A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

Mathematical Modeling and Evaluation of Reliability Parameters Based on Survival Possibilities under Uncertain Environment

In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.

Multivariate form of Hermite sampling series

In this paper,we establish a new multivariate Hermite sampling series involving samples from the function itself and its mixed and non-mixed partial derivatives of arbitrary order.This multivariate form of Hermite sampling will be valid for some classes of multivariate entire functions,satisfying certain growth conditions.We will show that many known results included in Commun Korean Math Soc,2002,17:731-740,Turk J Math,2017,41:387-403 and Filomat,2020,34:3339-3347 are special cases of our results.Moreover,we estimate the truncation error of this sampling based on localized sampling without decay assumption.Illustrative examples are also presented.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

Chemically Radiative MHD Flow of a Micropolar Nanofluid over a Stretching/ Shrinking Sheet with a Heat Source or Sink

This study examines the behavior of a micropolar nanofluidflowing over a sheet in the presence of a transverse magneticfield and thermal effects.In addition,chemical(first-order homogeneous)reactions are taken into account.A similarity transformation is used to reduce the system of governing coupled non-linear partial differ-ential equations(PDEs),which account for the transport of mass,momentum,angular momentum,energy and species,to a set of non-linear ordinary differential equations(ODEs).The Runge-Kutta method along with shoot-ing method is used to solve them.The impact of several parameters is evaluated.It is shown that the micro-rota-tional velocity of thefluid rises with the micropolar factor.Moreover,the radiation parameter can have a remarkable influence on theflow and temperature profiles and on the angular momentum distribution.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

Dynamics of Non-Markovianity, Quantum Correlations and Information Scrambling of Three Qubits Systems Interacting via Rashba Interaction

The behavior of the quantum correlations, information scrambling and the non-Markovianity of three entangling qubits systems via Rashba is discussed. The results showed that, the three physical quantities oscillate between their upper and lower bounds, where the number of oscillations increases as the Rashba interaction strength increases. The exchanging rate of these three quantities depends on the Rashba strength, and whether the entangled state is generated via direct/indirect interaction. Moreover, the coherence parameter can be used as a control parameter to maximize or minimize the three physical quantities.

Natural Convection and Irreversibility of Nanofluid Due to Inclined Magnetohydrodynamics(MHD)Filled in a Cavity with Y-Shape Heated Fin:FEM Computational

This study explains the entropy process of natural convective heating in the nanofluid-saturated cavity in a heated fin andmagnetic field.The temperature is constant on the Y-shaped fin,insulating the topwall while the remaining walls remain cold.All walls are subject to impermeability and non-slip conditions.The mathematical modeling of the problem is demonstrated by the continuity,momentum,and energy equations incorporating the inclined magnetic field.For elucidating the flow characteristics Finite ElementMethod(FEM)is implemented using stable FE pair.A hybrid fine mesh is used for discretizing the domain.Velocity and thermal plots concerning parameters are drawn.In addition,a detailed discussion regarding generation energy by monitoring changes in magnetic,viscous,total,and thermal irreversibility is provided.In addition,line graphs are created for the u and v components of the velocity profile to predict the flow behavior.Current simulations assume the dimensionless representative of magnetic field Hartmann number Ha between 0 and 100 and a magnetic field inclination between 0 and 90 degrees.A constant 4% volume proportion of nanoparticles is employed throughout all scenarios.

Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

Recent Developments in Authentication Schemes Used in Machine-Type Communication Devices in Machine-to-Machine Communication: Issues and Challenges

Machine-to-machine (M2M) communication plays a fundamental role in autonomous IoT (Internet of Things)-based infrastructure, a vital part of the fourth industrial revolution. Machine-type communication devices(MTCDs) regularly share extensive data without human intervention while making all types of decisions. Thesedecisions may involve controlling sensitive ventilation systems maintaining uniform temperature, live heartbeatmonitoring, and several different alert systems. Many of these devices simultaneously share data to form anautomated system. The data shared between machine-type communication devices (MTCDs) is prone to risk dueto limited computational power, internal memory, and energy capacity. Therefore, securing the data and devicesbecomes challenging due to factors such as dynamic operational environments, remoteness, harsh conditions,and areas where human physical access is difficult. One of the crucial parts of securing MTCDs and data isauthentication, where each devicemust be verified before data transmission. SeveralM2Mauthentication schemeshave been proposed in the literature, however, the literature lacks a comprehensive overview of current M2Mauthentication techniques and the challenges associated with them. To utilize a suitable authentication schemefor specific scenarios, it is important to understand the challenges associated with it. Therefore, this article fillsthis gap by reviewing the state-of-the-art research on authentication schemes in MTCDs specifically concerningapplication categories, security provisions, and performance efficiency.

