Search results for: simultaneous equation model

Authors: Houcine Naim, Abdelatif Hassini, Noureddine Benabadji, Alex Van Den Bossche

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In this paper, two models to estimate the overall monthly average daily radiation on a horizontal surface were applied to the site of Oran (35.38 ° N, 0.37 °W). We present a comparison between the first one is a regression equation of the Angstrom type and the second model is developed by the present authors some modifications were suggested using as input parameters: the astronomical parameters as (latitude, longitude, and altitude) and meteorological parameters as (relative humidity). The comparisons are made using the mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE). This comparison shows that the second model is closer to the experimental values that the model of Angstrom.

Keywords: meteorology, global radiation, Angstrom model, Oran

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: Pramod K. Prabhakar, Prem P. Srivastav

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Rohu (Labeo rohita) is an Indian major carp and highly relished freshwater food for its unique flavor, texture, and culinary properties. It is highly perishable and, spoilage occurs as a result of series of complicated biochemical changes brought about by enzymes which are the function of time and storage temperature also. The influence of storage temperature (5, 0, and -5 °C) on colour and texture of fish were studied during 14 days storage period in order to analyze kinetics of colour and textural changes. The rate of total colour change was most noticeable at the highest storage temperature (5°C), and these changes were well described by the first order reaction. Texture is an important variable of quality of the fish and is increasing concern to aquaculture industries. Textural parameters such as hardness, toughness and stiffness were evaluated on a texture analyzer for the different day of stored fish. The significant reduction (P ≤ 0.05) in hardness was observed after 2nd, 4th and 8th day for the fish stored at 5, 0, and -5 °C respectively. The textural changes of fish during storage followed a first order kinetic model and fitted well with this model (R2 > 0.95). However, the textural data with respect to time was also fitted to modified Maxwell model and found to be good fit with R2 value ranges from 0.96 to 0.98. Temperature dependence of colour and texture change was adequately modelled with the Arrhenius type equation. This fitted model may be used for the determination of shelf life of Rohu Rohu (Labeo rohita) Fish.

Keywords: first order kinetics, biochemical changes, Maxwell model, colour, texture, Arrhenius type equation

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Authors: Polvasut Mahaiamsiri, Piraphong Foosiri

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The purpose of this research is to explore the model of factors affecting decision making to select successor in family business of Thailand. A Structural Equation Model (SEM) was created from relevant theories and researches. Consequently, examine and analyse, the causal relation factors of Succession Plan, Recruitment Process and Strategic Planning, whether they have direct or indirect effects on Decision Making to Select Successor in family business. Units of analysis are selected from the family business, totalling 300 sampling. Population sampling is current owners or CEO from the percentage of six district areas in Thailand with multi-stage sampling. A set of questionnaires is used to collect data. An analysis of structural equation modelling (SEM) technique using AMOS 21 program is conducted to test the hypotheses and confirmatory factor analysis is performed and shows that these variables can be tested. The finding of this study revealed that these factors are separate constructs that combine to determine decision making to select successors.

Keywords: succession plan, family business, recruitment process, strategic planning, decision making to select successor

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Authors: James A. Adeyanju, John O. Olajide, Akinbode A. Adedeji

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A predictive mathematical model based on the fundamental principles of mass transfer was developed to simulate the moisture content and oil content during Deep-Fat Frying (DFF) process of dodo. The resulting governing equation, that is, partial differential equation that describes rate of moisture loss and oil uptake was solved numerically using explicit Finite Difference Technique (FDT). Computer codes were written in MATLAB environment for the implementation of FDT at different frying conditions and moisture loss as well as oil uptake simulation during DFF of dodo. Plantain samples were sliced into 5 mm thickness and fried at different frying oil temperatures (150, 160 and 170 ⁰C) for periods varying from 2 to 4 min. The comparison between the predicted results and experimental data for the validation of the model showed reasonable agreement. The correlation coefficients between the predicted and experimental values of moisture and oil transfer models ranging from 0.912 to 0.947 and 0.895 to 0.957, respectively. The predicted results could be further used for the design, control and optimization of deep-fat frying process.

