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By J. M. McKinley

Mineral exploration programmes around the world use data from remote sensing, geophysics, and direct sampling. On a regional scale, the combination of airborne geophysics and ground-based geochemical sampling can aid geological mapping and mineral exploration. Since airborne geophysical and traditional soil-sampling data are generated at different spatial resolutions, they are not immediately comparable due to their different sampling density. Several geostatistical techniques, including indicator cokriging and collocated cokriging, can be used to integrate different types of data into a geostatistical model. However, with increasing numbers of variables the inference of the crosscovariance model required for cokriging can be demanding in terms of effort and computational time. In this paper a Gaussian-based Bayesian updating approach is applied to integrate airborne radiometric data and ground-sampled geochemical soil data to maximize information generated from the soil survey, enabling more accurate geological interpretation for the exploration and development of natural resources. The Bayesian updating technique decomposes the collocated estimate into two models: prior and likelihood models. The prior model is built from primary information and the likelihood model is built from secondary information. The prior model is then updated with the likelihood model to build the final model. The approach allows multiple secondary variables to be simultaneously integrated into the mapping of the primary variable. The Bayesian updating approach is demonstrated using a case study from Northern Ireland. The geostatistical technique was used to improve the resolution of soil geochemistry, at a density of one sample per 2 km2, by integrating more closely measured airborne geophysical data from the GSNI Tellus Survey, measured over a footprint of 65 x 200 m. The directly measured geochemistry data were considered as primary data and the airborne radiometric data were used as secondary data. The approach produced more detailed updated maps and in particular enhanced information on the mapped distributions of zinc, copper, and lead. The enhanced delineation of an elongated northwest/southeast trending zone in the updated maps strengthened the potential for discovering stratabound base metal deposits..

Jan 1, 2014

By M. Dworzanowski

Beneficiation, in the context of this paper, has two distinct definitions. From an economic perspective, beneficiation relates to adding value to a mined raw material. From a metallurgy perspective, beneficiation relates to processes used to upgrade the mined raw material. Clearly then, ?economic beneficiation? is dependent on ?metallurgical beneficiation?. South Africa possesses the world?s largest mineral resources by value and is a significant global producer of many mined commodities. Significant metallurgical beneficiation of ores does occur in South Africa. The role of metallurgy in economic beneficiation will be examined in terms of current practice and the potential for expansion. South Africa?s main mining commodities will be covered ? namely gold, platinum, coal, iron ore, manganese, chromium, vanadium, copper, nickel, titanium, zirconium, uranium, and diamonds.

Sep 1, 2013

By Ö. Erdem

The investment decision making process in the insurance and finance industries is affected by new advances such as simulation techniques. These advances have improved the discounted cash flow method (DCF). In DCF, a dynamic and flexible model construction is not possible because it does not consider uncertain conditions. Each project should be evaluated taking into account the related uncertainties because the related uncertainties determine the characterization of the project. Related uncertainties can be processed in dynamic DCF, which is applicable to both financial and non-financial industries with different kind of uncertainties, such as power generation and petroleum projects. The dynamic DCF method can estimate net present value (NPV) while managing related project uncertainties with a simulation method like Monte Carlo Simulation. The simulation method is preferred because its output is unbiased. Therefore, a more realistic financial evaluation of the project can be concluded. In spite of the improvement of dynamic DCF, this project evaluation method is not used frequently in mining industry. However, the mining industry is ideally suited to this concept because it is highly dependent on estimations such as orebody size and ore grade. During the project evaluation stage, these uncertainties can be included with the dynamic DCF method. This study aims to contribute to increasing the usage of this method in mining projects. A copper reserve in Turkey is selected as a case study to apply uncertainty assessment for the evaluation of NPV.

Jan 1, 2012

By D. van Rensburg

Jointed rock slopes are generally stable, as there is no freedom of movement for blocks of rock. In an open- pit mining environment, blasting opens up space into which blocks of rock can fail, resulting in the common occurrence of slope failure. Prior to the blasting of a trim pattern, the immediate highwall is scaled, where loose rock material is removed by means of a mechanical scaler. As mining of the pit progresses, the height of the scaled highwall from the pit floor progressively increases. These highwalls are never scaled again for the remainder of the pit life, and time-dependant deterioration contributes to these highwalls becoming subject to rockfall and, sometimes, slope failure. This paper documents the development of a South African innovation, a remote-controlled mechanical highwall scaler, a world first for the mining industry. The scaler will enable open-pit highwalls to be scaled from crest to toe whenever the need arises. It will reduce the risk associated with highwalls and deliver on the Anglo American promise of producing safe, profitable platinum.

