronic diseases)and getting the vaccine late.Hence,the results showed that this rate and distribution of vaccines would not be enough to control the pandemic on the island.

A FRACTIONAL CRITICAL PROBLEM WITH SHIFTING SUBCRITICAL PERTURBATION

In this paper,we consider a class of fractional problem with subcritical perturbation on a bounded domain as follows:(P_(k)){(−△)^(s)u = g(x)[(u − k)+]^(q−1) +u^(2^(∗)_(s)−1), x ∈Ω ,u > 0, x∈Ω ,u = 0, x ∈Ω R^(N)\Ω. We prove the existence of nontrivial solutions u_(k) of(P_(k))for each k∈(0,∞).We also investigate the concentration behavior of the solutions u_(k) as k→∞.

Numerical simulation of two droplets impacting upon a dynamic liquid film

The impact of droplets on the liquid film is widely involved in industrial and agricultural fields.In recent years,plenty of works are limited to dry walls or stationary liquid films,and the research of multi-droplet impact dynamic films is not sufficient.Based on this,this paper employs a coupled level set and volume of fluid(CLSVOF) method to numerically simulate two-droplet impingement on a dynamic liquid film.In our work,the dynamic film thickness,horizontal central distance between the droplets,droplets’ initial impact speed,and simultaneously the flow velocity of the moving film are analyzed.The evolution phenomenon and mechanism caused by the collision are analyzed in detail.We find that within a certain period of time,the droplet spacing does not affect the peripheral crown height;when the droplet spacing decreases or the initial impact velocity increases,the height of the peripheral crown increases at the beginning,and then,because the crown splashed under Rayleigh-Plateau instability,this results in the reduction of the crown height.At the same time,it is found that when the initial impact velocity increases,the angle between the upstream peripheral jet and the dynamic film becomes larger.The more obvious the horizontal movement characteristics,the more restrained the crown height;the spread length increases with the increase of the dynamic film speed,droplet spacing and the initial impact velocity.When the liquid film is thicker,more fluid enters the crown,due to the crown being unstable,the surface tension is not enough to overcome the weight of the rim at the end of the crown,resulting in droplets falling off.