Search results for: Optimal Equilibrium Capacity.

Authors: Siliang Wang, Minghui Wang, Jun Hu

Abstract:

A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: M. P. Nanda Kumar, K. Dheeraj

Abstract:

The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: Inverse Optimal Control, Radial basis function neural network, Controller Design.

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Authors: Yasser M. Moustafa, Rania E. Morsi, Mohammed Fathy

Abstract:

Multiwall carbon nanotubes, prepared by chemical vapor deposition, have an average diameter of 60-100 nm as shown by High Resolution Transmittance Electron Microscope, HR-TEM. The Multiwall carbon nanotubes (MWCNTs) were further characterized using X-ray Diffraction and Raman Spectroscopy. Mercury uptake capacity of MWCNTs was studied using batch adsorption method at different concentration ranges up to 150 ppm. Mercury concentration (before and after the treatment) was measured using cold vapor atomic absorption spectroscopy. The effect of time, concentration, pH and adsorbent dose were studied. MWCNT were found to perform complete absorption in the sub-ppm concentrations (parts per billion levels) while for high concentrations, the adsorption efficiency was 92% at the optimum conditions; 0.1 g of the adsorbent at 150 ppm mercury (II) solution. The adsorption of mercury on MWCNTs was found to follow the Freundlich adsorption isotherm and the pseudo-second order kinetic model.

Keywords: Cold Vapor Atomic Absorption Spectroscopy, Hydride System, Mercury Removing, Multi Wall Carbon Nanotubes.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

The optimal grid spacing and turbulence model for the 2D numerical analysis of a vertical-axis water turbine (VAWaterT) operating in a 2 m/s freestream current has been investigated. The results of five different spatial domain discretizations and two turbulence models (k-ω SST and k-ε RNG) have been compared, in order to gain the optimal y+ parameter distribution along the blade walls during a full rotor revolution. The resulting optimal mesh has appeared to be quite similar to that obtained for the numerical analysis of a vertical-axis wind turbine.

Keywords: CFD, vertical axis water turbine, NACA 0025, blade y+.

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Authors: Hamed Sabahno

Abstract:

In this paper, an inventory model with finite and constant replenishment rate, price dependant demand rate, time value of money and inflation, finite time horizon, lead time and exponential deterioration rate and with the objective of maximizing the present worth of the total system profit is developed. Using a dynamic programming based solution algorithm, the optimal sequence of the cycles can be found and also different optimal selling prices, optimal order quantities and optimal maximum inventories can be obtained for the cycles with unequal lengths, which have never been done before for this model. Also, a numerical example is used to show accuracy of the solution procedure.

Keywords: Deteriorating items, Dynamic programming, Finitereplenishment rate, Inventory control, Operation Research.

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Authors: Edikan E. Akpanibah, Okwigbedi Oghen’Oro

Abstract:

In this paper, we studied the optimal portfolio selection in a defined contribution (DC) pension scheme with multiple contributors under constant elasticity of variance (CEV) model and the impact of stochastic additional voluntary contribution on the investment strategies. We assume that the voluntary contributions are stochastic and also consider investments in a risk free asset and a risky asset to increase the expected returns of the contributing members. We derived a stochastic differential equation which consists of the members’ monthly contributions and the invested fund and obtained an optimized problem with the help of Hamilton Jacobi Bellman equation. Furthermore, we find an explicit solution for the optimal investment strategy with stochastic voluntary contribution using power transformation and change of variables method and the corresponding optimal fund size was obtained. We discussed the impact of the voluntary contribution on the optimal investment strategy with numerical simulations and observed that the voluntary contribution reduces the optimal investment strategy of the risky asset.

Keywords: DC pension fund, Hamilton-Jacobi-Bellman, optimal investment strategies, power transformation method, stochastic, voluntary contribution.

