Search results for: nonlinear exponential model.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8176

Search results for: nonlinear exponential model.

7306 Model of Appropriate Science Teaching for Mathayomsuksa 3 (Grade 9) in Ang-Thong Province

Authors: Lertlop, W

Abstract:

This research aims to study the appropriate model of Science teaching for students, academic achievement and to survey students- attitudes toward using appropriate for students in Mathayomsuksa 3 in Ang-Thong province. The research results were as follows: 1. The appropriate model of Science teaching for Mathayomsuksa 3 students in Ang-Thong province including these following five steps: Step 1. The introduction of the lessons. Step 2. Setting the hypothesis. Step 3. Doing the experiment /survey. Step 4. Making conclusion. Step 5. Applying to daily life or other subjects. 2. There is no significant difference between using appropriate model teaching and regular teaching at 0.05 level significant difference. 3. There is a significant difference between before and after teaching using appropriate model of Science teaching at 0.05 level. 4. The satisfaction of students- attitudes to using the appropriate model of Science teaching for students was in intermediate level.

Keywords: Pedagogy, science teaching model, Ang-Thong province.

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7305 Improved Robust Stability and Stabilization Conditions of Discrete-time Delayed System

Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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7304 Existence and Stability Analysis of Discrete-time Fuzzy BAM Neural Networks with Delays and Impulses

Authors: Chao Wang, Yongkun Li

Abstract:

In this paper, the discrete-time fuzzy BAM neural network with delays and impulses is studied. Sufficient conditions are obtained for the existence and global stability of a unique equilibrium of this class of fuzzy BAM neural networks with Lipschitzian activation functions without assuming their boundedness, monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time. Some numerical examples are given to demonstrate the effectiveness of the obtained results.

Keywords: Discrete-time fuzzy BAM neural networks, ımpulses, global exponential stability, global asymptotical stability, equilibrium point.

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7303 On the Symbol Based Decision Feedback Equalizer

Authors: Mohammed Nafie

Abstract:

Decision Feedback equalizers (DFEs) usually outperform linear equalizers for channels with intersymbol interference. However, the DFE performance is highly dependent on the availability of reliable past decisions. Hence, in coded systems, where reliable decisions are only available after decoding the full block, the performance of the DFE will be affected. A symbol based DFE is a DFE that only uses the decision after the block is decoded. In this paper we derive the optimal settings of both the feedforward and feedback taps of the symbol based equalizer. We present a novel symbol based DFE filterbank, and derive its taps optimal settings. We also show that it outperforms the classic DFE in terms of complexity and/or performance.

Keywords: Coding, DFE, Equalization, Exponential Channelmodels.

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7302 Knowledge Management Model for Research Projects Masters Program

Authors: Víctor Hugo Medina García, Darío Alejandro Segura Torres

Abstract:

This paper presents the adaptation of the knowledge management model and intellectual capital measurement NOVA to the needs of work or research project must be developed when conducting a program of graduate-level master. Brackets are added in each of the blocks which is represented in the original model NOVA and which allows to represent those involved in each of these.

Keywords: Knowledge management, masters programs, Nova model, research projects

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7301 Toward a Risk Assessment Model Based On Multi-Agent System for Cloud Consumer

Authors: Saadia Drissi, Siham Benhadou, Hicham Medromi

Abstract:

The cloud computing is an innovative paradigm that introduces several changes in technology that have resulted a new ways for cloud providers to deliver their services to cloud consumers mainly in term of security risk assessment, thus, adapting a current risk assessment tools to cloud computing is a very difficult task due to its several characteristics that challenge the effectiveness of risk assessment approaches. As consequence, there is a need of risk assessment model adapted to cloud computing. This paper requires a new risk assessment model based on multi-agent system and AHP model as fundamental steps towards the development of flexible risk assessment approach regarding cloud consumers.

Keywords: Cloud computing, risk assessment model, multi-agent system, AHP model, cloud consumer.

