Search results for: equilibrium point.

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao,

Abstract:

In this paper, we study the existence, the boundedness and the asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equations xn+1 = A + k i=0 Bi xn-i , n= 0, 1, · · · . where (xn) is a sequence of positive fuzzy numbers, A,Bi and the initial values x-k, x-k+1, · · · , x0 are positive fuzzy numbers. k ∈ {0, 1, 2, · · ·}.

Keywords: Fuzzy difference equation, boundedness, persistence, equilibrium point, asymptotic behaviour.

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Authors: S. Madhavi, K. Baala Srinivas, G. Bharath, R. K. Indhuja, M. Kowser Chandini

Abstract:

Game theory is the study of how people interact and make decisions to handle competitive situations. It has mainly been developed to study decision making in complex situations. Humans routinely alter their behaviour in response to changes in their social and physical environment. As a consequence, the outcomes of decisions that depend on the behaviour of multiple decision makers are difficult to predict and require highly adaptive decision-making strategies. In addition to the decision makers may have preferences regarding consequences to other individuals and choose their actions to improve or reduce the well-being of others. Nash equilibrium is a fundamental concept in the theory of games and the most widely used method of predicting the outcome of a strategic interaction in the social sciences. A Nash Equilibrium exists when there is no unilateral profitable deviation from any of the players involved. On the other hand, no player in the game would take a different action as long as every other player remains the same.

Keywords: Game Theory, Nash Equilibrium, Rules of Dominance.

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Authors: J. Sulaiman, M. Othman, M. K. Hasan

Abstract:

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Keywords: MEG iteration, second-order finite difference, weighted parameter.

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Authors: Chengli Liu, C. K. M. Lee

Abstract:

The tradition competitive newsvendor game assumes decision makers are rational. However, there are behavioral biases when people make decisions, such as loss aversion, mental accounting and overconfidence. Overestimation of a subject’s own performance is one type of overconfidence. The objective of this research is to analyze the impact of the overestimated demand in the newsvendor competitive game with two players. This study builds a competitive newsvendor game model where newsvendors have private information of their demands, which is overestimated. At the same time, demands of each newsvendor forecasted by a third party institution are available. This research shows that the overestimation leads to demand steal effect, which reduces the competitor’s order quantity. However, the overall supply of the product increases due to overestimation. This study illustrates the boundary condition for the overestimated newsvendor to have the equilibrium order drop due to the demand steal effect from the other newsvendor. A newsvendor who has higher critical fractile will see its equilibrium order decrease with the drop of estimation level from the other newsvendor.

Keywords: Bias, competitive newsvendor, Nash equilibrium, overestimation.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

Abstract:

The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: Asymptotic stability, incubation period, Routh-Hurwitz criterion, Runge Kutta method.

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Authors: Jianqin Qu

Abstract:

This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: Covariant point, point matching, dimension free, rigid registration.

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Authors: E. Muzenda

Abstract:

Group contribution methods such as the UNIFAC are of major interest to researchers and engineers involved synthesis, feasibility studies, design and optimization of separation processes as well as other applications of industrial use. Reliable knowledge of the phase equilibrium behavior is crucial for the prediction of the fate of the chemical in the environment and other applications. The objective of this study was to predict the solubility of selected volatile organic compounds (VOCs) in glycol polymers and biodiesel. Measurements can be expensive and time consuming, hence the need for thermodynamic models. The results obtained in this study for the infinite dilution activity coefficients compare very well those published in literature obtained through measurements. It is suggested that in preliminary design or feasibility studies of absorption systems for the abatement of volatile organic compounds, prediction procedures should be implemented while accurate fluid phase equilibrium data should be obtained from experiment.

Keywords: Volatile organic compounds, Prediction, Phaseequilibrium, Environmental, Infinite dilution.

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Authors: John Kabuba, Antoine Mulaba-Bafubiandi

Abstract:

The elution process for the removal of Co and Cu from clinoptilolite as an ion-exchanger was investigated using three parameters: bed volume, pH and contact time. The present paper study has shown quantitatively that acid concentration has a significant effect on the elution process. The favorable eluant concentration was found to be 2 M HCl and 2 M H2SO4, respectively. The multi-component equilibrium relationship in the process can be very complex, and perhaps ill-defined. In such circumstances, it is preferable to use a non-parametric technique such as Neural Network to represent such an equilibrium relationship.

Keywords: Clinoptilolite, elution, modeling, neural network.

