Search results for: mathematical method

Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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Authors: A. Charlangsut, M. Boonthienthong, N. Rugthaicharoencheep

Abstract:

This paper proposes a mathematical model for transmission expansion employing optimization method with scenario analysis approach. Economic transmission planning, on the other hand, seeks investment opportunities so that network expansions can generate more economic benefits than the costs. This approach can be used as a decision model for building new transmission lines added to the existing transmission system minimizing costs of the entire system subject to various system’s constraints and consider of loss value of transmission system and N-1 checking. The results show that the proposed model is efficient to be applied for the larger scale of power system topology.

Keywords: Transmission Expansion Planning, Economic Dispatch, Scenario Analysis, Contingency.

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: Melting furnace, inverse heat transfer, enthalpy method, Levenberg–Marquardt Method.

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Authors: Meryem Kanzari, Rabah Boukhanouf, Hatem G. Ibrahim

Abstract:

Indirect Evaporative Cooling process has the advantage of supplying cool air at constant moisture content. However, such system can only supply air at temperatures above wet bulb temperature. This paper presents a mathematical model for a Sub-wet bulb temperature indirect evaporative cooling arrangement that can overcome this limitation and supply cool air at temperatures approaching dew point and without increasing its moisture content. In addition, the use of porous ceramics as wet media materials offers the advantage of integration into building elements. Results of the computer show the proposed design is capable of cooling air to temperatures lower than the ambient wet bulb temperature and achieving wet bulb effectiveness of about 1.17.

Keywords: Indirect evaporative cooling, porous ceramic, sub-wet bulb temperature.

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Authors: Talaat S. El-Danaf

Abstract:

In this paper, we develop quartic nonpolynomial spline method for the numerical solution of third order two point boundary value problems. It is shown that the new method gives approximations, which are better than those produced by other spline methods. Convergence analysis of the method is discussed through standard procedures. Two numerical examples are given to illustrate the applicability and efficiency of the novel method.

Keywords: Quartic nonpolynomial spline, Two-point boundary value problem.

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Authors: Jesús Everardo Olguín Tiznado, Rafael García Martínez, Claudia Camargo Wilson, Juan Andrés López Barreras, Everardo Inzunza González, Javier Ordorica Villalvazo

Abstract:

The response surface methodology (RSM) is a collection of mathematical and statistical techniques useful in the modeling and analysis of problems in which the dependent variable receives the influence of several independent variables, in order to determine which are the conditions under which should operate these variables to optimize a production process. The RSM estimated a regression model of first order, and sets the search direction using the method of maximum / minimum slope up / down MMS U/D. However, this method selects the step size intuitively, which can affect the efficiency of the RSM. This paper assesses how the step size affects the efficiency of this methodology. The numerical examples are carried out through Monte Carlo experiments, evaluating three response variables: efficiency gain function, the optimum distance and the number of iterations. The results in the simulation experiments showed that in response variables efficiency and gain function at the optimum distance were not affected by the step size, while the number of iterations is found that the efficiency if it is affected by the size of the step and function type of test used.

Keywords: RSM, dependent variable, independent variables, efficiency, simulation

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Authors: Jožef Ritonja

Abstract:

The biochemical industry is one of the most important modern industries. Biochemical reactors are crucial devices of the biochemical industry. The essential bioprocess carried out in bioreactors is the fermentation process. A thorough insight into the fermentation process and the knowledge how to control it are essential for effective use of bioreactors to produce high quality and quantitatively enough products. The development of the control system starts with the determination of a mathematical model that describes the steady state and dynamic properties of the controlled plant satisfactorily, and is suitable for the development of the control system. The paper analyses the fermentation process in bioreactors thoroughly, using existing mathematical models. Most existing mathematical models do not allow the design of a control system for controlling the fermentation process in batch bioreactors. Due to this, a mathematical model was developed and presented that allows the development of a control system for batch bioreactors. Based on the developed mathematical model, a control system was designed to ensure optimal response of the biochemical quantities in the fermentation process. Due to the time-varying and non-linear nature of the controlled plant, the conventional control system with a proportional-integral-differential controller with constant parameters does not provide the desired transient response. The improved adaptive control system was proposed to improve the dynamics of the fermentation. The use of the adaptive control is suggested because the parameters’ variations of the fermentation process are very slow. The developed control system was tested to produce dairy products in the laboratory bioreactor. A carbon dioxide concentration was chosen as the controlled variable. The carbon dioxide concentration correlates well with the other, for the quality of the fermentation process in significant quantities. The level of the carbon dioxide concentration gives important information about the fermentation process. The obtained results showed that the designed control system provides minimum error between reference and actual values of carbon dioxide concentration during a transient response and in a steady state. The recommended control system makes reference signal tracking much more efficient than the currently used conventional control systems which are based on linear control theory. The proposed control system represents a very effective solution for the improvement of the milk fermentation process.