Keywords: frying, moisture loss, modelling, oil uptake

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Authors: Somesh Misha, Smita Raghuvanshi, Suresh Gupta

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Increasing concentration of green house gases (GHG's), such as CO2 is of major concern and start showing its impact nowadays. The recent studies are focused on developing the continuous system using photoautotrophs for CO2 mitigation and simultaneous production of primary and secondary metabolites as a value addition. The advent of carbon concentrating mechanism had blurred the distinction between autotrophs and heterotrophs and now the paradigm has shifted towards the carbon capture and utilization (CCU) rather than carbon capture and sequestration (CCS). In the present work, a bioreactor was developed utilizing the chemolithotrophic bacterial species using CO2 mitigation and simultaneous value addition. The kinetic modeling was done and the biokinetic parameters are obtained for developing the bioreactor. The bioreactor was developed and studied for its operation and performance in terms of volumetric loading rate, mass loading rate, elimination capacity and removal efficiency. The characterization of effluent from the bioreactor was carried out for the products obtained using the analyzing techniques such as FTIR, GC-MS, and NMR. The developed bioreactor promised an economic, efficient and effective solution for CO2 mitigation and simultaneous value addition.

Keywords: CO2 mitigation, bio-reactor, chemolithotrophic bacterial species, FTIR, GC-MS, NMR

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Ross Calvert, Colin Whittaker, Alison Raby, Alistair G. L. Borthwick, Ton S. van den Bremer

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Large concentrations of plastic have polluted the seas in the last half century, with harmful effects on marine wildlife and potentially to human health. Plastic pollution will have lasting effects because it is expected to take hundreds or thousands of years for plastic to decay in the ocean. The question arises how waves transport plastic in the ocean. The predominant motion induced by waves creates ellipsoid orbits. However, these orbits do not close, resulting in a drift. This is defined as Stokes drift. If a particle is infinitesimally small and the same density as water, it will behave exactly as the water does, i.e., as a purely Lagrangian tracer. However, as the particle grows in size or changes density, it will behave differently. The particle will then have its own inertia, the fluid will exert drag on the particle, because there is relative velocity, and it will rise or sink depending on the density and whether it is on the free surface. Previously, plastic pollution has all been considered to be purely Lagrangian. However, the steepness of waves in the ocean is small, normally about α = k₀a = 0.1 (where k₀ is the wavenumber and a is the wave amplitude), this means that the mean drift flows are of the order of ten times smaller than the oscillatory velocities (Stokes drift is proportional to steepness squared, whilst the oscillatory velocities are proportional to the steepness). Thus, the particle motion must have the forces of the full motion, oscillatory and mean flow, as well as a dynamic buoyancy term to account for the free surface, to determine whether inertia is important. To track the motion of a floating inertial particle under wave action requires the fluid velocities, which form the forcing, and the full equations of motion of a particle to be solved. Starting with the equation of motion of a sphere in unsteady flow with viscous drag. Terms can added then be added to the equation of motion to better model floating plastic: a dynamic buoyancy to model a particle floating on the free surface, quadratic drag for larger particles and a slope sliding term. Using perturbation methods to order the equation of motion into sequentially solvable parts allows a parametric equation for the transport of inertial finite-sized floating particles to be derived. This parametric equation can then be validated using numerical simulations of the equation of motion and flume experiments. This paper presents a parametric equation for the transport of inertial floating finite-size particles by ocean waves. The equation shows an increase in Stokes drift for larger, less dense particles. The equation has been validated using numerical solutions of the equation of motion and laboratory flume experiments. The difference in the particle transport equation and a purely Lagrangian tracer is illustrated using worlds maps of the induced transport. This parametric transport equation would allow ocean-scale numerical models to include inertial effects of floating plastic when predicting or tracing the transport of pollutants.

Keywords: perturbation methods, plastic pollution transport, Stokes drift, wave flume experiments, wave-induced mean flow

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Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: A. Seleem, M. Mortada, M. El-Morsi, M. Younan

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Diffusion stills have been effective in water desalination. The present work represents a model of the distillation process by using vertical single-effect diffusion stills. A semi-analytical model has been developed to model the process. A software computer code using Engineering Equation Solver EES software has been developed to solve the equations of the developed model. An experimental setup has been constructed, and used for the validation of the model. The model is also validated against former literature results. The results obtained from the present experimental test rig, and the data from the literature, have been compared with the results of the code to find its best range of validity. In addition, a parametric analysis of the system has been developed using the model to determine the effect of operating conditions on the system's performance. The dominant parameters that affect the productivity of the still are the hot plate temperature that ranges from (55-90 °C) and feed flow rate in range of (0.00694-0.0211 kg/m2-s).

