Search results for: exponential decaying pressure gradient

Authors: O. W. Lawal, L. O. Ahmed, Y. K. Ali

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The unsteady MHD Poiseuille flow of a third grade fluid between two parallel horizontal nonconducting porous plates is studied with heat transfer. The two plates are fixed but maintained at different constant temperature with the Joule and viscous dissipation taken into consideration. The fluid motion is produced by a sudden uniform exponential decaying pressure gradient and external uniform magnetic field that is perpendicular to the plates. The momentum and energy equations governing the flow are solved numerically using Maple program. The effects of magnetic field and third grade fluid parameters on velocity and temperature profile are examined through several graphs.

Keywords: exponential decaying pressure gradient, MHD flow, Poiseuille flow, third grade fluid

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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: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: Jian-Li Shao

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Using Molecular Dynamic (MD) simulations, we simulated the microjet from the metal surface under decaying shock loading. The microjetting processes under release melting conditions are presented in detail, and some properties on the microjet mass and velocity are revealed. The phased increase of microjet mass with shock pressure is found. For all cases, the ratio of the maximal jetting velocity to the surface velocity approximately keeps a constant for liquid state. In addition, the temperature of the microjet can be always above the melting point. When introducing slow decaying profiles, the microjet mass begins to increase with the decay rate, which is dominated by the deformation of the bubble during pull-back. When the decay rate becomes fast enough, the microspall occurs as expected, meanwhile, the microjet appears to reduce because of the shock energy reduction.

Keywords: microjetting, shock, metal, molecular dynamics

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Authors: S. Ansari Sadrabadi, G. H. Rahimi

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In this paper, thick walled Cylindrical tanks or tubes made of functionally graded material under internal pressure and temperature gradient are studied. Material parameters have been considered as power functions. They play important role in the elastoplastic behavior of these materials. To clarify their role, different materials with different parameters have been used under temperature gradient. Finally, their effect and loading effect have been determined in first yield point. Also, the important role of temperature gradient was also shown. At the end the study has been results obtained from changes in the elastic modulus and yield stress. Also special attention is also given to the effects of this internal pressure and temperature gradient in the creation of tensile and compressive stresses.

Keywords: FGM, cylindrical pressure tubes, small deformation theory, yield onset, thermal loading

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Authors: A. Archibong-Eso, J. Shi, Y Baba, S. Alagbe, W. Yan, H. Yeung

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This study presents over 100 experiments conducted in a 25.4 mm internal diameter (ID) horizontal pipeline. Oil viscosity ranging from 3.5 Pa.s–5.0 Pa.s are used with superficial velocities of oil and water ranging from 0.06 to 0.55 m/s and 0.01 m/s to 1.0 m/s, respectively. Pressure gradient measurements and flow pattern observations are discussed. Numerical simulation of some flow conditions is performed using the commercial CFD code ANSYS Fluent® and the simulation results are compared with experimental results. Results indicate that CFD numerical simulation performed moderately well in predicting the flow configurations observed in this study while discrepancies were observed in the pressure gradient predictions.

Keywords: flow patterns, plug, pressure gradient, rivulet

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Authors: Morteza Mirhosseini, Amir B. Khoshnevis

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The boundary layer separation and new active flow control of a NACA 0025 airfoil were studied experimentally. This new flow control is sometimes known as a co-flow jet (cfj) airfoil. This paper presents the fluctuating velocity in a wall jet over the co-flow jet airfoil subjected to an adverse pressure gradient and a curved surface. In these results, the fluctuating velocity at the inner part increasing by increased the angle of attack up to 12^o and this has due to the jet energized, while the angle of attack 20^o has different. The airfoil cord based Reynolds number has 10⁵.

Keywords: adverse pressure gradient, fluctuating velocity, wall jet, co-flow jet airfoil

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Authors: Jurriaan Gillissen

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This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: Sajjad Negahban, Ruihe Wang, Baojiang Sun

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Gas-lift dual gradient drilling is a solution for deepwater drilling challenges. As well, Continuous development of drilling technology leads to increase employment of mineral oil based drilling fluids and synthetic-based drilling fluids, which have adequate characteristics such as: high rate of penetration, lubricity, shale inhibition and low toxicity. The paper discusses utilization of nitrified mineral oil base drilling for deepwater drilling and for more accurate prediction of pressure in DGD at marine riser, solubility and bubble pressure were considered in steady state hydraulic model. The Standing bubble pressure and solubility correlations, and two models which were acquired from experimental determination were applied in hydraulic model. The effect of the black oil correlations, and new solubility and bubble pressure models was evaluated on the PVT parameters such as oil formation volume factor, density, viscosity, volumetric flow rate. Eventually, the consequent simulated pressure profile due to these models was presented.