Keywords: Bioprocess engineering, biochemical reactor, fermentation process, modeling, adaptive control.

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Authors: A. M. Maqableh

Abstract:

Modelling techniques for a fluid coupling taken from published literature have been extended to include the effects of the filling and emptying of the coupling with oil and the variation in losses when the coupling is partially full. In the model, the fluid flow inside the coupling is considered to have two principal velocity components; one circumferentially about the coupling axis (centrifugal head) and the other representing the secondary vortex within the coupling itself (vortex head). The calculation of liquid mass flow rate circulating between the two halves of the coupling is based on: the assumption of a linear velocity variation in the circulating vortex flow; the head differential in the fluid due to the speed difference between the two shafts; and the losses in the circulating vortex flow as a result of the impingement of the flow with the blades in the coupling and friction within the passages between the blades.

Keywords: Fluid Coupling, Mathematical Modelling, partially filled.

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Authors: Moghadazadeh Zahra, Towfighi Jafar, Mofarahi Masoud

Abstract:

This article is presented an experimental and modeling study of a four-bed pressure swing adsorption process using zeolite13X to provide oxygen-enriched air. The binary mixture N2/O2 (79/21 vol %) was used as a feed stream. The effects of purge/feed ratio (P/F), adsorption pressure, cyclic time and product flow rate on product purity and recovery under nonisothermal condition were studied. The adsorption dynamics of process were determined using a mathematical model incorporated mass and energy balances. A Mathlab code using finite difference method was developed to solve the set of coupled differential-algebraic equations, and the simulation results are agreed well with experimental results.

Keywords: Pressure swing adsorption (PSA), Oxygen, Zeolite 13X.

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Authors: Ricardo Espinosa

Abstract:

The coherent Self-Averaging (CSA), is a new method proposed in this work; applied to simulated signals evoked potentials related to events (ERP) to find the wave P300, useful systems in the brain computer interface (BCI). The CSA method cleans signal in the time domain of white noise through of successive averaging of a single signal. The method is compared with the traditional method, coherent averaging or synchronized (CA), showing optimal results in the improvement of the signal to noise ratio (SNR). The method of CSA is easy to implement, robust and applicable to any physiological time series contaminated with white noise

Keywords: Evoked potentials, wave P300, Coherent Self-averaging, brain - computer interface (BCI).

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

Abstract:

In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: Bifurcation, heteroclinic orbits, steady state, traveling wave.

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Authors: Abdallah A. Hlayel

Abstract:

Operations research science (OR) deals with good success in developing and applying scientific methods for problem solving and decision-making. However, by using OR techniques, we can enhance the use of computer decision support systems to achieve optimal management for institutions. OR applies comprehensive analysis including all factors that effect on it and builds mathematical modeling to solve business or organizational problems. In addition, it improves decision-making and uses available resources efficiently. The adoption of OR by universities would definitely contributes to the development and enhancement of the performance of OR techniques. This paper provides an understanding of the structures, approaches and models of OR in problem solving and decisionmaking.

Keywords: Best candidates' method, decision making, decision support system, operations research.