Keywords: analytical model, solar distillation, sustainable water systems, vertical diffusion still

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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Authors: S. O. Oyamakin, A. U. Chukwu,

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We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a stabilizing parameter called θ using hyperbolic sine function into the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE, and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Jameelah Omolara Yaqub

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One of the main reasons for the existence of central bank is that it is believed that central banks have some influence on private sector decisions which will enable the Central Bank to achieve some of its objectives especially that of stable price and economic growth. By the assumption of the New Keynesian theory that prices are fully flexible in the short run, the central bank can temporarily influence real interest rate and, therefore, have an effect on real output in addition to nominal prices. There is, therefore, the need for the Central Bank to monitor, respond to, and influence private sector decisions appropriately. This thus shows that the Central Bank and the private sector will both affect and be affected by each other implying considerable interdependence between the sectors. The interdependence may be simultaneous or not depending on the level of information, readily available and how sensitive prices are to agents’ expectations about the future. The aim of this paper is, therefore, to determine whether the interdependence between asset prices and monetary policy are simultaneous or not and how important is this relationship. Studies on the effects of monetary policy have largely used VAR models to identify the interdependence but most have found small effects of interaction. Some earlier studies have ignored the possibility of simultaneous interdependence while those that have allowed for simultaneous interdependence used data from developed economies only. This study, therefore, extends the literature by using data from a developing economy where information might not be readily available to influence agents’ expectation. In this study, the direction of relationship among variables of interest will be tested by carrying out the Granger causality test. Thereafter, the interaction between asset prices and monetary policy in Nigeria will be tested. Asset prices will be represented by the NSE index as well as real estate prices while monetary policy will be represented by money supply and the MPR respectively. The VAR model will be used to analyse the relationship between the variables in order to take account of potential simultaneity of interdependence. The study will cover the period between 1980 and 2014 due to data availability. It is believed that the outcome of the research will guide monetary policymakers especially the CBN to effectively influence the private sector decisions and thereby achieve its objectives of price stability and economic growth.

Keywords: asset prices, granger causality, monetary policy rate, Nigeria

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Authors: Johnson Audu, Faisal Fairag

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In a bounded subset of R^d, d=2 or 3, we consider the Darcy-Forchheimer power model with the exponent 1 < m ≤ 2 for a single-phase strong-inertia fluid flow in a porous medium. Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence and uniqueness of solution (u, p) in L^(m+1 ) (Ω)^d X (W^(1,(m+1)/m) (Ω)^d ⋂L_0^2 (Ω)^d) and its stability.

Keywords: porous media, power law, strong inertia, nonlinear, monotone type

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Authors: Ted Silva

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Dietrich de Velsa's Équation à un inconnu / Equation to an Unknown hybridizes art cinema style with the sexually explicit aesthetics of pornography to envision a uniquely queer world unmoored by heteronormative influence. This stylization evokes the memory of a queer history that once approximated such a prospect. With this historical and political context in mind, this paper utilizes formal analysis to assess how the film frames queer sexual encounters as tender acts of care, sometimes literally mending physical wounds. However, Equation to Unknown also highlights the transience of these sexual exchanges. By emphasizing the homogeneity of the protagonist’s sexual conquests, the film reveals that these practices have a darker meaning when the men reject the individualized connection to pursue purely visceral gratification. Given the lack of diversity or even recognizable identifying factors, the men become more anonymous to each other the more they pair up. Ultimately, Equation to an Unknown both celebrates and problematizes its vision of a queer utopia, highlighting areas in the community wherein intimacy and care flourish and locating those spots in which they are neglected.