Keywords: solubility, bubble pressure, gas-lift dual gradient drilling, steady state hydraulic model

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Authors: Alexander V. Spirov, David M. Holloway, Ekaterina M. Myasnikova

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Segmentation of the early Drosophila embryo results from the dynamic establishment of spatial gene expression patterns. Patterning occurs on an embryo geometry which is a 'deformed' prolate ellipsoid, with anteroposterior and dorsal-ventral major and minor axes, respectively. Patterning is largely independent along each axis, but some interaction can be seen in the 'bending' of the segmental expression stripes. This interaction is not well understood. In this report, we investigate how 3D geometrical features of the early embryo affect the segmental expression patterning. Specifically, we study the effect of geometry on formation of the Bicoid primary morphogenetic gradient. Our computational results demonstrate that embryos with a much longer ventral than dorsal surface ('bellied') can produce curved Bicoid concentration contours which could activate curved stripes in the downstream pair-rule segmentation genes. In addition, we show that having an extended source for Bicoid in the anterior of the embryo may be necessary for producing the observed exponential form of the Bicoid gradient along the anteroposterior axis.

Keywords: Drosophila embryo, bicoid morphogenetic gradient, exponential expression profile, expression surface form, segmentation genes, 3D modelling

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Authors: P. I. Yachevskaya, S. A. Terentiev, M. S. Kuznetsov

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Several synthetic HPHT diamonds with metal inclusions have been studied. To have possibility of investigate the movement and transformation of the inclusions in the volume of the diamond the samples parallele-piped like shape has been made out of diamond crystals. The calculated value of temperature gradient in the samples of diamond which was placed in high-pressure cell was about 5-10 grad/mm. Duration of the experiments was in range 2-16 hours. All samples were treated several times. It has been found that the volume (dimensions) of inclusions, temperature, temperature gradient and the crystallographic orientation of the samples in the temperature field affects the movement speed of inclusions. Maximum speed of inclusions’ movement reached a value 150 µm/h.

Keywords: diamond, inclusions, temperature gradient, HPHT

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Authors: J. A. Louw Coetzee, Josua P. Meyer

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The thermodynamic properties of different refrigerants in combination with the variation in geometrical properties (hydraulic diameter, aspect ratio, and inclination angle) of a rectangular microchannel determine the two-phase frictional pressure gradient. The effect of aspect ratio on frictional pressure drop had not been investigated enough during adiabatic two-phase flow and condensation in rectangular microchannels. This experimental study was concerned with measurement of the frictional pressure gradient in a rectangular microchannel, with hydraulic diameter of 900 μm. The aspect ratio of this microchannel was varied over a range that stretched from 0.3 to 3 in order to capture the effect of aspect ratio variation. A commonly used refrigerant, R134a, was used in the tests that spanned over a mass flux range of 100 to 1000 kg m-2 s-1 as well as the whole vapour quality range. This study formed part of a refrigerant condensation experiment and was therefore conducted at a saturation temperature of 40 °C. The study found that there was little influence of the aspect ratio on the frictional pressure drop at the test conditions. The data was compared to some of the well known micro- and macro-channel two-phase pressure drop correlations. Most of the separated flow correlations predicted the pressure drop data well at mass fluxes larger than 400 kg m-2 s-1 and vapour qualities above 0.2.

Keywords: aspect ratio, microchannel, two-phase, pressure gradient

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Authors: Li Chen

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For an aerofoil or hydrofoil in high Reynolds number flows, broadband noise is generated efficiently as the result of the turbulence convecting over the trailing edge. This noise can be related to the surface pressure fluctuations, which can be predicted by either CFD or empirical models. However, in reality, the aerofoil or hydrofoil often operates at an angle of attack. Under this situation, the flow is subjected to an Adverse-Pressure-Gradient (APG), and as a result, a flow separation may occur. This study is to assess trailing-edge noise models for such flows. In the present work, the trailing-edge noise from a 2D airfoil at 6 degree of angle of attach is investigated. Under this condition, the flow is experiencing a strong APG, and the flow separation occurs. The flow over the airfoil with a chord of 300 mm, equivalent to a Reynold Number 4x10⁵, is simulated using RANS with the SST k-ɛ turbulent model. The predicted surface pressure fluctuations are compared with the published experimental data and empirical models, and show a good agreement with the experimental data. The effect of the APG on the trailing edge noise is discussed, and the associated trailing edge noise is calculated.