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Authors: Manish K. Khandelwal, P. Bera, A. Chakrabarti

Abstract:

This article presents a numerical study of the doublediffusive mixed convection in a vertical channel filled with porous medium by using non-equilibrium model. The flow is assumed fully developed, uni-directional and steady state. The controlling parameters are thermal Rayleigh number (RaT ), Darcy number (Da), Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer coefficient (H), and porosity scaled thermal conductivity ratio (γ). The Brinkman-extended non-Darcy model is considered. The governing equations are solved by spectral collocation method. The main emphasize is given on flow profiles as well as heat and solute transfer rates, when two diffusive components in terms of buoyancy ratio are in favor (against) of each other and solid matrix and fluid are thermally non-equilibrium. The results show that, for aiding flow (RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a certain value of H, beyond that decreases smoothly and converges to a constant, whereas in case of opposing flow (RaT = -1000), the result is same for N = 0 and 1. The variation of Nuf in (N, Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases (aiding and opposing) the flow destabilize on increasing N by inviting point of inflection or flow separation on the velocity profile. Overall, the buoyancy force have significant impact on the non-Darcy mixed convection under LTNE conditions.

Keywords: buoyancy ratio, mixed convection, non-Darcy model, thermal non-equilibrium

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Authors: Jing Zhang, Jie Chen

Abstract:

In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.

Keywords: Parking system, optimal location, response time, S/R machine.

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Authors: Reza Cheraghi Kootiani, Ariffin Bin Samsuri

Abstract:

To derive the fractional flow equation oil displacement will be assumed to take place under the so-called diffusive flow condition. The constraints are that fluid saturations at any point in the linear displacement path are uniformly distributed with respect to thickness; this allows the displacement to be described mathematically in one dimension. The simultaneous flow of oil and water can be modeled using thickness averaged relative permeability, along the centerline of the reservoir. The condition for fluid potential equilibrium is simply that of hydrostatic equilibrium for which the saturation distribution can be determined as a function of capillary pressure and therefore, height. That is the fluids are distributed in accordance with capillary-gravity equilibrium. This paper focused on the fraction flow of water versus cumulative oil recoveries using Buckley Leverett method. Several field cases have been developed to aid in analysis. Producing watercut (at surface conditions) will be compared with the cumulative oil recovery at breakthrough for the flowing fluid.

Keywords: Fractional Flow, Fluid Saturations, Permeability, Cumulative Oil Recoveries, Buckley Leverett Method.

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Authors: Ehab F. Badran, Guoxiang Gu

Abstract:

We consider optimal channel equalization for MIMO (multi-input/multi-output) time-varying channels in the sense of MMSE (minimum mean-squared-error), where the observation noise can be non-stationary. We show that all ZF (zero-forcing) receivers can be parameterized in an affine form which eliminates completely the ISI (inter-symbol-interference), and optimal channel equalizers can be designed through minimization of the MSE (mean-squarederror) between the detected signals and the transmitted signals, among all ZF receivers. We demonstrate that the optimal channel equalizer is a modified Kalman filter, and show that under the AWGN (additive white Gaussian noise) assumption, the proposed optimal channel equalizer minimizes the BER (bit error rate) among all possible ZF receivers. Our results are applicable to optimal channel equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers, OFDM (orthogonal frequency division multiplexing), and DS (direct sequence) CDMA (code division multiple access) wireless data communication systems. A design algorithm for optimal channel equalization is developed, and several simulation examples are worked out to illustrate the proposed design algorithm.

Keywords: Channel equalization, Kalman filtering, Time-varying systems.

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Authors: Ahmed S. Abdulrasool

Abstract:

Recently sand wall started to gain more attention as the sand is easy to compact by using vibroflotation technique. An advantage of sand wall is the availability of different additives that can be mixed with sand to increase the stiffness of the sand wall and hence to increase its performance. In this paper, the bearing capacity of circular foundation surrounded by sand wall stabilized with lime is evaluated through laboratory testing. The studied parameters include different sand-lime walls depth (H/D) ratio (wall depth to foundation diameter) ranged between (0.0-3.0). Effect of lime percentages on the bearing capacity of skirted foundation models is investigated too. From the results, significant change is occurred in the behavior of shallow foundations due to confinement of the soil. It has been found that (H/D) ratio of 2 gives substantial improvement in bearing capacity, and beyond (H/D) ratio of 2, there is no significant improvement in bearing capacity. The results show that the optimum lime content is 11%, and the maximum increase in bearing capacity reaches approximately 52% at (H/D) ratio of 2.

Keywords: Lime-sand wall, bearing capacity, circular foundation, clay soil.

