Magnitude Of Number Research Articles

Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.

Comparative analysis between copper ethylene-glycol and copper-iron oxide ethylene-glycol nanoparticles both experiencing Coriolis force, velocity and temperature jump

Sequel to the industrial usage of ethylene-glycol conveying copper nanoparticles, nothing is known on how the dynamics differ from ethylene-glycol conveying copper and iron oxide nanoparticles when there is Coriolis force, slip and thermal jump. This report presents the outcome of a study on the motion and heat transfer across both non-Newtonian electro-conducting Carreau hybridized nanofluids via the porous medium on a three-dimensional rotating stretchable plate. The model for hybridization of the mixture of copper (Cu) and Iron oxide (Fe3O4) nanoparticles in the ethylene-glycol base fluid under thermal radiation, uneven heat source and wall slip attributes were developed and presented. The reduction of the model equations from partial into ordinary differential equations was carried out using similarity transformation variables. Pseudo-Spectral Method (PSM) was employed to solve the emerged boundary value problem. Exponential space-based heat source/sink, stretching rates, and temperature jump levels, heat transfer rates are maximal during ethylene-glycol conveying copper nanoparticles but minimal during ethylene-glycol motion conveying copper and iron oxide nanoparticles. The hybridization of the nanoparticles induces a higher heat propagation than the unitary nanofluid for all the physical parameters considered, whereas the strength of the surface drag force depreciates with a higher magnitude of the Weissenberg number.

Developmental trajectories of numerical magnitude representations of fractions and decimals.

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as fraction and decimal 0-1 and 0-5 number line estimation tasks. Magnitude representations of decimals became accurate earlier, improved more rapidly, and reached a higher asymptotic accuracy than magnitude representations of fractions. Analyses of individual differences revealed positive relations between the accuracy of decimal and fraction magnitude representations at all ages. In Experiment 2, we presented an additional set of 24 fourth graders (14 girls and 10 boys) with the same tasks but with the decimals that were being compared varying in the number of decimal digits. The decimal advantage continued to be present for both magnitude comparison and estimation tasks, indicating that the greater accuracy with decimals was not limited to decimals with equal numbers of decimal digits, though unequal numbers of decimal digits did impact performance with decimals on both magnitude comparison and number line estimation tasks. Implications for understanding numerical development and education are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Impact of needle size and distinct flow conditions on thermal performance of TiO2–MWCNTs hybrid nanofluid flow past thin needle using Casson fluid model

AbstractHybrid nanofluids comprising carbon nanotubes (CNTs) are finding applications in advanced heat exchange technologies due to the unusually high thermal conductivity and chemically inert nature of CNTs. The thermal performance of a hybrid nanofluid, comprising MWCNTs and TiO2 nanoparticles and flowing past a thin hot needle, is investigated in the present article. The Sakiadis and Blasius hybrid nanofluid flow scenarios around a parabolically shaped thin hot needle are modeled by using a non‐Newtonian Casson fluid model coupled with the energy equation. The governing equations are coupled non‐linear partial differential equations which are solved by the shooting method along with the 4th order Runge–Kutta method. The main aim of the study is to perform a comparative analysis among the base fluid (which is a 50:50 mixture of ethylene glycol [EG] and water), TiO2/EG–water nanofluid, and TiO2–MWCNTs/EG–water hybrid nanofluid and to analyze which fluid is the best transporter of heat. Apart from this, the impact of needle size and different flow conditions on heat transport is investigated. The numerical results reveal that the rate of heat transfer is maximum for TiO2–MWCNTs/EG–water hybrid nanofluid among the base fluid, nanofluid, and hybrid nanofluid. The magnitude of the Nusselt number is high for the case of the Blasius flow than for the Sakiadis flow.

A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media

Groundwater constitutes a critical component in providing fresh water for various human endeavors. Nevertheless, its susceptibility to contamination by pollutants represents a significant challenge. A comprehensive understanding of the dynamics of solute transport in groundwater and soils is essential for predicting the spatial and temporal distribution of these contaminants. Presently, conventional models such as the mobile–immobile (MIM) model and the rate-limited sorption (RLS) model are widely employed to describe the non-Fickian behavior of solute transport. In this research, we present a novel approach to solute transport that is founded on the temporally relaxed theory of Fick’s Law. Our methodology introduces two relaxation times to account for solute particle collisions and attachment, leading to the derivation of a new advection–dispersion equation. Our findings indicate that the relaxation times possess similar properties to the transport parameters in the MIM and RLS models, and our solution can be applied to accurately predict transport parameters from soil column experiments. Additionally, we discovered that the relaxation times are proportional to the magnitude of Peclet number. This innovative approach provides a deeper insight into solute transport and its impact on groundwater contamination.