Keywords: aero-acoustics, adverse-pressure gradient, computational fluid dynamics, trailing-edge noise

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Authors: Rafik Baouche, Rabah Chaouchi

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This work reports the first comprehensive stress field interpretation from the eleven recently drilled wells in the Berkaoui Basin, Algerian Sahara. A cumulative length of 7000+m acoustic image logs from 06 vertical wells were investigated, and a mean NW-SE (128°-145° N) maximum horizontal stress (SHMax) orientation is inferred from the B-D quality wellbore breakouts. The study integrates log-based approach with the downhole measurements to infer pore pressure, in-situ stress magnitudes. Vertical stress (Sv), interpreted from the bulk-density profiles, has an average gradient of 22.36 MPa/km. The Ordovician and Cambrian reservoirs have a pore pressure gradient of 13.47-13.77 MPa/km, which is more than the hydrostatic pressure regime. A 17.2-18.3 MPa/km gradient of minimum horizontal stress (Shmin) is inferred from the fracture closure pressure in the reservoirs. Breakout widths constrained the SHMax magnitude in the 23.8-26.5 MPa/km range. Subsurface stress distribution in the central Saharan Algeria indicates that the present-day stress field in the Berkaoui Basin is principally strike-slip faulting (SHMax > Sv > Shmin). Inferences are drawn on the regional stress pattern and drilling and reservoir development.

Keywords: stress, imagery, breakouts, sahara

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Authors: Ahmed I. Raheem

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In this thesis, stratified and stratified wavy flow regimes have been investigated numerically for the oil (1.57 mPa s viscosity and 780 kg/m3 density) and water twophase flow in small and large horizontal steel pipes with a diameter between 0.0254 to 0.508 m by ANSYS Fluent software. Volume of fluid (VOF) with two phases flows using two equations family models (Realizable k-

Keywords: CFD, two-phase flow, pressure gradient, volume of fluid, large diameter, horizontal pipe, oil-water stratified and stratified wavy flow

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Abeer Ahmed Abdelhamed

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Introduction: Postoperative pulmonary complications (PPCs) are the most common complications observed and managed after abdominal or cardiothoracic surgery. Hypoxemia, atelectasis, pleural effusion, or diaphragmatic dysfunction, are often a source of morbidity in cardiac surgery patients, and are more common in patients receiving unilateral or bilateral internal mammary artery (IMT) grafts than patients receiving saphenous vein (SV) grafts alone. Purpose: The aim of this work was to investigate the effect of Threshold load inspiratory muscle training on pulmonary gas exchange and maximum inspiratory pressure (MIP) in patient undergoing coronary revascularization. Subject: Thirty three male patients eligible for coronary revascularization were selected to participate in the study. Method: They were divided into two groups(17 patients in the intervention group and 16 patients in the control group), the interventional group received inspiratory muscle training at 30% of their maximum inspiratory pressure throughout the hospitalization period in addition to routine post operative care. Result: The results of this study showed a significant improvement on maximum inspiratory pressure(MIP), Arterial-alveolar pressure gradient (A-a gradient) and oxygen saturation in the intervention group. Conclusion: Inspiratory muscle training using threshold mode significantly improves maximum inspiratory pressure, pulmonary gas exchange tested by alveolar-arterial gradient and oxygen saturation in Patients undergoing coronary revascularization.

Keywords: coronary revascularization, inspiratory muscle training, maximum inspiratory pressure, pulmonary gas exchange

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Authors: Nadia Ben Youssef, Aicha Bouzid

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Gradient estimation is one of the most fundamental tasks in the field of image processing in general, and more particularly for color images since that the research in color image gradient remains limited. The widely used gradient method is Di Zenzo’s gradient operator, which is based on the measure of squared local contrast of color images. The proposed gradient mechanism, presented in this paper, is based on the principle of the Di Zenzo’s approach using quaternion representation. This edge detector is compared to a marginal approach based on multiscale product of wavelet transform and another vector approach based on quaternion convolution and vector gradient approach. The experimental results indicate that the proposed color gradient operator outperforms marginal approach, however, it is less efficient then the second vector approach.

Keywords: gradient, edge detection, color image, quaternion

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Authors: G. Lei, P. C. Dong, X. Q. Cen, S. Y. Mo

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One of the most significant parameters, describing the effect of water flooding in porous media, is flood-response time, and it is an important index in oilfield development. The responding time in low permeability reservoir is usually calculated by the method of stable state successive substitution neglecting the effect of medium deformation. Numerous studies show that the media deformation has an important impact on the development for low permeability reservoirs and can not be neglected. On the base of streamline tube model, we developed a method to interpret responding time with medium deformation factor. The results show that: the media deformation factor, threshold pressure gradient and well spacing have a significant effect on the flood response time. The greater the media deformation factor, threshold pressure gradient or well spacing is, the lower the flood response time is. The responding time of different streamlines varies. As the angle with the main streamline increases, the water flooding response time delays as a "parabola" shape.