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7300 Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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7299 2D and 3D Unsteady Simulation of the Heat Transfer in the Sample during Heat Treatment by Moving Heat Source

Authors: Z. Veselý, M. Honner, J. Mach

Abstract:

The aim of the performed work is to establish the 2D and 3D model of direct unsteady task of sample heat treatment by moving source employing computer model on the basis of finite element method. Complex boundary condition on heat loaded sample surface is the essential feature of the task. Computer model describes heat treatment of the sample during heat source movement over the sample surface. It is started from 2D task of sample cross section as a basic model. Possibilities of extension from 2D to 3D task are discussed. The effect of the addition of third model dimension on temperature distribution in the sample is showed. Comparison of various model parameters on the sample temperatures is observed. Influence of heat source motion on the depth of material heat treatment is shown for several velocities of the movement. Presented computer model is prepared for the utilization in laser treatment of machine parts.

Keywords: Computer simulation, unsteady model, heat treatment, complex boundary condition, moving heat source.

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7298 The Estimation of Human Vital Signs Complexity

Authors: L. Bikulciene, E. Venskaityte, G. Jarusevicius

Abstract:

Nonstationary and nonlinear signals generated by living complex systems defy traditional mechanistic approaches, which are based on homeostasis. Previous our studies have shown that the evaluation of the interactions of physiological signals by using special analysis methods is suitable for observation of physiological processes. It is demonstrated the possibility of using deep physiological model, based on the interpretation of the changes of the human body’s functional states combined with an application of the analytical method based on matrix theory for the physiological signals analysis, which was applied on high risk cardiac patients. It is shown that evaluation of cardiac signals interactions show peculiar for each individual functional changes at the onset of hemodynamic restoration procedure. Therefore, we suggest that the alterations of functional state of the body, after patients overcome surgery can be complemented by the data received from the suggested approach of the evaluation of functional variables’ interactions.

Keywords: Cardiac diseases, Complex systems theory, ECG analysis, matrix analysis.

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7297 Adaptive Gaussian Mixture Model for Skin Color Segmentation

Authors: Reza Hassanpour, Asadollah Shahbahrami, Stephan Wong

Abstract:

Skin color based tracking techniques often assume a static skin color model obtained either from an offline set of library images or the first few frames of a video stream. These models can show a weak performance in presence of changing lighting or imaging conditions. We propose an adaptive skin color model based on the Gaussian mixture model to handle the changing conditions. Initial estimation of the number and weights of skin color clusters are obtained using a modified form of the general Expectation maximization algorithm, The model adapts to changes in imaging conditions and refines the model parameters dynamically using spatial and temporal constraints. Experimental results show that the method can be used in effectively tracking of hand and face regions.

Keywords: Face detection, Segmentation, Tracking, Gaussian Mixture Model, Adaptation.

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7296 External Effects on Dynamic Competitive Model of Domestic Airline and High Speed Rail

Authors: Shih-Ching Lo, Yu-Ping Liao

Abstract:

Social-economic variables influence transportation demand largely. Analyses of discrete choice model consider social-economic variables to study traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. Also, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, models with different social-economic variables, which are oil price, GDP per capita, CPI and economic growth rate, are compared. From the results, the model with the oil price is better than models with the other social-economic variables.

Keywords: forecasting, passenger volume, dynamic competitive model, social-economic variables, oil price.

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7295 Javanese Character Recognition Using Hidden Markov Model

Authors: Anastasia Rita Widiarti, Phalita Nari Wastu

Abstract:

Hidden Markov Model (HMM) is a stochastic method which has been used in various signal processing and character recognition. This study proposes to use HMM to recognize Javanese characters from a number of different handwritings, whereby HMM is used to optimize the number of state and feature extraction. An 85.7 % accuracy is obtained as the best result in 16-stated vertical model using pure HMM. This initial result is satisfactory for prompting further research.

Keywords: Character recognition, off-line handwritingrecognition, Hidden Markov Model.

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7294 Research on Reservoir Lithology Prediction Based on Residual Neural Network and Squeeze-and- Excitation Neural Network

Authors: Li Kewen, Su Zhaoxin, Wang Xingmou, Zhu Jian Bing

Abstract:

Conventional reservoir prediction methods ar not sufficient to explore the implicit relation between seismic attributes, and thus data utilization is low. In order to improve the predictive classification accuracy of reservoir lithology, this paper proposes a deep learning lithology prediction method based on ResNet (Residual Neural Network) and SENet (Squeeze-and-Excitation Neural Network). The neural network model is built and trained by using seismic attribute data and lithology data of Shengli oilfield, and the nonlinear mapping relationship between seismic attribute and lithology marker is established. The experimental results show that this method can significantly improve the classification effect of reservoir lithology, and the classification accuracy is close to 70%. This study can effectively predict the lithology of undrilled area and provide support for exploration and development.