Assessment of transient thermal distribution in a moving porous plate with temperature-dependent internal heat generation using Levenberg–Marquardt backpropagation neural network

ABSTRACT In the present paper, the transient temperature distribution within a moving porous plate is scrutinized by considering the internal heat generation, convection and radiation condition. Furthermore, an effective artificial intelligence technique is proposed for discussing the transient thermal behavior in a moving plate by employing the Levenberg-Marquardt backpropagation network. Using suitable non-dimensional terms, the governing partial differential equation (PDE) is transformed into its non-dimensional form. The transformed equation is then solved using the finite difference method (FDM) and the obtained thermal values (datasets) are used as target values in the process of neural network mapping. This network uses the training, testing, and validation processes to determine the solution of several scenarios established at various process times. The behavior of dimensionless transient temperature profile has been inspected for diverse values of non-dimensional parameters such as heat generation number, radiative parameter, porosity parameter, and conductive parameter with the assistance of graphs. The significant outcomes elucidate that, the transient temperature profile of the porous plate increases with the change in time. Further, it enriches for rise in the magnitude of Peclet number and heat generation number while it drops for enhanced values of porosity parameter.

Size and Charge Effects on Crossover of Flow Battery Reactants Evaluated by Quinone Permeabilities Through Nafion

Organic reactants are promising candidates for long-lifetime redox flow batteries, and synthetic chemistry unlocks a wide design space for new molecules. Minimizing crossover of these molecules through ion exchange membranes is one important design consideration, but the ways in which the crossover rate depends on the structure of the crossing species remain unclear. Here, we contribute a systematic evaluation of size- and charge-based effects on dilute-solution small molecule permeability through the Nafion NR212 cation exchange membrane. We found that increasing the magnitude of charge number z with the same sign as membrane fixed charges, achieved here by successive sulfonation of quinone redox cores, results in more than an order of magnitude permeability reduction per sulfonate. Size-based effects, understood by comparing the Stokes radii of the quinones studied, also reduces permeability with increasing effective molecule size, but doubling the effective size of the redox reactants resulted in a permeability decrease of less than a factor of three.

Large-eddy simulation of a planar offset-jet with heat transfer: The effects of ventilation

Several industrial and engineering applications employ ventilated offset-jets such as flow separation control devices, upper surface blowing used in short take-off and landing aircraft, drying processes, and fuel injection systems. The design and efficient operation of these devices relies on controlling the turbulence levels, heat transfer rates, and the locations of flow reattachment points. Therefore, an understanding of the flow and thermal characteristics of ventilated offset-jets helps in the design and operation of these devices. The present study aims to address this by performing large-eddy simulations (LES) of a planar turbulent offset-jet for different velocities of the ventilated-jet. To understand and quantify the effects of ventilation on the offset-jet, a range of velocity-ratios of 0, 0.1, 0.14, and 0.18 are considered for a primary offset-jet Reynolds number of 14,000. First, a grid-sensitivity study is performed to establish the convergence of the solver and the LES index of quality of resolution is obtained to ascertain the quality of the mesh. Thereafter, the mean and second-order statistics of the streamwise component of velocity are compared with reference data from the literature to validate the numerical solver. The effects of ventilation on the offset-jet are studied using the decay of streamwise velocity, jet-spread, the evolution of pressure coefficient, friction coefficient, the mean Nusselt number, and the unsteady characteristics. As the velocity-ratio increases, the suction pressure in the initial region of the domain decreases, which causes the jet to spread away from the bottom wall. Further the peak magnitudes of the mean Nusselt number and coefficient of pressure decrease exponentially with an increase in the velocity-ratio. The peak magnitude of the mean Nusselt number for the unventilated-jet case – the offset-jet without the ventilated-jet – is the largest and its value for the ventilated-jet cases decreases as the velocity-ratio is increased. It is concluded that in the initial region, the ventilated-jet has a profound effect on the offset-jet flow and as the flow develops into a wall-jet the effects of ventilation vanish.

Influences of cognitive control on number processing: New evidence from switching between two numerical tasks.