Jan 1, 2012

By I. Mc Dougall

Finite element models were generated of two submerged arc furnaces of different geometries. A 48MW circular furnace and a 68MW 6-in-line rectangular furnace were studied. The electrodes, raw material, slag and molten metal were included in the model. ANSYS/Multiphysics was used to predict the current density distribution in the electrodes, raw material, slag and molten metal as a result of the three phase AC current. The effect of the electrode immersion on the current path was studied. The ?proximity effect? caused a pronounced asymmetry in the electrode currents in the circular furnace, whilst the electrode currents in the rectangular furnace exhibited radial symmetry. The current distribution in the melt in both furnaces indicated that the bulk of the current flows between phases. The current density is greatest between electrodes. Results were compared to qualitatively similar published work, operating experience and results of furnace dig-outs.

Jan 1, 2007

By P. R. Brenchley

Main ore pass systems should last the life of a mine, and too often expensive and hazardous remedial measures are required to repair a damaged ore pass in an attempt to extend its life. In order to maximize the life expectancy of all ore passes at Moab Khotsong, ?wearing blocks? and ?softer support? systems, combined with basic rock engineering principles, have been implemented. Failure of an ore pass can have severe financial implications, both indirectly because the ore pass cannot deliver the broken rock either from level to level or directly in the shaft ore pass system to the required level for tramming to take place, and directly due to the cost of the repair work that is required. Several factors need to betaken into consideration so that production interruptions are eliminated or minimized. Investigations of damaged ore passes at Moab Khotsong and surrounding mines revealed some interesting mechanisms of damage, and some innovative methods of reducing or eliminating the damage have been implemented at Moab Khotsong. The system design was based on 30 years, experience in main shaft rock passes. The design was to counteract scaling, hang-ups and dust problems associated with main rock passes, and the objective was to increase the life of rockpasses. These problems, including the initial design aspects to try and eliminate the repair measures, are discussed in detail.

Jan 1, 2006

The distribution of chrome spinels in a magnetically fractionated ilmenite concentrate sourced from the Murray Basin was characterized by XRF assaying, quantitative electron microprobeanalysis, grain mapping, automated mineral phase clustering, and modal analysis. At least 14 distinct chrome spinel types were present in the concentrate. There is considerable variation in the amount of each chrome spinel type present, although a high-Mg, high-Al phase makes up close to 45 per cent of the total spinel population. Magnetic fractionation results showed significant variation in the composition and relative abundance of spinels reporting to each fraction. Low magnetic field strength fractions (ie. high susceptibility grains) were dominated by chrome spinels that are mid-range in Al and Cr. These spinels have the highest magnetite, ulvospinel and Fe(Al,Cr)2O4components. In comparison, the high field strength fractions (i.e. low susceptibility grains) have the majority of the grains with high-Al contents indicating a higher proportion of Mg(Al,Cr)2O4component. Spinels high in a (Al,Cr)2.67O4non-stoichiometriccomponent are absent at low field strengths but tend to be concentrated in the high field strength, non-magnetic fractions. Intermediate field strength fractions tend to exhibit a broad spread in spinel compositional types. A mild roast treatment of the sample had no clear effect on the distribution of chrome spinels between different magnetic fractions, but it did cause a change in the magnetic properties of the accompanying ilmenite grains. The effect of more extreme roasting conditions on the magnetic properties of the chrome spinels is to be determined.