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Authors: Jiří F. Urbánek, David Král

Abstract:

Small and Middle Enterprises (SME) have a specific mission, characteristics, and behavior in global business competitive environments. They must respect policy, rules, requirements and standards in all their inherent and outer processes of supply - customer chains and networks. Paper aims and purposes are to introduce computational assistance, which enables us the using of prevailing operation system MS Office (SmartArt...) for mathematical models, using DYVELOP (Dynamic Vector Logistics of Processes) method. It is providing for SMS´s global environment the capability and profit to achieve its commitment regarding the effectiveness of the quality management system in customer requirements meeting and also the continual improvement of the organization’s and SME´s processes overall performance and efficiency, as well as its societal security via continual planning improvement. DYVELOP model´s maps - the Blazons are able mathematically - graphically express the relationships among entities, actors, and processes, including the discovering and modeling of the cycling cases and their phases. The blazons need live PowerPoint presentation for better comprehension of this paper mission – added value analysis. The crisis management of SMEs is obliged to use the cycles for successful coping of crisis situations.  Several times cycling of these cases is a necessary condition for the encompassment of the both the emergency event and the mitigation of organization´s damages. Uninterrupted and continuous cycling process is a good indicator and controlling actor of SME continuity and its sustainable development advanced possibilities.

Keywords: Blazons, computational assistance, DYVELOP method, small and middle enterprises.

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Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: Jun Wan, Zehua Chen, Yingwu Chen, Zhidong Bai

Abstract:

This paper proposes a novel feature extraction method, based on Discrete Wavelet Transform (DWT) and K-L Seperability (KLS), for the classification of Functional Data (FD). This method combines the decorrelation and reduction property of DWT and the additive independence property of KLS, which is helpful to extraction classification features of FD. It is an advanced approach of the popular wavelet based shrinkage method for functional data reduction and classification. A theory analysis is given in the paper to prove the consistent convergence property, and a simulation study is also done to compare the proposed method with the former shrinkage ones. The experiment results show that this method has advantages in improving classification efficiency, precision and robustness.

Keywords: classification, functional data, feature extraction, K-Lseperability, wavelet.

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Authors: Amir Abolfazl Suratgar, Mohammad Bagher Tavakoli, Abbas Hoseinabadi

Abstract:

In this paper a modification on Levenberg-Marquardt algorithm for MLP neural network learning is proposed. The proposed algorithm has good convergence. This method reduces the amount of oscillation in learning procedure. An example is given to show usefulness of this method. Finally a simulation verifies the results of proposed method.

Keywords: Levenberg-Marquardt, modification, neural network, variable learning rate.

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Authors: L. Sriphong, A. Chaidedgumjorn, K. Chaisuroj

Abstract:

A spectrophotometric method was developed for simultaneous quantification of pseudoephedrine hydrochloride (PSE) triprolidine hydrochloride (TRI) using second derivative method (zero-crossing technique). The second derivative amplitudes of PSE and TRI were measured at 271 and 321 nm, respectively. The calibration curves were linear in the range of 200 to 1,000 g/ml for PSE and 10 to 50 g/ml for TRI. The method was validated for specificity, accuracy, precision, limit of detection and limit of quantitation. The proposed method was applied to the assaying and dissolution of PSE and TRI in commercial tablets without any chemical separation. The results were compared with those obtained by the official USP31 method and statistical tests showed that there is no significant between the methods at 95% confidence level. The proposed method is simple, rapid and suitable for the routine quality control application. KeywordsTriprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

Keywords: Triprolidine, Pseudoephedrine, Derivative spectrophotometry, Dissolution testing.

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Authors: Zanariah Abdul Majid, Mohamed Suleiman

Abstract:

The aim of this paper is to investigate the performance of the developed two point block method designed for two processors for solving directly non stiff large systems of higher order ordinary differential equations (ODEs). The method calculates the numerical solution at two points simultaneously and produces two new equally spaced solution values within a block and it is possible to assign the computational tasks at each time step to a single processor. The algorithm of the method was developed in C language and the parallel computation was done on a parallel shared memory environment. Numerical results are given to compare the efficiency of the developed method to the sequential timing. For large problems, the parallel implementation produced 1.95 speed-up and 98% efficiency for the two processors.

Keywords: Numerical methods, parallel method, block method, higher order ODEs.

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Authors: Ek Ngoy, A F Mulaba-Bafubiandi

Abstract:

Cobalt was acid nitric leached from a mixed cobaltcopper oxide with variable acid concentration. Resulting experimental data were used to analyze effects of increase in acid concentration, based on a shrinking core model of the process. The mathematical simulation demonstrated that the time rate of the dissolution mechanism is an increasing function of acid concentration. It was also shown that the magnitude of the acid concentration effect is time dependent and the increase in acid concentration is more effective at earlier stage of the dissolution than at later stage. The remaining process parameters are comprehensively affected by acid concentration and their interaction is synergetic.