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Authors: Alireza Dehghani Pilehvarani, Mojtaba Hakimzadeh, Mohammad Jafari Far, Reza Sedaghati

Abstract:

Distributed Generation (DG) can help in reducing the cost of electricity to the costumer, relieve network congestion and provide environmentally friendly energy close to load centers. Its capacity is also scalable and it provides voltage support at distribution level. Hence, DG placement and penetration level is an important problem for both the utility and DG owner. DG allocation and capacity determination is a nonlinear optimization problem. The objective function of this problem is the minimization of the total loss of the distribution system. Also high levels of penetration of DG are a new challenge for traditional electric power systems. This paper presents a new methodology for the optimal placement of DG and penetration level of DG in distribution system based on General Algebraic Modeling System (GAMS) and Genetic Algorithm (GA).

Keywords: Distributed Generation, Location, Loss Reduction, Distribution Network, GA, GAMS.

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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: 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: M. Movahedi Rad

Abstract:

In this study, a general approach to the reliability based limit analysis of laterally loaded piles is presented. In engineering practice the uncertainties play a very important role. The aim of this study is to evaluate the lateral load capacity of free-head and fixed-head long pile when plastic limit analysis is considered. In addition to the plastic limit analysis to control the plastic behaviour of the structure, uncertain bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. The solution to reliability-based problems is obtained by a computer program which is governed by the reliability index calculation.

Keywords: Reliability, laterally loaded pile, residual strain energy, probability, limit analysis.

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Authors: Zeynep Orman, Sabri Arik

Abstract:

This paper presents a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for Cohen-Grossberg neural networks with multiple time delays. The results establish a relationship between the network parameters of the neural system independently of the delay parameters. The results are also compared with the previously reported results in the literature.

Keywords: Equilibrium and stability analysis, Cohen-Grossberg Neural Networks, Lyapunov Functionals.

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Authors: Fulya Aydın, Ayşe Kuleyin

Abstract:

The purpose of this study is to investigate the capacity of natural Turkish zeolite for NH4-N removal from landfill leachate. The effects of modification and initial concentration on the removal of NH4-N from leachate were also investigated. The kinetics of adsorption of NH4-N has been discussed using three kinetic models, i.e., the pseudo-second order model, the Elovich equation, the intraparticle diffuion model. Kinetic parameters and correlation coefficients were determined. Equilibrium isotherms for the adsorption of NH4-N were analyzed by Langmuir, Freundlich and Tempkin isotherm models. Langmuir isotherm model was found to best represent the data for NH4-N.

Keywords: Leachate, Ammonium, zeolite

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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: 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: R. Rajeshkannan, M. Rajasimman, N. Rajamohan

Abstract:

In this study, the sorption of Malachite green (MG) on Hydrilla verticillata biomass, a submerged aquatic plant, was investigated in a batch system. The effects of operating parameters such as temperature, adsorbent dosage, contact time, adsorbent size, and agitation speed on the sorption of Malachite green were analyzed using response surface methodology (RSM). The proposed quadratic model for central composite design (CCD) fitted very well to the experimental data that it could be used to navigate the design space according to ANOVA results. The optimum sorption conditions were determined as temperature - 43.5oC, adsorbent dosage - 0.26g, contact time - 200min, adsorbent size - 0.205mm (65mesh), and agitation speed - 230rpm. The Langmuir and Freundlich isotherm models were applied to the equilibrium data. The maximum monolayer coverage capacity of Hydrilla verticillata biomass for MG was found to be 91.97 mg/g at an initial pH 8.0 indicating that the optimum sorption initial pH. The external and intra particle diffusion models were also applied to sorption data of Hydrilla verticillata biomass with MG, and it was found that both the external diffusion as well as intra particle diffusion contributes to the actual sorption process. The pseudo-second order kinetic model described the MG sorption process with a good fitting.

Keywords: Response surface methodology, Hydrilla verticillata, malachite green, adsorption, central composite design

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Authors: Edikan E. Akpanibah Obinichi C. Mandah Imoleayo S. Asiwaju

Abstract:

In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.

Keywords: Defined contribution pension scheme, extended Hamilton Jacobi Bellman equations, optimal portfolio policies, refund of premium clauses, supplementary premium.