Keywords: Convolutional neural network, lithology, prediction of reservoir lithology, seismic attributes.

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7293 Improving Image Segmentation Performance via Edge Preserving Regularization

Authors: Ying-jie Zhang, Li-ling Ge

Abstract:

This paper presents an improved image segmentation model with edge preserving regularization based on the piecewise-smooth Mumford-Shah functional. A level set formulation is considered for the Mumford-Shah functional minimization in segmentation, and the corresponding partial difference equations are solved by the backward Euler discretization. Aiming at encouraging edge preserving regularization, a new edge indicator function is introduced at level set frame. In which all the grid points which is used to locate the level set curve are considered to avoid blurring the edges and a nonlinear smooth constraint function as regularization term is applied to smooth the image in the isophote direction instead of the gradient direction. In implementation, some strategies such as a new scheme for extension of u+ and u- computation of the grid points and speedup of the convergence are studied to improve the efficacy of the algorithm. The resulting algorithm has been implemented and compared with the previous methods, and has been proved efficiently by several cases.

Keywords: Energy minimization, image segmentation, level sets, edge regularization.

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7292 FPGA Implementation of RSA Encryption Algorithm for E-Passport Application

Authors: Khaled Shehata, Hanady Hussien, Sara Yehia

Abstract:

Securing the data stored on E-passport is a very important issue. RSA encryption algorithm is suitable for such application with low data size. In this paper the design and implementation of 1024 bit-key RSA encryption and decryption module on an FPGA is presented. The module is verified through comparing the result with that obtained from MATLAB tools. The design runs at a frequency of 36.3 MHz on Virtex-5 Xilinx FPGA. The key size is designed to be 1024-bit to achieve high security for the passport information. The whole design is achieved through VHDL design entry which makes it a portable design and can be directed to any hardware platform.

Keywords: RSA, VHDL, FPGA, modular multiplication, modular exponential.

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7291 A New Approach for Network Reconfiguration Problem in Order to Deviation Bus Voltage Minimization with Regard to Probabilistic Load Model and DGs

Authors: Mahmood Reza Shakarami, Reza Sedaghati

Abstract:

Recently, distributed generation technologies have received much attention for the potential energy savings and reliability assurances that might be achieved as a result of their widespread adoption. The distribution feeder reconfiguration (DFR) is one of the most important control schemes in the distribution networks, which can be affected by DGs. This paper presents a new approach to DFR at the distribution networks considering wind turbines. The main objective of the DFR is to minimize the deviation of the bus voltage. Since the DFR is a nonlinear optimization problem, we apply the Adaptive Modified Firefly Optimization (AMFO) approach to solve it. As a result of the conflicting behavior of the single- objective function, a fuzzy based clustering technique is employed to reach the set of optimal solutions called Pareto solutions. The approach is tested on the IEEE 32-bus standard test system.

Keywords: Adaptive Modified Firefly Optimization (AMFO), Pareto solutions, feeder reconfiguration, wind turbines, bus voltage.

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7290 Analytical Model to Predict the Shear Capacity of Reinforced Concrete Beams Externally Strengthened with CFRP Composites Conditions

Authors: Rajai Al-Rousan

Abstract:

This paper presents a proposed analytical model for predicting the shear strength of reinforced concrete beams strengthened with CFRP composites as external reinforcement. The proposed analytical model can predict the shear contribution of CFRP composites of RC beams with an acceptable coefficient of correlation with the tested results. Based on the comparison of the proposed model with the published well-known models (ACI model, Triantafillou model, and Colotti model), the ACI model had a wider range of 0.16 to 10.08 for the ratio between tested and predicted ultimate shears at failure. Also, an acceptable range of 0.27 to 2.78 for the ratio between tested and predicted ultimate shears by the Triantafillou model. Finally, the best prediction (the ratio between the tested and predicted ones) of the ultimate shear capacity is observed by using Colotti model with a range of 0.20 to 1.78. Thus, the contribution of the CFRP composites as external reinforcement can be predicted with high accuracy by using the proposed analytical model.

Keywords: Predicting, shear capacity, reinforced concrete, beams, strengthened, externally, CFRP composites.