A growing body of research suggests that basic numerical abilities such as number magnitude and number parity processing are influenced by cognitive control. So far, however, evidence for number processing being influenced by cognitive control came primarily from observed adaptations to stimulus set characteristics (e.g., ratio or order of specific stimulus types) and switches between a numerical and non-numerical task. Complementing this previous research, the present study employed a task switching paradigm exclusively involving numerical tasks (i.e., magnitude comparisons and parity judgements) to examine how cognitive control processes influence number processing. Participants were presented with a single-digit number and had to either judge its parity or compare its magnitude with a standard of 5, depending on a preceding cue. Based on previous results, we expected the numerical distance effect and the spatial-numerical association of response codes (SNARC) effect to be modulated in switch trials requiring the exertion of cognitive control. Partly in line with our expectations, the numerical distance effect was reduced in switch trials. However, no modulation of the SNARC effect was observed. The results pattern suggests that number processing is influenced by cognitive control, depending on task requirements and the type of numerical information (i.e., numerical magnitude vs spatial association of numbers) that is processed. To reconcile the present and previous results, we propose an information prioritisation account, suggesting that cognitive control primarily influences the processing of the information type that requires the most explicit processing.

SENSITIVITY ANALYSIS AND IMPACT OF AN IMPERFECT VACCINE OF TWO STRAINS OF HEPATITIS B VIRUS INFECTION

A mathematical model considering two strains of hepatitis B virus (HBV) chronic carriers, to assess the impact of dose-structured imperfect vaccine, in a population, is designed and analyzed. The model is shown to have a locally and globally asymptotically stable disease-free equilibrium (DFE) whenever its associated reproduction number is numerically less than unity. Numerical analysis of the model shows that with the expected 50% minimum efficacy of the first vaccine dose, vaccinating 55% of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of hepatitis B infection. Such effective control can also be achieved if 50% of the first vaccine dose recipients take the second dose. Threshold analysis reveals that an imperfect HBV vaccine should have positive or negative population-level effect. Latin hypercube sampling–PRCC analysis illustrates that disease transmission rate, birth rate, natural death rate and proportion of children born with maternal immunity are most influential parameters in the disease dynamics. In this paper, the sensitivity analysis based on mathematical and in addition statistical techniques have been performed to determine the significance of the model parameters. It is observed that a number of the parameters play an important role to determine the magnitude of the basic reproduction number. Sensitivity analysis is achieved to determine model parameters’ importance in disease dynamics. It is observed that the reproduction number is the most responsive quantity to the potent transmission rate of HBV and in addition also vital to control the spread of the disease.

Effects of gas viscosity and liquid-to-gas density ratio on liquid jet atomization in crossflow

Atomization of liquid jets in gaseous crossflows has many natural and industrial applications, for example, in fuel atomization in gas turbine engines, rocket engines, film cooling, and, recently, suspension and solution precursor plasma spraying processes for the development of advanced coatings. Viscosity and density of the gaseous medium may significantly vary in applications such as plasma spraying, which can affect the instability waves on the liquid jet column, resulting in a major change in the mechanism of primary and secondary breakups. In this study, a numerical model is used to investigate the impact of gas viscosity on breakup mechanisms for a wide range of density ratios and Weber numbers. Due to many challenges, only a few comprehensive atomization measurements have been performed on this subject. However, novel computational models could provide the atomization process with a thorough picture in the last two decades. The incompressible variable-density Navier–Stokes equations are solved by using finite volume schemes, and a geometric volume-of-fluid technique is used to track the gas–liquid interface. In our parametric study, three sets of density ratios and Weber numbers are chosen. In each set, four cases with different orders of magnitude of gaseous Reynolds number are simulated. Different characteristics of jet atomization are analyzed, such as the jet trajectory, breakup location, and surface instabilities generated along the jet column. Ultimately, the effects of gaseous Reynolds number, density ratio, and Weber number on jet deformation and breakup mechanisms are discussed.

A mixed formulation of limit analysis for seismic slope stability

This paper presents a mixed formulation based on the node-based smoothed finite-element method for estimating seismic slope stability. The final form of Hellinger–Reissner is cast as the min–max optimisation problem with conic constraints. Solving the second-order cone programming directly determines both master fields, stress and displacement. It is shown from the numerical results that the stability numbers obtained are almost equal to the exact collapse loads for the relatively flat slopes. Moreover, the effects of the dilation angle on the seismic stability number are studied by incorporating a simple iterative technique in the algorithm cast as max-min programming, arriving at the observation that both the static and the seismic stability numbers are susceptible to the dilation angle. Although the magnitude of the seismic stability number largely depends on the vertical seismic acceleration for a broad range of typical slope angles, the seismic stability number for the relatively flat slopes in cohesive-frictional soils is likely independent of the seismic acceleration in the vertical direction.