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Authors: Ekow A. Kwofie, Emmanuel K. Anto, Godfred Mensah

Abstract:

In this paper, CYME Distribution software has been used to assess the impacts of solar Photovoltaic (PV) distributed generation (DG) plant on the Electricity Company of Ghana (ECG) 33 kV sub-transmission network at different PV penetration levels. As ECG begins to encourage DG PV interconnections within its network, there has been the need to assess the impacts on the sub-transmission losses and voltage contribution. In Tema, a city in Accra - Ghana, ECG has a 33 kV sub-transmission network made up of 20 No. 33 kV buses that was modeled. Three different locations were chosen: The source bus, a bus along the sub-transmission radial network and a bus at the tail end to determine the optimal location for DG PV interconnection. The optimal location was determined based on sub-transmission technical losses and voltage impact. PV capacities at different penetration levels were modeled at each location and simulations performed to determine the optimal PV penetration level. Interconnection at a bus along (or in the middle of) the sub-transmission network offered the highest benefits at an optimal PV penetration level of 80%. At that location, the maximum voltage improvement of 0.789% on the neighboring 33 kV buses and maximum loss reduction of 6.033% over the base case scenario were recorded. Hence, the optimal location for DG PV integration within the 33 kV sub-transmission utility network is at a bus along the sub-transmission radial network.

Keywords: Distributed generation photovoltaic, DG PV, optimal location, penetration level, sub-transmission network.

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Authors: Imran Khan, Shujaat Ali Khan Tanoli, Nandana Rajatheva

Abstract:

This paper presents an analysis on the capacity and performance of MIMO-OFDM systems. The work is focused on the capacity of MIMO-OFDM systems over rician fading channel, in the case of the channel being known at the receiver only, which is more practical case of the channel. Simple expression for capacity is derived for the case of correlated rician fading. The performance of some MIMO-OFDM implementations with rician fading model is presented using an Alamouti coding scheme and Simulation results are obtained for both capacity and performance analysis.

Keywords: MIMO, OFDM, rician distribution, space time blockcodes (STBC).

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Authors: Wei Bai, Ling-Wei Kong, Ai-Guo Guo

Abstract:

Base on extenics theory, the statistical physical and mechanical properties from laboratory experiments are used to evaluate the bearing capacity of lateritic soil foundation. The properties include water content, bulk density, liquid limit, cohesion, and so on. The matter-element and the dependent function are defined. Then the synthesis dependent degree and the final grade index are calculated. The results show that predicted outcomes can be matched with the in-situ test data, and a evaluate grade associate with bearing capacity can be deduced. The results provide guidance to assess and determine the bearing capacity grade of lateritic soil foundation.

Keywords: Lateritic soil, bearing capacity, extenics theory, plate loading test.

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Authors: N. Rugthaicharoencheep, S. Auchariyamet

Abstract:

Optimal capacitor allocation in distribution systems has been studied for a long times. It is an optimization problem which has an objective to define the optimal sizes and locations of capacitors to be installed. In this works, an overview of capacitor placement problem in distribution systems is briefly introduced. The objective functions and constraints of the problem are listed and the methodologies for solving the problem are summarized.

Keywords: Capacitor Placement, Distribution Systems, Optimization Techniques

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Shashikant R. Kuchekar, Haribhau R. Aher, Priti M. Dhage

Abstract:

The removal vanadium from aqueous solution using natural exchanger was investigated. The effects of pH, contact time and exchanger dose were studied at ambient temperature (25 ⁰C ± 2 ⁰C). The equilibrium process was described by the Langmuir isotherm model with adsorption capacity for vanadium. The natural exchanger i.e. tamarindus seeds powder was treated with formaldehyde and sulpuric acid to increase the adsorptivity of metals. The maximum exchange level was attained as 80.1% at pH 3 with exchanger dose 5 g and contact time 60 min. Method is applied for removal of vanadium from industrial effluents.

Keywords: Industrial effluent, natural ion exchange, Tamarindus indica, vanadium.

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Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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Authors: G.B. Nurlikhina, G.N. Azhimetova, R. M. Ashimova

Abstract:

Currently, one of the main directions is developing of development based on the clustering of economic operations of Kazakhstan, providing for the organization and concentration of production capacity in one region or the most optimal system. In the modern economic literature clustering is regarded as one of the most effective tools to ensure competitive businesses, and improve their business itself.

Keywords: A cluster, food market, innovation cluster.

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