Keywords: low permeability, flood-response time, threshold pressure gradient, medium deformation

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Saikat Datta

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Incompressible laminar time-varying flow is investigated over a rounded backward-facing step for a triangular piston motion at the inlet of a straight channel with very high acceleration, followed by a slow deceleration experimentally and through numerical simulation. The backward-facing step is an important test-case as it embodies important flow characteristics such as separation point, reattachment length, and recirculation of flow. A sliding piston imparts two successive triangular velocities at the inlet, constant acceleration from rest, 0≤t≤t0, and constant deceleration to rest, t0≤tKeywords: laminar boundary layer separation, rounded backward facing step, separation bubble, unsteady separation, unsteady vortex flows

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Authors: Satish Kumar Dewangan, Santosh Kumar Senapati

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The present work focuses on the investigation of the effect of non-Newtonian behavior on the oil-water stratified flow in a horizontal channel using ANSYS Fluent. Coupled level set and volume of fluid (CLSVOF) has been used to capture the evolving interface assuming unsteady, coaxial flow with constant fluid properties. The diametric variation of oil volume fraction, mixture velocity, total pressure and pressure gradient has been studied. Non-Newtonian behavior of oil has been represented by the power law model in order to investigate the effect of flow behavior index. Stratified flow pattern tends to assume dispersed flow pattern with the change in the behavior of oil to non-Newtonian. The pressure gradient is found to be very much sensitive to the flow behavior index. The findings could be useful in designing the transportation pipe line in petroleum industries.

Keywords: oil-water stratified flow, horizontal channel, CLSVOF, non–Newtonian behaviour.

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

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Authors: M. Yaqub Khan, Usman Shabbir

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History of plasma reveals that continuous struggle of experimentalists and theorists are not fruitful for confinement up to now. It needs a change to bring the research through entropy. Approximately, all the quantities like number density, temperature, electrostatic potential, etc. are connected to entropy. Therefore, it is better to change the way of research. In ion temperature gradient mode with the help of Braginskii model, Boltzmannian electrons, effect of velocity shear is studied inculcating entropy in the magnetoplasma. New dispersion relation is derived for ion temperature gradient mode, and dependence on entropy gradient drift is seen. It is also seen velocity shear enhances the instability but in anomalous transport, its role is not seen significantly but entropy. This work will be helpful to the next step of tokamak and space plasmas.

Keywords: entropy, velocity shear, ion temperature gradient mode, drift

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Authors: Belloufi Mohammed, Sellami Badreddine

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This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: Mustafa Arda, Metin Aydogdu

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Carbon nanotubes (CNTs) have many possible application areas because of their superior physical properties. Nonlocal Theory, which unlike the classical theories, includes the size dependency. Nonlocal Stress and Strain Gradient approaches can be used in nanoscale static and dynamic analysis. In the present study, torsional vibration of CNTs was investigated according to nonlocal stress and strain gradient theories. Effects of the small scale parameters to the non-dimensional frequency were obtained. Results were compared with the Molecular Dynamics Simulation and Lattice Dynamics. Strain Gradient Theory has shown more weakening effect on CNT according to the Stress Gradient Theory. Combination of both theories gives more acceptable results rather than the classical and stress or strain gradient theory according to Lattice Dynamics.

Keywords: torsional vibration, carbon nanotubes, nonlocal gradient theory, stress, strain

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Authors: Grienggrai Rajchakit

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This paper is concerned with the exponential stability of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, a switching rule for the exponential stability of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of LMIs. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Keywords: exponential stability, hybrid systems, time-varying delays, lyapunov-krasovskii functional, leibniz-newton's formula

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Ayman Baklizi

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Based on type II censored data, we consider interval estimation of the quantiles of the two-parameter exponential distribution and the difference between the quantiles of two independent two-parameter exponential distributions. We derive asymptotic intervals, Bayesian, as well as intervals based on the generalized pivot variable. We also include some bootstrap intervals in our comparisons. The performance of these intervals is investigated in terms of their coverage probabilities and expected lengths.

Keywords: asymptotic intervals, Bayes intervals, bootstrap, generalized pivot variables, two-parameter exponential distribution, quantiles

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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