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7289 Accurate Crosstalk Analysis for RLC On-Chip VLSI Interconnect

Authors: Susmita Sahoo, Madhumanti Datta, Rajib Kar

Abstract:

This work proposes an accurate crosstalk noise estimation method in the presence of multiple RLC lines for the use in design automation tools. This method correctly models the loading effects of non switching aggressors and aggressor tree branches using resistive shielding effect and realistic exponential input waveforms. Noise peak and width expressions have been derived. The results obtained are at good agreement with SPICE results. Results show that average error for noise peak is 4.7% and for the width is 6.15% while allowing a very fast analysis.

Keywords: Crosstalk, distributed RLC segments, On-Chip interconnect, output response, VLSI, noise peak, noise width.

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7288 An Enhanced Artificial Neural Network for Air Temperature Prediction

Authors: Brian A. Smith, Ronald W. McClendon, Gerrit Hoogenboom

Abstract:

The mitigation of crop loss due to damaging freezes requires accurate air temperature prediction models. An improved model for temperature prediction in Georgia was developed by including information on seasonality and modifying parameters of an existing artificial neural network model. Alternative models were compared by instantiating and training multiple networks for each model. The inclusion of up to 24 hours of prior weather information and inputs reflecting the day of year were among improvements that reduced average four-hour prediction error by 0.18°C compared to the prior model. Results strongly suggest model developers should instantiate and train multiple networks with different initial weights to establish appropriate model parameters.

Keywords: Time-series forecasting, weather modeling.

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7287 Discovering the Dimension of Abstractness: Structure-Based Model that Learns New Categories and Categorizes on Different Levels of Abstraction

Authors: Georgi I. Petkov, Ivan I. Vankov, Yolina A. Petrova

Abstract:

A structure-based model of category learning and categorization at different levels of abstraction is presented. The model compares different structures and expresses their similarity implicitly in the forms of mappings. Based on this similarity, the model can categorize different targets either as members of categories that it already has or creates new categories. The model is novel using two threshold parameters to evaluate the structural correspondence. If the similarity between two structures exceeds the higher threshold, a new sub-ordinate category is created. Vice versa, if the similarity does not exceed the higher threshold but does the lower one, the model creates a new category on higher level of abstraction.

Keywords: Analogy-making, categorization, learning of categories, abstraction, hierarchical structure.

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7286 A Mean–Variance–Skewness Portfolio Optimization Model

Authors: Kostas Metaxiotis

Abstract:

Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.

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7285 The Gasoil Hydrofining Kinetics Constants Identification

Authors: C. Patrascioiu, V. Matei, N. Nicolae

Abstract:

The paper describes the experiments and the kinetic parameters calculus of the gasoil hydrofining. They are presented experimental results of gasoil hidrofining using Mo and promoted with Ni on aluminum support catalyst. The authors have adapted a kinetic model gasoil hydrofining. Using this proposed kinetic model and the experimental data they have calculated the parameters of the model. The numerical calculus is based on minimizing the difference between the experimental sulf concentration and kinetic model estimation.

Keywords: Hydrofining, kinetic, modeling, optimization.

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7284 Neural Network Implementation Using FPGA: Issues and Application

Authors: A. Muthuramalingam, S. Himavathi, E. Srinivasan

Abstract:

.Hardware realization of a Neural Network (NN), to a large extent depends on the efficient implementation of a single neuron. FPGA-based reconfigurable computing architectures are suitable for hardware implementation of neural networks. FPGA realization of ANNs with a large number of neurons is still a challenging task. This paper discusses the issues involved in implementation of a multi-input neuron with linear/nonlinear excitation functions using FPGA. Implementation method with resource/speed tradeoff is proposed to handle signed decimal numbers. The VHDL coding developed is tested using Xilinx XC V50hq240 Chip. To improve the speed of operation a lookup table method is used. The problems involved in using a lookup table (LUT) for a nonlinear function is discussed. The percentage saving in resource and the improvement in speed with an LUT for a neuron is reported. An attempt is also made to derive a generalized formula for a multi-input neuron that facilitates to estimate approximately the total resource requirement and speed achievable for a given multilayer neural network. This facilitates the designer to choose the FPGA capacity for a given application. Using the proposed method of implementation a neural network based application, namely, a Space vector modulator for a vector-controlled drive is presented

Keywords: FPGA implementation, multi-input neuron, neural network, nn based space vector modulator.