Jan 1, 2003

By M. Shapiro, L. A. le Grange, B. Henning

Effective pyrometallurgical process vessel design requires accurate assessment of the heat fluxes through the walls of the furnace. This is particularly important for freeze lining operation which is designed to protect refractory materials exposed to chemically corrosive molten contents, or facilitate high temperature operation when the refractory materials are used at conditions close to their service limits. Numerical modelling of fluid flow and heat transfer in process vessels is often used to aid in the design of process vessels. Sophisticated models are used to analyse the three dimensional flow and heat transfer predicting the effects of electrical heating, magnetic stirring, buoyancy, shear forces, various cooling effects and ultimately heat fluxes at the walls of the furnace and refractory. Traditionally these models are applied to the separate single fluid systems in a vessel such as the freeboard region including the arc, the slag region and the metal bath. Boundary conditions such as shear forces and heat fluxes between connecting regions such as the slag and metal bath are either estimated or carried over from separate solutions. Shortcomings in these traditional approaches include the estimation of sometimes critical boundary conditions leading to unreliable heat flux calculations. Also when boundary conditions are carried over between solutions, the process is difficult to set up, time-consuming and finally not fully coupled. In this paper the definition and results of a fully integrated numerical model of a complete arc furnace are presented. The most important mechanisms acting in an arc furnace were considered, including the fields of electrical potential, current, magnetism, momentum, heat transfer and radiation. Temperature dependant properties included electrical conductivity, density, viscosity, and thermal conductivity. The geometry consists of the freeboard, the arc, slag, metal baths and different refractory regions. Although the combined model of air, slag and metal would be defined as a multi-phase problem it is not solved as such. Instead the different fluids are separated by sets of special solid baffles. These baffles allow the implicit transfer of current, magnetism, heat transfer and shear forces between the different fluids and disallow mixing of the separate fluids. The strengths of the integrated model are threefold: Firstly, it provides robustness in defining the geometry and boundary conditions for the overall model. Secondly, it provides the capability to switch on and off individual mechanisms such as buoyancy, magnetic stirring and shear forces in order to observe their individual importance. Finally, it provides a useful tool in the design process through its ability to obtain results of parameter changes in short time scales.

Jan 1, 2004

In exploiting the ultra-deep, narrow reef ore bodies of the Witwatersrand, the ventilation and cooling systems within the stopes play a critical role because of high concentrations of active workers. This paper examines the heat, ventilation and cooling effects of a number of different stoping layouts for narrow reef mining in ultra-deep operations in very hot rock. The stope ventilation and cooling needs are driven primarily by the difference between the air temperature and that of the rock front being excavated. These needs depend on the face utilization, geometry, face advance (rate and direction), layout, backfill, use of water and machinery1,2,3. Detailed studies of different stoping configurations have been undertaken for mining operations extending to depths of 5000m below surface, where virgin rock temperatures approach 70°C. Extensive work has been completed with regard to evaluating ventilation and cooling requirements to maintain air reject temperatures of 28°C wet-bulb and better. This knowledge is being used to determine overall cooling requirements, reduce operational costs and maximize the efficiency of cooling systems. These issues are important when considering both the local and regional air conditioning systems and the most effective application of in-stope chilled water.

Jan 1, 2001

By C. Haberfield, J. Szymakowski

Recent studies by the authors into the behaviour of jointed rock masses using direct shear testing have confirmed that joint spacing has a significant effect on rock mass strength. The rock mass failure envelopes assessed from these tests have been compared to failure envelopes obtained using the Hoek-Brown GSI criterion. Good agreement between measured and estimated GSI strength envelopes where obtained when joint spacing was considered in the assessment of GSI. Les études récentes conduites par les auteurs sur le comportement des joints rocheux employant l'essai direct de cisaillement ont confirmé que l'espacement a un effet significatif sur la force de la masse rocheuse. Les enveloppes de ruptures obtenues pour ces essais ont été comparées à l'enveloppe de rupture obtenue en utilisant le critère GSI Hoek-Brown. Une bonne corrélation a été constatée entre les enveloppes obtenues expérimentalement et les enveloppes calculées par la méthode GSI quand l'espacement des joints a été pris en considération dans l'évaluation de GSI. Kuerzliche Untersuchungen der Autoren betreffs Reaktionen von gebrochenen Felsmassen zu direkter Scherkraft, bestaetigen, dass die Abstaende von Rissen einen deutlichen Einfluss auf den Widerstand der Felsmassen hat. Die Bruchbereiche der Felsmassen die von diesen Untersuchungen entwickelt wurden, wurden verglichen mit den Bruchbereichen, die man mit der Anwendund der Hoek-Brown GSI Formulierung erhaelt. Eine gute Uebereinstimmung zwischen gemessenen und errechneten GSI Festigkeitsbereichen wurde erzielt, wenn der Abstand der Risse in der Berechnung der GSI in Betracht gezogen wurde.