Keywords: Acid effect, Cobalt, Cobalt-copper oxide, Leaching, Simulation

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Authors: Smarajit Ghosh , Karma Sonam Sherpa

Abstract:

This paper reports a new and accurate method for load-flow solution of radial distribution networks with minimum data preparation. The node and branch numbering need not to be sequential like other available methods. The proposed method does not need sending-node, receiving-node and branch numbers if these are sequential. The proposed method uses the simple equation to compute the voltage magnitude and has the capability to handle composite load modelling. The proposed method uses the set of nodes of feeder, lateral(s) and sub lateral(s). The effectiveness of the proposed method is compared with other methods using two examples. The detailed load-flow results for different kind of load-modellings are also presented.

Keywords: Load−flow, Feeder, Lateral, Power, Voltage, Composite, Exponential

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Authors: Chen Zhang, Bernhard Schwarz-Röhr, Alexander Härting

Abstract:

To acquire accurate ship motions at the center of gravity, a single low-cost inertial sensor is utilized and applied on board to measure ship oscillating motions. As observations, the three axes accelerations and three axes rotational rates provided by the sensor are used. The mathematical model of processing the observation data includes determination of the distance vector between the sensor and the center of gravity in x, y, and z directions. After setting up the transfer matrix from sensor’s own coordinate system to the ship’s body frame, an extended Kalman filter is applied to deal with nonlinearities between the ship motion in the body frame and the observation information in the sensor’s frame. As a side effect, the method eliminates sensor noise and other unwanted errors. Results are not only roll and pitch, but also linear motions, in particular heave and surge at the center of gravity. For testing, we resort to measurements recorded on a small vessel in a well-defined sea state. With response amplitude operators computed numerically by a commercial software (Seaway), motion characteristics are estimated. These agree well with the measurements after processing with the suggested method.

Keywords: Extended Kalman filter, nonlinear estimation, sea trial, ship motion estimation.

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Authors: Yasin Tadayonrad, Alassane Ballé Ndiaye

Abstract:

Most of the supply chain networks have many nodes starting from the suppliers’ side up to the customers’ side that each node sends/receives the raw materials/products from/to the other nodes. One of the major concerns in this kind of supply chain network is finding the best schedule for loading/unloading the shipments through the whole network by which all the constraints in the source and destination nodes are met and all the shipments are delivered on time. One of the main constraints in this problem is the loading/unloading capacity in each source/destination node at each time slot (e.g., per week/day/hour). Because of the different characteristics of different products/groups of products, the capacity of each node might differ based on each group of products. In most supply chain networks (especially in the Fast-moving consumer goods (FMCG) industry), there are different planners/planning teams working separately in different nodes to determine the loading/unloading timeslots in source/destination nodes to send/receive the shipments. In this paper, a mathematical problem has been proposed to find the best timeslots for loading/unloading the shipments minimizing the overall delays subject to respecting the capacity of loading/unloading of each node, the required delivery date of each shipment (considering the lead-times), and working-days of each node. This model was implemented on Python and solved using Python-MIP on a sample data set. Finally, the idea of a heuristic algorithm has been proposed as a way of improving the solution method that helps to implement the model on larger data sets in real business cases, including more nodes and shipments.

Keywords: Supply chain management, transportation, multiple-multiple network, timeslots management, mathematical modeling, mixed integer programming.

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: Dimitra Alexiou

Abstract:

In an urban area the location allocation of emergency services mobile units, such as ambulances, police patrol cars must be designed so as to achieve a prompt response to demand locations. In this paper the partition of a given urban network into distinct sub-networks is performed such that the vertices in each component are close and simultaneously the sums of the corresponding population in the sub-networks are almost uniform. The objective here is to position appropriately in each sub-network a mobile emergency unit in order to reduce the response time to the demands. A mathematical model in framework of graph theory is developed. In order to clarify the corresponding method a relevant numerical example is presented on a small network.