Using the Number Line to Develop Understanding of Whole Number Magnitude and Operations

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems. The authors draw from the existing research base to describe practices for incorporating number line representations to (a) support students’ conceptual understanding of number and (b) teach addition and subtraction computational strategies. Specific examples are provided for teachers to integrate number line representations with other mathematical models to support the development of whole number understanding for students with LD in mathematics.

A comparative thermal case study on thermophysical aspects in thermally magnetized flow regime with variable thermal conductivity

It is well consensus among researchers affiliated with the field of thermal engineering that the thermophysical characteristics of heat transfer in fluid science own abundant applications like thermal distillation systems, heat exchangers, steam-electric power generation, electronic cooling, solar collectors, refrigeration systems and spacecraft thermal protection are to mention just a few. Considering such importance we offer a thermal case study on thermophysical aspects in a thermally magnetized non-Newtonian fluid along with a first-order chemical reaction effect. The flow field is carried with the following thermophysical effects namely, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent variable thermal conductivity. We have offered comparative analysis for temperature and Nusselt number by considering thermally radiative and non-radiative thermal flow fields. The thermal outcomes on temperature and Nusselt number are also reported for both the absence and presence of the heat generation effect. For both radiative and non-radiative Casson flow, the temperature shows an inciting nature towards Casson and variable thermal conductivity parameters. The magnitude of the Nusselt number towards Eckert, Prandt numbers, curvature, heat generation, and Casson fluid parameters is higher for the presence of thermal radiations while the opposite is the case for positive variation in the thermal conductivity parameter.

Predicting entropy generation of a hybrid nanofluid in microchannel heat sink with porous fins integrated with high concentration photovoltaic module using artificial neural networks

This paper evaluates the characteristic of second law of thermodynamic, including Bejan number and entropy generation for hybrid nanofluid containing graphene-silver nanofluid through a MCHS whit porous fins. Finite-volume technique is utilized to solve the governing equations. To simulate the problem, different porous medium thicknesses, nanoparticle concentrations, and inlet mass flow rates are used while the heat flux remains constant. The minimum values of the frictional and thermal entropy generation are 5 × 10−4 and 6.25 × 10−2, while the maximum values are 3.2 × 10−4 and 9.75 × 10−2. With increasing nanoparticle concentration up to 0.06% wt at constant porous thickness tp=200 µm, frictional entropy generation rises up by 3 × 10−5 and heat transfer rate go up while, thermal entropy generation decreases by 1.5 × 10−2. In addition, by doubling the input mass flow rate and reaching 0.02% at constant nanoparticle concentration (0.06%), thermal entropy generation decreases by 2 × 10−2 while the frictional entropy generation increases by 2.4 × 10−4. The minimum magnitude of Bejan number is 0.994. This show that the irreversibility is derived significantly from thermal entropy generation rate. Finally, an artificial neural network is employed to obtain a model for entropy generation.

KNOWLEDGE OF FLEXIBLE MENTAL COMPUTATION OF PRE-SERVICE ELEMENTARY MATHEMATICS TEACHERS UPON ENTRY TO UNIVERSITY

This study sets out to determine the knowledge of flexible mental computation of pre-service elementary mathematics teachers when enrolling at university. Knowledge of the existing flexible mental computation skills of pre-service teachers could inform teacher educators’ preparation for teaching by determining the algorithms that pre-service teachers are unable to calculate. Such knowledge could also inform teacher educators as to why pre-service teachers are unable to calculate the algorithms. The study produced a domain-specific instrument in the form of a diagnostic test that teacher educators could adopt in their teaching to elicit pre-service teachers’ knowledge, a gap that this study aims to bridge. A diagnostic test comprising 21 items was administered by the researcher to 51 year-one pre-service teachers who agreed to participate in the study. Findings of the study indicate that the majority of the pre-service teachers who participated in the study have a limited understanding of the magnitude of numbers, of basic number facts, of the relationship between numbers and of the relationship between basic operations to calculate flexibly. The argument of the study is that teacher educators’ instruction would be relevant and successful if focused on the cognitive needs of pre-service teachers and the mathematical concepts that they are going to teach. Therefore, this study recommends that teacher educators establish pre-service teachers’ knowledge prior to instruction for relevance and for the success of teaching.