Chemical Determination of Base Status Metals in Soil Sediments and Particulate Matter in Wellington Industrial Estate Location

This research study explored the levels of base status metals in soil sediments and particulate matter in the wellington industrial estate location;the main objectives were to: 1) determine sodium and potassium, 2) determine calcium and magnesium, 3) determine available iron. The following hypotheses were put forward;H0a: there is no significant difference in the concentration levels between Ca and Mg in the study area, H1a: there is significant difference in the concentration levels between Ca and Mg in the study area, H0b: there is no significant difference in the concentration levels between Na and K in the study area, H1b: there is significant difference in the concentration levels between Na and K in the study area. Six locations were used to collect samples with the aid of scoop and gravel free auger (at varying depths of 0 - 5 cm and 5 - 10 cm) which are Wellington Industrial Estate Area 1 (WIEL 1), (WIEL 2), (WIEL 3), (WIEL 4), (WIEL 5), (WIEL 6);the samples were given laboratory treatment. Flame photometer, EDTA, and Spectrophotometer were used in the determinations of sodium and potassium, calcium and magnesium, and available iron respectively. The results indicated that levels of potassium were in medium range (moderately high);sodium levels were generally low when compared to Brook’s classification table. Levels of calcium were generally low and those of magnesium were moderate based on Brook’s table of classification. Levels of available iron which fall within the range of Quijano-Guerta (2003) were high;this implies such levels can lead to toxicity. In all locations, there was decrease in the levels of each metal in the samples with (5 - 10 cm) depth.

Assessment of Heavy Metal Exposure in Soils of Ihwrekreka Communities, Delta State, Nigeria

Crude oil pollution in the Niger Delta, perpetrated by both local communities and industrial actors, has brought about soil pollution with its consequent ecological, human health and food challenges. The purpose of this research was to examine the concentration and distribution of heavy metals in soil from communities contaminated by crude oil in Niger Delta, and to evaluate the potential health risks to residents from exposure to these contaminants. To achieve this, soil samples were collected from the Ihwrekreka community and analyzed for heavy metal content using inductively coupled plasma mass spectrometry (ICP-MS). The analytical results in mg/kg revealed a significant metals pollution level derived from the oil spill in the soil ranging from 4.85 - 17,078 (Cu), 1.01 - 16.1 (Cd), 0.22 - 36.8 (Cr), 8.28 - 40.9 (Ni), 7.51 - 6474 (Pb), and 8.84 - 12,851 (Zn) respectively. Most of the metals were above the permissible limits of World Health Organization, with Cu, Zn, and Pb as the most contaminating metals. Lead was found to be the main contributor to the hazard index (HI) values for both children and adults in the study area, with its concentration exceeding the permitted limits set by the WHO and the EC. The hazard index (HI) values of Pb, Cu, Zn, Cd, Ni, and Cr were significantly higher than 1. These findings suggest that the release of heavy metals from an oil-contaminated site may pose a risk to human health and the environment.

Extended Deep Learning Algorithm for Improved Brain Tumor Diagnosis System

At present,the prediction of brain tumors is performed using Machine Learning(ML)and Deep Learning(DL)algorithms.Although various ML and DL algorithms are adapted to predict brain tumors to some range,some concerns still need enhancement,particularly accuracy,sensitivity,false positive and false negative,to improve the brain tumor prediction system symmetrically.Therefore,this work proposed an Extended Deep Learning Algorithm(EDLA)to measure performance parameters such as accuracy,sensitivity,and false positive and false negative rates.In addition,these iterated measures were analyzed by comparing the EDLA method with the Convolutional Neural Network(CNN)way further using the SPSS tool,and respective graphical illustrations were shown.The results were that the mean performance measures for the proposed EDLA algorithm were calculated,and those measured were accuracy(97.665%),sensitivity(97.939%),false positive(3.012%),and false negative(3.182%)for ten iterations.Whereas in the case of the CNN,the algorithm means accuracy gained was 94.287%,mean sensitivity 95.612%,mean false positive 5.328%,and mean false negative 4.756%.These results show that the proposed EDLA method has outperformed existing algorithms,including CNN,and ensures symmetrically improved parameters.Thus EDLA algorithm introduces novelty concerning its performance and particular activation function.This proposed method will be utilized effectively in brain tumor detection in a precise and accurate manner.This algorithm would apply to brain tumor diagnosis and be involved in various medical diagnoses aftermodification.If the quantity of dataset records is enormous,then themethod’s computation power has to be updated.