Jan 1, 2003

By K. G. Tshilombo

It should be possible to use an oxygen probe to follow iron removal during converting, if local equilibrium is established between iron in the matte and the iron oxides in the fayalitic slag. The oxygen activity is expected to increase strongly as the iron content of the matte decreases (and the iron activity in the matte drops) while the iron oxide activity in the slag remains constant. To test this idea, oxygen activities were measured in synthetic mattes (made up of mixtures of Cu2S, FeS and Ni3S2) when in contact with silica saturated SiO2-FeO slags, and silica and (initially) magnetite saturated SiO2-FeO-Fe3O4slags. The measurements were performed on laboratory scale at 1250°C, using an oxygen probe consisting of an MgO-stabilized zirconia electrolyte and Fe/FeO reference, and containing the sample in a silica crucible. Electrical contact to the matte was by means of a platinum wire. The measured oxygen activity was sensitive to the iron content of the matte, and insensitive to the composition of the gas atmosphere over the melt. The measured oxygen activity was generally close to that predicted by Fact Sage calculations. This indicates that such oxygen activity measurements could be useful to monitor iron removal during converting of nickel-copper-iron mattes.

Jan 1, 2007

By C. Lemmer

The resolution with which the different categories of resources are forecast for Witwatersrand gold reefs should ideally tie in with block sizes that are optimal in terms of the variability structures of the reefs. A tool, called the ?variancegram?, is proposed as a basis for block size choice. A variancegram is intrinsic to the particular reef and mine concerned. A further requirement is the ability to attach global confidence limits to weighted average estimates built up from combinations of local kriged estimates. Approximations to derive global kriging variances based on variables derived from local kriging deliver hugely inflated results if ordinary kriging is used, and markedly better, but not accurate, values if simple kriging is used. These approximations improve as the number of samples used in kriging each block is increased. It is shown that the behaviour of the different components of the global kriging variance with increasing number of samples, all differs, but they all link to the variancegram for the particular reef. The variancegram can thus be used to correct the different components to the values they would have had if all samples were used in kriging each block, and so deliver the ?correct? global kriging variance, even though only a limited number of samples were used in kriging each block. The desirability of having very stable solutions implemented in production systems is taken into account in the proposals. It is anticipated that the same variancegram findings will also hold for other densely sampled deposits, but this remains to be investigated.

Jan 1, 2014

Resolution Copper Mine is planned to be a 2000 m deep panel cave mine with virgin rock temperatures above 80°C in rock with a high crystalline silica content. The planned run-of-mine production rate is 120 kt/day. The project is in prefeasibility evaluation. This paper discusses features of the ventilation system design, which include multiple ventilation shafts with total flow of about 3000 m³/s and both surface and underground refrigeration systems with more than 140 MW total capacity. This will be a very challenging mine to ventilate, but this work has demonstrated that it will be technically achievable with the application of existing technology.

Jan 1, 2014

By I. Bock

Selective Blast Mining (SBM) makes use of milli-second sequential blasting technology to separate the valuable reef material from waste rock in the blasting operation at stope faces in the mining of tabular ore bodies such as exist in the gold and platinum mines in South Africa. The waste rock is cast blast to the back of the stoping area, and the reef material is fractured and deposited close to the stope face. Only the reef material is transported to the surface. A simplified economic model is presented to evaluate the economic benefits of SBM. Although premature, in that adequate experimental demonstration of the validity of the model has not yet been possible, the model is presented since it indicates substantial benefits in the case of narrow reef gold mines. It is suggested that many marginal mines should seriously consider SBM. Benefits can also be realised in platinum mines, but a lot more experimental work is necessary to establish cost parameters more reliably. Some practical experience in the use of SBM in the mining of the UG2 reef is presented.