Keywords: Distances, Emergency Service, Graph Partition, location.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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Authors: Bogusław Schreyer

Abstract:

The paper enquires on the two methods of the wheeled robot braking torque control. Those two methods are applied when the adhesion coefficient under left side wheels is different from the adhesion coefficient under the right side wheels. In case of the select-low (SL) method the braking torque on both wheels is controlled by the signals originating from the wheels on the side of the lower adhesion. In the select-high (SH) method the torque is controlled by the signals originating from the wheels on the side of the higher adhesion. The SL method is securing stable and secure robot behaviors during the braking process. However, the efficiency of this method is relatively low. The SH method is more efficient in terms of time and braking distance but in some situations may cause wheels blocking. It is important to monitor the velocity of all wheels and then take a decision about the braking torque distribution accordingly. In case of the SH method the braking torque slope may require significant decrease in order to avoid wheel blocking.

Keywords: Select-high method, select-low method, torque distribution, wheeled robot.

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Authors: J. Ritonja, B. Grcar

Abstract:

For the synchronous generator simulation and analysis and for the power system stabilizer design and synthesis a mathematical model of synchronous generator is needed. The model has to accurately describe dynamics of oscillations, while at the same time has to be transparent enough for an analysis and sufficiently simplified for design of control system. To study the oscillations of the synchronous generator against to the rest of the power system, the model of the synchronous machine connected to an infinite bus through a transmission line having resistance and inductance is needed. In this paper, the linearized reduced order dynamic model of the synchronous generator connected to the infinite bus is presented and analysed in details. This model accurately describes dynamics of the synchronous generator only in a small vicinity of an equilibrium state. With the digression from the selected equilibrium point the accuracy of this model is decreasing considerably. In this paper, the equations’ descriptions and the parameters’ determinations for the linearized reduced order mathematical model of the synchronous generator are explained and summarized and represent the useful origin for works in the areas of synchronous generators’ dynamic behaviour analysis and synchronous generator’s control systems design and synthesis. The main contribution of this paper represents the detailed analysis of the accuracy of the linearized reduced order dynamic model in the entire synchronous generator’s operating range. Borders of the areas where the linearized reduced order mathematical model represents accurate description of the synchronous generator’s dynamics are determined with the systemic numerical analysis. The thorough eigenvalue analysis of the linearized models in the entire operating range is performed. In the paper, the parameters of the linearized reduced order dynamic model of the laboratory salient poles synchronous generator were determined and used for the analysis. The theoretical conclusions were confirmed with the agreement of experimental and simulation results.

Keywords: Eigenvalue analysis, mathematical model, power system stability, synchronous generator.

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Authors: Anton Purnama

Abstract:

Multiport diffusers are the effective engineering devices installed at the modern marine outfalls for the steady discharge of effluent streams from the coastal plants, such as municipal sewage treatment, thermal power generation and seawater desalination. A mathematical model using a two-dimensional advection-diffusion equation based on a flat seabed and incorporating the effect of a coastal tidal current is developed to calculate the compounded concentration following discharges of desalination brine from a sea outfall with multiport diffusers. The analytical solutions are computed graphically to illustrate the merging of multiple brine plumes in shallow coastal waters, and further approximation will be made to the maximum shoreline's concentration to formulate dilution of a multiport diffuser discharge.

Keywords: Desalination brine discharge, mathematical model, multiport diffuser, two sea outfalls.

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Authors: Petri Solanti, Russell Klein

Abstract:

Many designers are asking for an automated path from an abstract mathematical MATLAB model to a high-quality Register-Transfer Level (RTL) hardware description. Manual transformations of MATLAB or intermediate code are needed, when the design abstraction is changed. Design conversion is problematic as it is multidimensional and it requires many different design steps to translate the mathematical representation of the desired functionality to an efficient hardware description with the same behavior and configurability. Yet, a manual model conversion is not an insurmountable task. Using currently available design tools and an appropriate design methodology, converting a MATLAB model to efficient hardware is a reasonable effort. This paper describes a simple and flexible design methodology that was developed together with several design teams.

Keywords: Design methodology, high-level synthesis, MATLAB, verification.

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Authors: Francisco Echarte, José Javier Astrain, Alberto Córdoba, Jesús Villadangos

Abstract:

Ontologies and tagging systems are two different ways to organize the knowledge present in the current Web. In this paper we propose a simple method to model folksonomies, as tagging systems, with ontologies. We show the scalability of the method using real data sets. The modeling method is composed of a generic ontology that represents any folksonomy and an algorithm to transform the information contained in folksonomies to the generic ontology. The method allows representing folksonomies at any instant of time.

Keywords: Folksonomies, ontologies, OWL, semantic web.

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