Numerical Simulations of Hydromagnetic Mixed Convection Flow of Nanofluids inside a Triangular Cavity on the Basis of a Two-Component Nonhomogeneous Mathematical Model

Nanofluids have enjoyed a widespread use in many technological applications due to their peculiar properties.Numerical simulations are presented about the unsteady behavior of mixed convection of Fe_(3)O_(4)-water,Fe_(3)O_(4)-kerosene,Fe_(3)O_(4)-ethylene glycol,and Fe_(3)O_(4)-engine oil nanofluids inside a lid-driven triangular cavity.In particular,a two-component non-homogeneous nanofluid model is used.The bottom wall of the enclosure is insulated,whereas the inclined wall is kept a constant(cold)temperature and various temperature laws are assumed for the vertical wall,namely:
θ=1(Case 1),θ=Yð1YÞ(Case 2),andθ=sinð2-YÞ(Case 3).A tilted magnetic field of uniform strength is also present in the fluid domain.From a numerical point of view,the problem is addressed using the Galerkin weighted residual finite element method.The role played by different parameters is assessed,discussed critically and interpreted from a physical standpoint.We find that a higher aspect ratio can produce an increase in the average Nusselt number.Moreover,the Fe_(3)O_(4)-EO and Fe_(3)O_(4)-H2O nanofluids provide the highest and smallest rate of heat transfer,respectively,for all the considered(three variants of)thermal boundary conditions.

Mathematical Analysis of Novel Coronavirus (2019-nCov) Delay Pandemic Model

In this manuscript,the mathematical analysis of corona virus model with time delay effect is studied.Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological,engineering,physical,social,behavioural problems and many more.Most of infectious diseases are dreadful such as HIV/AIDS,Hepatitis and 2019-nCov.Unfortunately,due to the non-availability of vaccine for 2019-nCov around the world,the delay factors like,social distancing,quarantine,travel restrictions,holidays extension,hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov.We have analysed the reproduction number𝐑𝐑𝐧𝐧𝐧𝐧𝐧𝐧𝐧𝐧of delayed model.Two key strategies from the reproduction number of 2019-nCov model,may be followed,according to the nature of the disease as if it is diminished or present in the community.The more delaying tactics eventually,led to the control of pandemic.Local and global stability of 2019-nCov model is presented for the strategies.We have also investigated the effect of delay factor on reproduction number𝐑R_(nCov).Finally,some very useful numerical results are presented to support the theoretical analysis of the model.

On Solving Mathematical Problems the Spatial-Visual Ways

This study investigated the effectiveness of spatial-visualization-based instruction on the mathematical problem-solving performance of 35 mathematics education students using one-group pretest-posttest quasi-experimental design. It also aimed to describe how spatial visualization is applied in solving mathematical problems. The findings of the study revealed that spatial-visualization-based instruction improved the mathematical problem-solving performance of students. The spatial-visualization ability can be applied in solving mathematical problems.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

An Approximate Numerical Methods for Mathematical and Physical Studies for Covid-19 Models

The advancement in numerical models of serious resistant illnesses is a key research territory in different fields including the nature and the study of disease transmission.One of the aims of these models is to comprehend the elements of conduction of these infections.For the new strain of Covid-19(Coronavirus),there has been no immunization to protect individuals from the virus and to forestall its spread so far.All things being equal,control procedures related to medical services,for example,social distancing or separation,isolation,and travel limitations can be adjusted to control this pandemic.This article reveals some insights into the dynamic practices of nonlinear Coronavirus models dependent on the homotopy annoyance strategy(HPM).We summon a novel sign stream chart that is utilized to depict the Coronavirus model.Through the numerical investigations,it is uncovered that social separation of the possibly tainted people who might be conveying the infection and the healthy virus-free people can diminish or interrupt the spread of the infection.The mathematical simulation results are highly concurrent with the statistical forecasts.The free balance and dependability focus for the Coronavirus model is discussed and the presence of a consistently steady arrangement is demonstrated.

Describe the Mathematical Model for Exchanging Waves Between Bacterial and Cellular DNA

In this article,we have shown that bacterial DNA could act like some coils which interact with coil-like DNA of host cells.By decreasing the separating distance between two bacterial cellular DNA,the interaction potential,entropy,and the number of microstates of the system grow.Moreover,the system gives its energy to the medium and the temperature of the host body grows.This could be seen as fever in diseases.By emitting some special waves and changing the temperature of the medium,the effects of bacterial waves could be reduced and bacterial diseases could be controlled.Many investigators have shown that bacterial DNA could emit or absorb electromagnetic waves.One of the main experiments about bacterial waves has been done by Montagnier and his group.They have shown that the genomic DNA of most pathogenic bacteria includes sequences that are able to emit electromagnetic waves.The results have shown that wave affects the crucial physicochemical processes in both Gram-positive and Gram-negative bacteria.The emphasis in this survey is on the development of controlling model equations and computer emulation of the model equations rather than on mathematical methods for solving the model equations and differential equations of epidemics.