Jan 1, 1998

By W. I. van Drunick

AngloGold Ashanti Metallurgy has recently been involved in the successful installation of intelligent, expert control systems on the milling circuits. The benefits of expert systems in these highly interactive circuits are obvious. Existing comminution tools, which have been developed and can now be incorporated into online control, include improved modelling techniques and understanding, robust and competent simulation methods, sampling techniques, and optimization methods. The minerals processing industry has seen the benefits of predominantly research-based centres turning their focus to commercial applications of comminution circuit modelling packages, which in turn can be utilized within expert control systems. Expert mill control has been successfully installed at AngloGold Ashanti South Africa?s Mponeng and Kopanang Gold Plants. Expert control has also been installed at AngloGold Ashanti?s West African Sadiola Mine operation. The implementation of the systems has produced a number of positive outcomes. Plant surveys usually result in the identification of sub-optimal areas, and the control philosophy is then configured to ensure that these areas (along with the entire circuit) are optimized and maintained. Outdated PID loops have generally resulted in oscillatory control with large amplitude deviations from set-point. Significant improvements in SAR Metallurgy operations have been realized, firstly through achieving stability in the load and cyclone control, and secondly through online identification and implementation of optimized set-point conditions for mill mass, discharge density, etc. Soft sensors are configured to accurately estimate parameters that were historically not measurable, viz. breakage rate, mill load condition, onlinekWh/t-75 microns, mill discharge density and cyclone overflow grading. The Mponeng Plant system achieved circuit stability and improved overall grind. The Plant was able to pay back the control installation after 3 months, based on the additional recovery obtained from the finer grind. The system at Kopanang Plant has also resulted in enhanced plant recovery as a result of a finer grind and a lower residue gold content. The payback for this system was calculated at approximately 6 months. AngloGold Ashanti Metallurgy is currently expanding the installation of expert control to its other operations. It is also evaluating the performance of various suppliers of advanced control systems.

Jan 1, 2005

Mr G H Park was born and brought up in Zimbabwe, in mining from the University of the Witwatersrand. Starting as a Learner Official at Rand Mines, he went Mr D J van Niekerk was educated at Helpmekaar Boys' High School in Johannesburg and the University of Pretoria. Mr C J C Janse van Vuuren was educated at Klerksdorp High School, Pretoria Technical Colege, the University of Pretoria, and Unisa. He holds the folowing degrees: BSc (I&S), BSc Hons (Met Pta), ND (Met Tech), AEP (Unisa). Prof. R F Sandenbergh was educated at the Afrikaanse Hoerskool Germiston and the University of Pretoria. He holds the degrees of B Ing (Chem), M Ing (Chem), and D Ing (Metal). President's Award Professor Jannie van Deventer, Head of the Department of Metalurgical Engineering at the University of Stelenbosch, has been honoured with one of the five President's Awards for 1990. These awards are made by the CSIR's Foundation for Research Development. G R Bozzoli Awards* Prof. Alan Kemp, Dean of the Faculty of Engineering at the University of the Witwatersrand, has appealed to industry not to cut bursary funding during recessionary times.

Jan 1, 1990

By R. H. Estrada-Ruiz

This work analyses a new approach to estimates bubble size distribution of froth surfaces using artificial neural networks (ANN).Also, the robustness of ANN to interpret images with illumination perturbations, produced by light problems or dirt attached to the window of the video camera is evaluated. The experimental work was carried out in a laboratory flotation column, instrumented with an image acquisition system. The images were processed making use of a perceptron model with a hidden layer, sigmoidal transfer function and unitary bias, and the ANN trained with a back propagation algorithm. The results of validation show that ANN are reliable for learning and producing generalized predictions of the froth mean bubble diameter and bubble size distribution, when the model is trained using a database that contains information on the illumination intensity. Keywords: image analysis, neural networks, bubble diameter, bubble size distribution.

Jan 1, 2009

By M Lipalile, A B. Tunono, A W. Naismith

Konkola No 3 shaft experienced severe mining induced stress and time related deterioration in ground conditions in an area where an over-cut and bench (OCB) mining method was used to extract a shallow dipping wide orebody. This caused an unacceptable risk for safe mining operations to sustain the required levels of production. After a review of the conditions it was decided to change the mining method to CASCADE to recover ore in the affected area and modify the OCB method and use a modified over-cut and bench method (MOCB) for new mining sections. This paper describes the geotechnical criteria included to derive the mining standards for the MOCB. The geotechnical risks are identified and taken into account to develop stope design parameters, stoping sequences and support requirements. A monitoring programme to assess conditions as mining progresses is also discussed.