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Authors: S. Noor, M. W. Siddiqi

Abstract:

This study examines causal link between energy use and economic growth for five South Asian countries over period 1971-2006. Panel cointegration, ECM and FMOLS are applied for short and long run estimates. In short run unidirectional causality from per capita GDP to per capita energy consumption is found, but not vice versa. In long run one percent increase in per capita energy consumption tend to decrease 0.13 percent per capita GDP. i.e. Energy use discourage economic growth. This short and long run relationship indicate energy shortage crisis in South Asia due to increased energy use coupled with insufficient energy supply. Beside this long run estimated coefficient of error term suggest that short term adjustment to equilibrium are driven by adjustment back to long run equilibrium. Moreover, per capita energy consumption is responsive to adjustment back to equilibrium and it takes 59 years approximately. It specifies long run feedback between both variables.

Keywords: Energy consumption, Income, Panel co-integration, Causality.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the global exponential stability of the equilibrium point of Hopfield neural networks with delays and impulsive perturbation. Some new exponential stability criteria of the system are derived by using the Lyapunov functional method and the linear matrix inequality approach for estimating the upper bound of the derivative of Lyapunov functional. Finally, we illustrate two numerical examples showing the effectiveness of our theoretical results.

Keywords: Hopfield Neural Networks, Exponential stability.

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Authors: M. Delavar, A.A. Ghoreyshi, M. Jahanshahi, M. Irannejad

Abstract:

This study investigates the capacity of granular activated carbon (GAC) for the storage of methane through the equilibrium adsorption. An experimental apparatus consist of a dual adsorption vessel was set up for the measurement of equilibrium adsorption of methane on GAC using volumetric technique (pressure decay). Experimental isotherms of methane adsorption were determined by the measurement of equilibrium uptake of methane in different pressures (0-50 bar) and temperatures (285.15-328.15°K). The experimental data was fitted to Freundlich and Langmuir equations to determine the model isotherm. The results show that the experimental data is equally well fitted by the both model isotherms. Using the experimental data obtained in different temperatures the isosteric heat of methane adsorption was also calculated by the Clausius-Clapeyron equation from the Sips isotherm model. Results of isosteric heat of adsorption show that decreasing temperature or increasing methane uptake by GAC decrease the isosteric heat of methane adsorption.

Keywords: Methane adsorption, Activated carbon, Modelisotherm, Isosteric heat

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Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

Abstract:

Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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Authors: Herti Utami, Sutijan, Roto, Wahyudi Budi Sediawan

Abstract:

α-Pinene is the main component of the most turpentine oils. The hydration of α-pinene with acid catalysts leads to a complex mixture of monoterpenes. In order to obtain more valuable products, the α-pinene in the turpentine can be hydrated in dilute mineral acid solutions to produce α-terpineol. The design of separation processes requires information on phase equilibrium and related thermodynamic properties. This paper reports the results of study on liquid-liquid equilibrium (LLE) of system containing α- pinene + water and α-terpineol + water. Binary LLE for α-pinene + water system, and α-terpineol + water systems were determined by experiment at 301K and atmospheric pressure. The two component mixture was stirred for about 30min, then the mixture was left for about 2h for complete phase separation. The composition of both phases was analyzed by using a Gas Chromatograph. The experimental data were correlated by considering both NRTL and UNIQUAC activity coefficient models. The LLE data for the system of α-pinene + water and α-terpineol + water were correlated successfully by the NRTL model. The experimental data were not satisfactorily fitted by the UNIQUAC model. The NRTL model (α =0.3) correlates the LLE data for the system of α-pinene + water at 301K with RMSD of 0.0404%. And the NRTL model (α =0.61) at 301K with RMSD of 0.0058 %. The NRTL model (α =0.3) correlates the LLE data for the system of α- terpineol + water at 301K with RMSD of 0.1487% and the NRTL model (α =0.6) at 301K with RMSD of 0.0032%, between the experimental and calculated mole fractions.

Keywords: α-Pinene, α-Terpineol, Liquid-liquid Equilibrium, NRTL model, UNIQUAC model

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Authors: M. Moosavi, H. Khatibzadeh

Abstract:

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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Authors: Saktioto, F.D Ismail, P.P. Yupapin, J. Ali

Abstract:

The equilibrium process of plasma nitrogen species by chemical kinetic reactions along various pressures is successfully investigated. The equilibrium process is required in industrial application to obtain the stable condition when heating up the material for having homogenous reaction. Nitrogen species densities is modeled by a continuity equation and extended Arrhenius form. These equations are used to integrate the change of density over the time. The integration is to acquire density and the reaction rate of each reaction where temperature and time dependence are imposed. A comparison is made with global model within pressure range of 1- 100mTorr and the temperature of electron is set to be higher than other nitrogen species. The results shows that the chemical kinetic model only agrees for high pressure because of no power imposed; while the global model considers the external power along the pressure range then the electron and nitrogen species give highly quantity densities by factor of 3 to 5.