Keywords: pornography studies, queer cinema, French cinema, history

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Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

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The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: fractional model predictive control, fractional order systems, thermal system, predictive control

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Authors: Mohammad Reza Shojaei, Mahdeih Mirzaeinia

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We have studied the cluster structure of even-even stable isotopes of Ge and Sr. The Schrodinger equation has been solved using the generalized parametric Nikiforov-Uvarov method with a phenomenological potential. This potential is the sum of the attractive Yukawa-like potential, a Manning-Rosen-type potential, and the repulsive Yukawa potential for interaction between the cluster and the core. We have shown that the available experimental data of the first rotational band energies can be well described by assuming a binary system of the α cluster and the core and using an analytical solution. Our results were consistent with experimental values. Hence, this model can be applied to study the other even-even isotopes

Keywords: cluser model, NU method, ge and Sr, potential central

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Authors: Sherry Ann Ganase, Sandra Sookram

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This study examines adaptation measures and factors that influence adaptation decisions in Bequia by using multiple linear regression and a structural equation model. Using survey data, the results suggest that households are knowledgeable and concerned about climate change but lack knowledge about the measures needed to adapt. The findings from the SEM suggest that a positive relationship exist between vulnerability and adaptation, vulnerability and perception, along with a negative relationship between perception and adaptation. This suggests that being aware of the terms associated with climate change and knowledge about climate change is insufficient for implementing adaptation measures; instead the risk and importance placed on climate change, vulnerability experienced with household flooding, drainage and expected threat of future sea level are the main factors that influence the adaptation decision. The results obtained in this study are beneficial to all as adaptation requires a collective effort by stakeholders.

Keywords: adaptation, Bequia, multiple linear regression, structural equation model

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: F. Z. Mahi, H. Marinchio, C. Palermo, L. Varani

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We propose an analytical approach for the admittance response calculation of the high mobility InGaAs channel transistors. The development of the small-signal admittance takes into account the longitudinal and transverse electric fields through a pseudo two-dimensional approximation of the Poisson equation. The total currents and the potentials matrix relation between the gate and the drain terminals determine the frequency-dependent small-signal admittance response. The analytical results show that the admittance spectrum exhibits a series of resonant peaks corresponding to the excitation of plasma waves. The appearance of the resonance is discussed and analyzed as functions of the channel length and the temperature. The model can be used, on one hand, to control the appearance of plasma resonances, and on the other hand, can give significant information about the admittance phase frequency dependence.

Keywords: small-signal admittance, Poisson equation, currents and potentials matrix, the drain and the gate terminals, analytical model

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Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

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We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

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Authors: S. Mousavian, A. Abedianpour, A. Khanmohammadi, S. Hematian, Gh. Eidi Veisi

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Distillation is one of the most important and utilized separation methods in the industrial practice. There are different ways to design of distillation column. One of these ways is short cut method. In short cut method, material balance and equilibrium are employed to calculate number of tray in distillation column. There are different methods that are classified in short cut method. One of these methods is Fenske-Underwood-Gilliland method. In this method, minimum reflux ratio should be calculated by underwood equation. Underwood proposed an equation that is useful for simple distillation column with one feed and one top and bottom product. In this study, underwood method is developed to predict minimum reflux ratio for column with one side stream upper than feed. The result of this model compared with McCabe-Thiele method. The result shows that proposed method able to calculate minimum reflux ratio with very small error.

Keywords: minimum reflux ratio, side stream, distillation, Underwood’s method

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

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The solution of the nonlinear dynamic equilibrium equations of base-isolated structures adopting a conventional monolithic solution approach, i.e. an implicit single-step time integration method employed with an iteration procedure, and the use of existing nonlinear analytical models, such as differential equation models, to simulate the dynamic behavior of seismic isolators can require a significant computational effort. In order to reduce numerical computations, a partitioned solution method and a one dimensional nonlinear analytical model are presented in this paper. A partitioned solution approach can be easily applied to base-isolated structures in which the base isolation system is much more flexible than the superstructure. Thus, in this work, the explicit conditionally stable central difference method is used to evaluate the base isolation system nonlinear response and the implicit unconditionally stable Newmark’s constant average acceleration method is adopted to predict the superstructure linear response with the benefit in avoiding iterations in each time step of a nonlinear dynamic analysis. The proposed mathematical model is able to simulate the dynamic behavior of seismic isolators without requiring the solution of a nonlinear differential equation, as in the case of widely used differential equation model. The proposed mixed explicit-implicit time integration method and nonlinear exponential model are adopted to analyze a three dimensional seismically isolated structure with a lead rubber bearing system subjected to earthquake excitation. The numerical results show the good accuracy and the significant computational efficiency of the proposed solution approach and analytical model compared to the conventional solution method and mathematical model adopted in this work. Furthermore, the low stiffness value of the base isolation system with lead rubber bearings allows to have a critical time step considerably larger than the imposed ground acceleration time step, thus avoiding stability problems in the proposed mixed method.