Jan 1, 2005

By H. Aykul

The choice of which mining method to use at many large surface coal mines is often dicated by what machinery is available or what experience the mine management can offer. One of the most significant surface coal mines in Turkey is owned and operated by the Turkish National Coal Board, located to the west of the city of Kütahya. The Seyitömer Lignite Enterprise (SLE) extracts low quality coal, the majority of which is supplied to an adjacent power station. The coal seems at SLE contain bands of ash which under normal mining conditions are extracted with the coal. This increases the ash content of the run of mine coal and results in lower efficiency at the power station and financial penalties for SLE. In this paper, therefore, selection of the best possible equipment and production method was identified to achieve high selective mining at SLE. The research found that two different high selective mining methods were suitable for selective excavation of the B3 seam, which were hydraulic excavator and truck and surface miner and truck combinations. It was also found that high selective excavation could provide the desired coal quality at 52% lower costs when the whole process (excavation, transportation, processing, etc.) was considered. Keywords: coal mining, surface mining, selective mining.

Jan 1, 2007

By M. Arlandi, J. C. Monge

In this paper, the finite element method is used to obtain deformations of a rock tunnel. More than 3,000 numerical simulations and calculations were carried out. The analysis of this results has allowed to achieve mathematical formulations and graphs, to obtain in advance support monitored displacements in tunnelling construction, so they can be predicted before excavation and supporting woks. The application of the presented formulations and charts will aid engineers to control tunnel monitoring, reducing decision time when problems occur. The analysis is limited to cases involving elastic behaviour of the terrain for tunnels of average to good quality in rock, and to excavation sections of average or smaller dimensions for road tunnels. The results show that, in all cases, mathematical expressions to obtain induced displacements around tunnel excavations, have similar pattern than Kirsch (1898) expressions for circular excavations. As corollary of the achieved results, a method to estimate in situ natural geostress ratio K0=sh/sv , by means of convergence measurements, is presented. In diesem Beitrag wurden die Verschiebungen eines Tunnels durch die Methode de Finiten Elemente berechnet. Mehr als 3000 numerische Simulationen und Berechnungen wurden ausgeführt. Die Analyse dieser Resultate hat es ermöglicht, mathematische Formeln und Grafiken zu entwickeln, die zur Voraussage der Verschiebungen in Tunnel dienen, auch unter Betrachtung der verschiedenartigen Abstützungen. So können die Verschiebungen vor den Erdarbeiten und dem Bau der Abstützung abgeschätzt werden. Die abgeleiteten Formeln und Grafiken werden vor allem einen grossen Dienst für Ingenieure bei der Mithilfe zu zeitsparenden Entscheidungen im Tunnelbau und bei der Tunnelkontrolle leisten. Die analysierten Fälle sind auf eine elastische Modellierung des Baugrunds beschränkt, sowie auf eine mittlere bis gute Qualität des Felsens und auf die Aushebung von Abtragungsabschnitten mittlerer oder geringer Grösse für den Strassenverkehr. Die Resultate zeigen, dass in allen Fällen die hergeleiteten Formeln zur Berechnung der durch den Tunnelbau verursachten Verschiebungen um den Tunnel die gleiche mathematische Struktur haben wie diejenigen von Kirsch (1898) für kreisförmigen Bodenaushub. Als Korollarium der ausgeführten Berechnungen wird eine Methode zur Abschätzung der vorherrschenden in situ Geospannungs-Verhälniss K0=sh/sv angegeben, die von den Messungen der Verschiebungen im Tunnel ausgeht. Dans cet article, la méthode des éléments finis est utilisée pour obtenir les déformations d’un tunnel creusé dans la roche. Plus de 3000 simulations numériques et calculs ont été effectuées. L’analyse de ces résultats a permis de définir des modèles mathématiques et des abaques afin de prédire, avant l’excavation et les travaux de soutènement, les déplacements auscultés pendant la construction du tunnel. L’application de ces modèles et abaques permettra donc aux ingénieurs de contrôler les déplacements durant l’auscultation du tunnel et de réduire le temps de décision lorsque des problèmes surviennent. L’analyse est limitée au cas du comportement élastique du terrain pour des tunnels creusés dans de la roche de moyenne a bonne qualité, et à de sections d’excavation de petites à moyennes dimensions pour des tunnels routiers. Les résultats montrent que, dans tous les cas, les expressions mathématiques permettant d’obtenir les déplacements induits autour des excavations de tunnel, présentent des similitudes avec celles de Kirsch (1898) pour des excavations circulaires. Comme corollaire aux résultats obtenus, une méthode pour estimer le rapport des

Jan 1, 2003