Keywords: chemical kinetic model, Arrhenius equation, nitrogen plasma, low pressure discharge

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Authors: Jelena Zagorska, Inga Ciprovica

Abstract:

The freezing point of milk is in important indicator of the milk quality. The freezing point of milk is determined primarily to prove milk adulteration with water and to determine the amount of water in it. Chemical composition and properties of milk, thermal treatment and presence of any substance can influence freezing point of product. There are different substances, which can be added to milk with main purpose to prolong shelf-life of raw milk. There are detergent, preservatives, formaldehyde, hydrogen peroxide, antibiotics, sodium carbonate, and hydrogen peroxide. Therefore the aim of the present study was to determine freezing point of milk, skimmed milk, pasteurized milk and milk with different substances (formaldehyde, antibiotics, sodium carbonate, hydrogen peroxide, disinfectant, and detergent) in different concentrations. The thermal treatment and different undesirable substances presence in milk have significant influence on freezing point of it.

Keywords: Antibiotics, freezing point, milk, pH, thermal treatment.

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Authors: Farshad Rahimpour, Ali Reza Baharvand

Abstract:

The phase diagrams and compositions of coexisting phases have been determined for aqueous two-phase systems containing poly(propylene glycol) with average molecular weight of 425 and sodium citrate at various pH of 3.93, 4.44, 4.6, 4.97, 5.1, 8.22. The effect of pH on the salting-out effect of poly (propylene glycol) by sodium citrate has been studied. It was found that, an increasing in pH caused the expansion of two-phase region. Increasing pH also increases the concentration of PPG in the PPGrich phase, while the salt-rich phase will be somewhat mole diluted.

Keywords: Aqueous two-phase system, Phase equilibrium, Biomolecules purification

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Authors: M. Ilyas, M. W. Siddiqi

Abstract:

This study employs auto-regressive distributed lag (ARDL) bounds approach to cointegration for long run and errorcorrection modeling (ECM) for short run analysis to examine the relationship between revenue gap and economic growth for Pakistan using annual time series data over the period 1980 to 2008. The short and long run results indicate that revenue gap is statistical significant and negatively effect economic growth. The significant and negative coefficient of error correction term in ECM indicates that after a shock, the long rum equilibrium will again converge towards equilibrium about 10.406 percent within a year.

Keywords: ARDL cointegration, Economic Growth, RevenueGap, Pakistan.

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Authors: Oral Lacin, Turan Calban, Fatih Sevim, Taner Celik

Abstract:

In this study, Pb²⁺ uptake by the hydroxyapatite nanopowders (n-Hap) from aqueous solutions was investigated by using batch adsorption techniques. The adsorption equilibrium studies were carried out as a function of contact time, adsorbent dosage, pH, temperature, and initial Pb²⁺ concentration. The results showed that the equilibrium time of adsorption was achieved within 60 min, and the effective pH was selected to be 5 (natural pH). The maximum adsorption capacity of Pb²⁺ on n-Hap was found as 565 mg.g^-1. It is believed that the results obtained for adsorption may provide a background for the detailed mechanism investigations and the pilot and industrial scale applications.

Keywords: Nanopowders, hydroxyapatite, heavy metals, adsorption.

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Authors: Idoko J. O., Nwajiaku I.

Abstract:

Unripe and ripe plantain were dried and milled into flour and used with wheat flour in biscuit production to determine the best plantain-wheat composite flour for biscuit production. The blends as follows: 100% wheat flour, 100% ripe plantain flour, 100% unripe plantain flour, 50% wheat flour and 50% ripe plantain flour and 50% wheat flour and 50% unripe plantain flour. The Biscuit samples were stored at ambient temperature for 8 weeks after which the equilibrium moisture content and water activity were determined. The sensory evaluation of the biscuit samples was also determined. The results of these analyses showed 100% unripe plantain flour as the most stable of the BISCUIT samples judging from its equilibrium moisture content level of 0.32% and water activity of 0.62. The sensory evaluation results showed Biscuit made from 150:50 ripe plantain and wheat flour as most generally accepted at 5% level of significance.

Keywords: Biscuit, equilibrium moisture content, performance, plantain, water activity.

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Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: Temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli.

