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.

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.

Bayesian and Non-Bayesian Analysis for the Sine Generalized Linear Exponential Model under Progressively Censored Data

This article introduces a novel variant of the generalized linear exponential(GLE)distribution,known as the sine generalized linear exponential(SGLE)distribution.The SGLE distribution utilizes the sine transformation to enhance its capabilities.The updated distribution is very adaptable and may be efficiently used in the modeling of survival data and dependability issues.The suggested model incorporates a hazard rate function(HRF)that may display a rising,J-shaped,or bathtub form,depending on its unique characteristics.This model includes many well-known lifespan distributions as separate sub-models.The suggested model is accompanied with a range of statistical features.The model parameters are examined using the techniques of maximum likelihood and Bayesian estimation using progressively censored data.In order to evaluate the effectiveness of these techniques,we provide a set of simulated data for testing purposes.The relevance of the newly presented model is shown via two real-world dataset applications,highlighting its superiority over other respected similar models.

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.

A Study on Computer Consciousness on Intuitive Geometry Based on Mathematics Experiments and Statistical Analysis

In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.

Topological Aspects of Dendrimers via Connection-Based Descriptors

Topological indices(TIs)have been practiced for distinct wide-ranging physicochemical applications,especially used to characterize and model the chemical structures of various molecular compounds such as dendrimers,nanotubes and neural networks with respect to their certain properties such as solubility,chemical stability and low cytotoxicity.Dendrimers are prolonged artificially synthesized or amalgamated natural macromolecules with a sequential layer of branches enclosing a central core.A present-day trend in mathematical and computational chemistry is the characterization of molecular structure by applying topological approaches,including numerical graph invariants.Among topological descriptors,Zagreb connection indices(ZCIs)have much importance.This manuscript involves the establishment of general results to calculate ZCIs,namely first ZCI(FZCI),second ZCI(SZCI),third ZCI(TZCI),modified FZCI,modified SZCI and modified TZCI of two special types of dendrimers nanostars,namely,poly propylene imine octamin(PPIO)dendrimer and poly(propyl)ether imine(PPEtIm)dendrimer.Furthermore,we provide the numerical and graphical comparative analysis of our calculated results for both types of dendrimers with each other.

Influence of Thermophoresis and Brownian Motion of Nanoparticles on Radiative Chemically-Reacting MHD Hiemenz Flow over a Nonlinear Stretching Sheet with Heat Generation

In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper,the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed.A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations,which are then solved numerically by a fourth–order Runge–Kutta method.It is found that the linear fluid velocity decreases with the enhancement of the porosity,boundary,and suction parameters.Conversely,it increases with the micropolar and injection parameters.The angular velocity grows with the boundary,porosity,and suction parameters,whereas it is reduced if the micropolar and injection parameters become larger.It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Nanoparticle Shape Effect on a Sodium–Alginate Based Cu–Nanofluid under a Transverse Magnetic Field

Sodium-alginate(SA)based nanofluids represent a new generation of fluids with improved performances in terms of heat transfer.This work examines the influence of the nanoparticle shape on a non–Newtonian viscoplastic Cu–nanofluid pertaining to this category.In particular,a stretching/shrinking sheet subjected to a transverse magnetic field is considered.The proposed Cu–nanofluid consists of four different nanoparticles having different shapes,namely bricks,cylinders,platelets,and blades dispersed in a mixture of sodium alginate with Prandtl number Pr=6.45.Suitable similarity transformations are employed to reduce non–linear PDEs into a system of ODEs and these equations and related boundary conditions are solved numerically by means of a Runge–Kutta–Fehlberg(RKF)method.Moreover,analytical solutions are obtained through the application of a MAPLE built–in differential equation solver(Dsolve).The behavior of prominent parameters against velocity and temperature is analyzed.It is found that the temperature increases for all shapes of nanoparticles with the viscoplastic parameter and the Eckert number.

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles:an analytical study

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion,vicious,and Darcy dissipation is studied.The first region consists of a clear fluid,and the second one is filled with a nanofluid saturated with a porous medium.The behaviors of Cu-H_(2)O,In-H_(2)O,and Au-H_(2)O nanofluids are analyzed.The transport properties are assumed to be constant.The coupled non-linear equations of the flow model are transformed into the dimensionless form,and the solutions for the velocity,temperature,and concentration are obtained by the regular perturbation technique.Investigations are carried out on the flow characteristics for various values of the material parameters.The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number,solutal Grashof number,and Brinkman number while decrease with the porosity parameter and solid volume fraction.