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7283 Solution of First kind Fredholm Integral Equation by Sinc Function

Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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7282 Dissipation Capacity of Steel Building with Fiction Pendulum Base-Isolation System

Authors: A. Ras, I. Nait Zerrad, N. Benmouna, N. Boumechra

Abstract:

Use of base isolators in the seismic design of structures has attracted considerable attention in recent years. The major concern in the design of these structures is to have enough lateral stability to resist wind and seismic forces. There are different systems providing such isolation, among them there are friction- pendulum base isolation systems (FPS) which are rather widely applied nowadays involving to both affordable cost and high fundamental periods. These devices are characterised by a stiff resistance against wind loads and to be flexible to the seismic tremors, which make them suitable for different situations. In this paper, a 3D numerical investigation is done considering the seismic response of a twelve-storey steel building retrofitted with a FPS. Fast nonlinear time history analysis (FNA) of Boumerdes earthquake (Algeria, May 2003) is considered for analysis and carried out using SAP2000 software. Comparisons between fixed base, bearing base isolated and braced structures are shown in a tabulated and graphical format. The results of the various alternatives studies to compare the structural response without and with this device of dissipation energy thus obtained were discussed and the conclusions showed the interesting potential of the FPS isolator. This system may to improve the dissipative capacities of the structure without increasing its rigidity in a significant way which contributes to optimize the quantity of steel necessary for its general stability.

Keywords: Steel structure, energy dissipation, friction-pendulum system, nonlinear analysis.

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7281 Sway Reduction on Gantry Crane System using Delayed Feedback Signal and PD-type Fuzzy Logic Controller: A Comparative Assessment

Authors: M.A. Ahmad

Abstract:

This paper presents the use of anti-sway angle control approaches for a two-dimensional gantry crane with disturbances effect in the dynamic system. Delayed feedback signal (DFS) and proportional-derivative (PD)-type fuzzy logic controller are the techniques used in this investigation to actively control the sway angle of the rope of gantry crane system. A nonlinear overhead gantry crane system is considered and the dynamic model of the system is derived using the Euler-Lagrange formulation. A complete analysis of simulation results for each technique is presented in time domain and frequency domain respectively. Performances of both controllers are examined in terms of sway angle suppression and disturbances cancellation. Finally, a comparative assessment of the impact of each controller on the system performance is presented and discussed.

Keywords: Gantry crane, anti-sway control, DFS controller, PD-type Fuzzy Logic Controller.

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7280 Variable Rough Set Model and Its Knowledge Reduction for Incomplete and Fuzzy Decision Information Systems

Authors: Da-kuan Wei, Xian-zhong Zhou, Dong-jun Xin, Zhi-wei Chen

Abstract:

The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is the generalization of the variable precision rough set model for incomplete information system and that of rough set model for incomplete and fuzzy decision information system. The knowledge reduction and heuristic algorithm, built on the method and theory of precision reduction, are proposed.

Keywords: Rough set, Incomplete and fuzzy decision information system, Limited valued tolerance relation, Knowledge reduction, Variable rough set model

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7279 DMC with Adaptive Weighted Output

Authors: Ahmed Abbas, M.R. M Rizk, Mohamed El-Sayed

Abstract:

This paper presents a new adaptive DMC controller that improves the controller performance in case of plant-model mismatch. The new controller monitors the plant measured output, compares it with the model output and calculates weights applied to the controller move. Simulations show that the new controller can help improve control performance and avoid instability in case of severe model mismatches.

Keywords: Adaptive control, dynamic matrix control, DMC, model predictive control

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7278 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

Authors: Suparman

Abstract:

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: Piecewise, Bayesian, reversible jump MCMC, segmentation.

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7277 Model-Based Software Regression Test Suite Reduction

Authors: Shiwei Deng, Yang Bao

Abstract:

In this paper, we present a model-based regression test suite reducing approach that uses EFSM model dependence analysis and probability-driven greedy algorithm to reduce software regression test suites. The approach automatically identifies the difference between the original model and the modified model as a set of elementary model modifications. The EFSM dependence analysis is performed for each elementary modification to reduce the regression test suite, and then the probability-driven greedy algorithm is adopted to select the minimum set of test cases from the reduced regression test suite that cover all interaction patterns. Our initial experience shows that the approach may significantly reduce the size of regression test suites.

Keywords: Dependence analysis, EFSM model, greedy algorithm, regression test.

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