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Authors: Adnene Arbi, Chaouki Aouiti, Abderrahmane Touati

Abstract:

In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.

Keywords: Hopfield neural networks, uniform asymptotic stability, global asymptotic stability, exponential stability.

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Authors: Pakkinee Chitsakul

Abstract:

In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: Cut locus, flat torus, geodesics.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

Dengue, a disease found in most tropical and subtropical areas of the world. It has become the most common arboviral disease of humans. This disease is caused by any of four serotypes of dengue virus (DEN1-DEN4). In many endemic countries, the average age of getting dengue infection is shifting upwards, dengue in pregnancy and infancy are likely to be encountered more frequently. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the pregnant, infant human and the vector populations. The stability of each equilibrium point is given. The epidemic dynamic is discussed. Moreover, the numerical results are shown for difference values of dengue antibody.

Keywords: Dengue antibody, infant, pregnant human, mathematical model.

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Authors: M. R. Yadav, A. K. Sharma, B. S. Thakur

Abstract:

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

Keywords: Cyclic contraction, rational cyclic contraction, best proximity point and complete metric space.

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Authors: Tinuade Jolaade Afolabi, Theresa Ibibia Edewor

Abstract:

Experimental liquid-liquid equilibra of butan-2-ol - ethanol -water; pentan-1-ol - ethanol - water and toluene - acetone - water ternary systems were investigated at (25oC). The reliability of the experimental tie-line data was ascertained by using Othmer-Tobias and Hand plots. The distribution coefficients (D) and separation factors (S) of the immiscibility region were evaluated for the three systems.

Keywords: Distribution coefficient, Liquid-liquid equilibrium, separation factors, thermodynamic models

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Authors: Mauricio Pe˜na, Adriana Luna, Carol Rodr´ıguez

Abstract:

In the following article we begin from a multi-parameter unstable nonlinear model of a Quadrotor. We design a control to stabilize and assure the attitude of the device, starting off a linearized system at the equilibrium point of the null angles of Euler (hover), which provides us a control with limited capacities at small angles of rotation of the vehicle in three dimensions. In order to clear this obstacle, we propose the identification of models in different angles by means of simulations and the design of a controller specifically implemented for the identification task, that in future works will allow the development of controllers according to fast and agile angles of Euler for Quadrotor.

Keywords: Quadrotor, model, control, identification.

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Authors: Anuj K. Sharma, Amit Sharma, Kulbhushan Agnihotri

Abstract:

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited continuously.Further,biological and bionomic equilibria of the system are obtained and an optimal harvesting policy is also analysed using the Pantryagin’s Maximum Principle.Finally analytical findings are also supported by some numerical simulations.

Keywords: Phytoplankton-Zooplankton, Global stability, Bionomic Equilibrium, Pontrying-Maximum Principal.

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Authors: H. Zare Aliabadi

Abstract:

The equilibrium chemical reactions taken place in a converter reactor of the Khorasan Petrochemical Ammonia plant was studied using the minimization of Gibbs free energy method. In the minimization of the Gibbs free energy function the Davidon– Fletcher–Powell (DFP) optimization procedure using the penalty terms in the well-defined objective function was used. It should be noted that in the DFP procedure along with the corresponding penalty terms the Hessian matrices for the composition of constituents in the Converter reactor can be excluded. This, in fact, can be considered as the main advantage of the DFP optimization procedure. Also the effect of temperature and pressure on the equilibrium composition of the constituents was investigated. The results obtained in this work were compared with the data collected from the converter reactor of the Khorasan Petrochemical Ammonia plant. It was concluded that the results obtained from the method used in this work are in good agreement with the industrial data. Notably, the algorithm developed in this work, in spite of its simplicity, takes the advantage of short computation and convergence time.

Keywords: Gibbs free energy, converter reactors, Chemical equilibrium

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Authors: R. C. Ferreira, H. H. C. De Lima, A. A. Cândido, O. M. Couto Junior, P. A. Arroyo, K. Q De Carvalho, G. F. Gauze, M. A. S. D. Barros

Abstract:

Removal of the widespread used drug paracetamol from water was investigated using activated carbon originated from dende coconut mesocarp and babassu coconut mesocarp. Kinetic and equilibrium data were obtained at different values of pH. Both activated carbons showed high efficiency when pH ≤ pHPZC as the carbonil group of paracetamol molecule are adsorbed due to positively charged carbon surface. Microporosity also played an important role in such process. Pseudo-second order model was better adjusted to the kinetic results. Equilibrium data may be represented by Langmuir equation.

Keywords: Adsorption, activated carbon, babassu, dende.

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