Keywords: base-isolated structures, earthquake engineering, mixed time integration, nonlinear exponential model

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Authors: Alakija Temitope Olufunmilayo, Akinyemi, Yagba Joy

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Hepatitis is the inflammation of the liver tissue that can cause whiteness of the eyes (Jaundice), lack of appetite, vomiting, tiredness, abdominal pain, diarrhea. Hepatitis is acute if it resolves within 6 months and chronic if it last longer than 6 months. Acute hepatitis can resolve on its own, lead to chronic hepatitis or rarely result in acute liver failure. Chronic hepatitis may lead to scarring of the liver (Cirrhosis), liver failure and liver cancer. Modelling Hepatitis B may become necessary in order to reduce its spread. So, dynamic SIR model can be used. This model consists of a system of three coupled non-linear ordinary differential equation which does not have an explicit formula solution. It is an epidemiological model used to predict the dynamics of infectious disease by categorizing the population into three possible compartments. In this study, a five-compartment dynamic model of Hepatitis B disease was proposed and developed by adding control measure of sensitizing the public called awareness. All the mathematical and statistical formulation of the model, especially the general equilibrium of the model, was derived, including the nonlinear least square estimators. The initial parameters of the model were derived using nonlinear least square embedded in R code. The result study shows that the proportion of Hepatitis B patient in the study population is 1.4 per 1,000,000 populations. The estimated Hepatitis B induced death rate is 0.0108, meaning that 1.08% of the infected individuals die of the disease. The reproduction number of Hepatitis B diseases in Nigeria is 6.0, meaning that one individual can infect more than 6.0 people. The effect of sensitizing the public on the basic reproduction number is significant as the reproduction number is reduced. The study therefore recommends that programme should be designed by government and non-governmental organization to sensitize the entire Nigeria population in order to reduce cases of Hepatitis B disease among the citizens.

Keywords: hepatitis B, modelling, non-linear ordinary differential equation, sihar model, sensitization

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Authors: Archana Rao R., Deepak P., Chayashree P. D., Darshan H. S.

Abstract:

Cognitive abilities in bilinguals have been widely studied over the last few decades. Bilingualism has been found to extensively facilitate the ability to store and manipulate information in Working Memory (WM). The mechanism of WM includes primary memory, attentional control, and secondary memory, each of which makes a contribution to WM. Many researches have been done in an attempt to measure WM capabilities through both verbal (phonological) and nonverbal tasks (visuospatial). Since there is a lot of speculations regarding the relationship between WM and bilingualism, further investigation is required to understand the nature of WM in bilinguals, i.e., with respect to sequential and simultaneous bilinguals. Hence the present study aimed to highlight the verbal working memory abilities in sequential and simultaneous bilinguals with respect to the processing and recall abilities of nouns and verbs. Two groups of bilinguals aged between 18-30 years were considered for the study. Group 1 consisted of 20 (10 males and 10 females) sequential bilinguals who had acquired L1 (Kannada) before the age of 3 and had exposure to L2 (English) for a period of 8-10 years. Group 2 consisted of 20 (10 males and 10 females) simultaneous bilinguals who have acquired both L1 and L2 before the age of 3. Working memory abilities were assessed using two tasks, and a set of stimuli which was presented in gradation of complexity and the stimuli was inclusive of frequent and infrequent nouns and verbs. The tasks involved the participants to judge the correctness of the sentence and simultaneously remember the last word of each sentence and the participants are instructed to recall the words at the end of each set. The results indicated no significant difference between sequential and simultaneous bilinguals in processing the nouns and verbs, and this could be attributed to the proficiency level of the participants in L1 and the alike cognitive abilities between the groups. And recall of nouns was better compared to verbs, maybe because of the complex argument structure involved in verbs. Similarly, authors found a frequency of occurrence of nouns and verbs also had an effect on WM abilities. The difference was also found across gradation due to the load imposed on the central executive function and phonological loop.

Keywords: bilinguals, nouns, verbs, working memory

Procedia PDF Downloads 96

Authors: Ahmet Kaya

Abstract:

Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

Procedia PDF Downloads 303