No conclusive evidence for number-induced attentional shifts in a temporal order judgement task.

The Spatial Numerical Association of Response Codes (SNARC) effect refers to the observation that relatively small (e.g., 1) and large numbers (e.g., 9) elicit faster left- and right-sided manual responses, respectively. In a variation known as the attentional SNARC effect, merely looking at numbers caused a left- or right-ward shift in covert spatial attention, depending on the number's magnitude. In our study, we probed the notion that numbers induce shifts of spatial attention in accordance with their position on a mental number line (MNL). Critically, we removed any putative spatial response code that may contaminate the responses. We used a square and a tilted square as targets, thereby situating the decisive response dimension in the ventral, non-spatial processing stream. In two experiments where numbers were used as non-informative cues preceding a temporal order judgement (TOJ) task, we did not observe a deflection of the locus of spatial attention as a function of the numerical magnitude of the cue. In a third experiment, finding a significant modulation of TOJ performance as a function of the pointing direction of arrow cues allowed us to rule out the possibility that the absence of any significant modulation in Experiments 1 and 2 was due to a lack of sensitivity of our task set-up. We conclude from the current findings that the spatial codes that the perception and naming of numbers potentially elicit are not in and by themselves sufficient to elicit deflections of spatial attention.

Phototaxis of Chlamydomonas arises from a tuned adaptive photoresponse shared with multicellular Volvocine green algae.

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equationof motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.

Prediction of COVID-19 positive cases, a nation-wide SARS-CoV-2 wastewater-based epidemiology study

Taking advantage of Estonia's small size and population, we have employed wastewater-based epidemiology approach to monitor the spread of SARS-CoV-2, releasing weekly nation-wide updates. In this study we report results obtained between August 2020 and December 2021. Weekly 24 h composite samples were collected from wastewater treatment plants of larger towns already covered 65% of the total population that was complemented up to 40 additional grab samples from smaller towns/villages and the specific sites of concern.The N3 gene abundance was quantified by RT-qPCR. The N3 gene copy number (concentration) in wastewater fluctuated in accordance with the SARS-CoV-2 spread within the total population, with N3 abundance starting to increase 1.25 weeks (9 days) (95% CI: [1.10, 1.41]) before a rise in COVID-19 positive cases. Statistical model between the load of virus in wastewater and number of infected people validated with the Alpha variant wave (B.1.1.17) could be used to predict the order of magnitude in incidence numbers in Delta wave (B.1.617.2) in fall 2021. Targeted testing of student dormitories, retirement and nursing homes and prisons resulted in successful early discovery of outbreaks. We put forward a SARS-CoV-2 Wastewater Index (SARS2-WI) indicator of normalized virus load as COVID-19 infection metric to complement the other metrics currently used in disease control and prevention: dynamics of effective reproduction number (Re), 7-day mean of new cases, and a sum of new cases within last 14 days. In conclusion, an efficient surveillance system that combines analysis of composite and grab samples was established in Estonia. There is considerable discussion how the viral load in wastewater correlates with the number of infected people. Here we show that this correlation can be found. Moreover, we confirm that an increased signal in wastewater is observed before the increase in the number of infections. The surveillance system helped to inform public health policy and place direct interventions during the COVID-19 pandemic in Estonia via early warning of epidemic spread in various regions of the country.

A Comparative Numerical Study of Heat and Mass Transfer Individualities in Casson Stagnation Point Fluid Flow Past a Flat and Cylindrical Surfaces

There is a consensus among researchers that the simultaneous involvement of heat and mass transfer in fluid flow owns numerous daily life applications like energy systems, automobiles, cooling of electronic devices, power generation by the stream, electric power, and diagnosing and characterizing diseases, to mention just a few. Owing to such motivation, we considered both heat and mass transfer aspects in non-Newtonian fluid flow regimes. The Casson fluid is considered as a non-Newtonian fluid. For better novelty the flow is considered at both flat and cylindrical surfaces along with stagnation point, magnetic field, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent thermal conductivity. The ultimate differential equations are nonlinear, and hence difficult to solve analytically. Therefore, a numerical scheme, namely the shooting method with the Runge–Kutta algorithm, is adopted to report an acceptable solution for flow field description. The outcomes are shared comparatively for flat and cylindrical surfaces. We have seen that compared to a flat surface, the cylindrical surface has a larger Nusselt number magnitude.