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By Janne Kytökari

Controlling a wide range of minerals processes with single control system is an ordinary way to operate in mines all over the world these days. However the potential of these systems is not yet fully recognized nor utilized. The key issue is to manage the information in a way that enables automating the day-to-day tasks, quality control and safety functions. At the same time it provides means for optimization and constant improvement of processes creating a working environment where the system helps employees to do their key tasks instead of searching, modifying, and transmitting the huge number of information arising every day. The distribution of control system nodes enables the other processes to run heedless of a problem occurring in one of the sub-processes. Also the control room can be in remote location such as in large city removing the need to travel substantially long distances to plant sites every day. When all essential information is brought to the same place there is less risk for a mishap to happen due to information breaks that are often the cause of them. One of the biggest single reasons that result in production losses are break downs of machinery usually caused by normal wear, misuse, incorrect utilization rate etc. For this reason it is important to measure the condition of machines using vibration measurement and diagnostics. By moving from failure or time-based maintenance towards predictive or performance maintenance generates eventually a steady and predictable process but also results in significant long term savings. The mineral process at Talvivaara mine is based on bioheapleaching, whereby metals are leached from ore as a result of bacterial action. Bioleaching is a fairly new technology used in metals recovery. Therefore it is important for the mine to collect and analyze data from different stages of the minerals process. Talvivaara mine?s Metso DNA system has integrated machine condition monitoring and information management. These are not only necessary but also crucial in environmental conditions where the outside temperature can drop below -35°C, where ice and snow dominate the landscape and impact the equipment for four months a year and where distances between equipment can be up to 7.5 kilometers. Keywords: DCS, analyzer, machine condition monitoring, automation, remote communications, optimization, mining, metso DNA, Talvivaara

Sep 1, 2012

The status of utilization of copper ore resources, and the application and development of biohydrometallury technology in the world is reviewed. Based on the characterization of Zambia?s copper resources, biohydrometallurgy technology is shown to be a practical approach to extract and utilize the enormous low grade copper resource, such as ore tailings and low grade copper ore in this country. Through the cooperation of CSU, China and MMMD, Zambia, ?CNMC-CSU Demonstration Base of Biohydrometallurgy Technology in Zambia? was launched and several biohydrometallurgy plants are being constructed. This indicates that the biohdyrometallurgy technology would be applied soon in Zambia and in the whole Africa. Biohydrometallurgy technology stands as an efficient alternative to the traditional pyrometallurgy process and it can be the key to unlock mineral resources value. Keywords: biohydrometallurgy, low grade copper ore, Zambia, Central South University

Sep 1, 2012

By W. H. Cheung

Nickel (Ni) plays a major role in the production of steel and other major alloys. There are two sources of Ni: laterite and sulphide ores. Global reserves of sulphide ores are being rapidly depleted, while there are enormous reserves of Ni laterite, much of it in Australia. As well as being present in huge amounts, Ni laterites have the advantage of containing cobalt (Co), a valuable mineral. Over the past decade, these factors have been driving the industry to explore the processing of Ni laterite. A route that has been used commercially in processing nickel laterite ore involves the thermal activation of the minerals by pre-reduction followed by ammoniacal leaching (Caron). Although this process has been effective in processing the goethite rich laterite minerals, the higher-grade serpentine-based minerals have been shown to be less susceptible to this process. This has been attributed to the formation of inert olivine phases. In this study, we examined the use of an alternative lixiviant, sulphuric acid, in leaching pre-reduced limonite and weathered saprolite nickel laterite ores. The specific aim of this study was to examine the sulphuric acid leaching of Ni and Co from pre-reduced laterite minerals, and to understand the role of mineral transformations in this metal dissolution. Synchrotron based X-ray diffraction was used to examine the transformation of goethite (FeOOH) to spinels and serpentine mineral ((Mg,Fe)3Si2O5(OH)4) to olivine. Reduction tests were carried out using CO and CO2 reducing gas mixtures and temperatures from 400 °C to 700 °C. The rate of formation and disappearance of specific Bragg peaks during reduction of specific minerals were used to derive an understanding of these solid-state reactions. Laboratory based reduction tests and leaching in sulphuric acid were used to validate the effect of these mineral transformations. The results suggest the versatility of sulphuric acid in leaching nickel from spinels and olivine, which was achieved at the expense of lower selectivity. Cobalt dissolution was found to be dependent on the nature of ferro-cobalt alloy formed during reduction.

Jan 1, 2014

Under the AMIRA P9 project the three-product cyclone-an off-shoot of the conventional hydro-cyclone-that produces three distinct products has been developed. The three-product cyclone shows great promise as a classifier in mineral processing. Industrial and pilot plant trials performed to assess its performance in the classification of the UG2 platinum ore, indicate that the presence of an extra overflow product stream that captures the mid-sized particles, provides improved classification efficiency. To assess the split on component density, samples from the feed and product streams were screened and assays by size for chromite (? = 4.8) and silica (? = 2.65) were obtained. Results from tests performed using this type of hydrocyclone in a number of applications indicates that it can be applied successfully in circuit configurations where the conventional hydrocyc-lone is not suitable. Utilising the three-product cyclone to classify the UG2 platinum ore resulted in an intermediate overflow product stream containing the mid-sized low density silicates and relatively fine high density chromite particles while the finer overflow contained mostly fine silicates and chromite particles. The coarse chromite and silicates reported to the underflow. Due to the increased number of products, the method of using efficiency curves was extended to cater for the increased number of products in the three-product cyclone. Although significant differences in the classification performance of the three-product cyclone were noticed with variations in machine variables a consistent method of assessing the performance was applied. The efficiency curve was adopted and applied and separate efficiency curve properties were obtained for each product stream. The methodology was applied to the component data, and efficiency curve proper-ties for each key component were obtained and compared. This paper discusses the application of the efficiency curve to cyclones producing more than two products and extending the methodology to the different components in the feed.

Jan 1, 2014

By Gökçe Törenli, Okay Tutar

"Predicting the performance of plant-scale comminution circuits is essential to monitor the energy use and product size distribution, allowing us to control and optimize the whole process. In the light of this issue, with the assist of recent technologies, simulation techniques utilize the chance of putting the theory into practice in the most accurate way. For this purpose, this study aims to evaluate and optimize the efficiency of a plant-scale ball mill circuit by using perfect-mixing ball mill model on a simulation environment. The comminution circuit is selected from a specific copper-ore processing plant in Turkey. The essential parameters which are required for this study such as fresh feed Bond work index, size distribution etc. are determined by laboratory experiments. The forecasted data which are calculated by third-party software will be compared by the industrial operating data, in order to determine the performance of comminution circuit. In addition to that, this methodology provides a greater ability to analyse, optimize and understand the comminution circuit of ore treatment plant. The authors believe this work will provide supplementary data for further studies on simulation and subsequent optimization of comminution circuits.INTRODUCTION By the assist of mathematical models of the grinding mills and classifiers, simulation of the grinding circuits become more common in comminution because it is relatively economical and able to consider many variables simultaneously. It’s proceeds depends on the accuracy of the models and capability of reflect real operations. Computer-based simulation studies would provide the quantified information about the effects of the proposed changes on the comminution circuit performance in terms of size distribution, mass flow rates, equipment efficiency etc. Then the mentioned data used in order to check the suitability of the current equipment to the modified conditions, and for equipment selection. The outputs of circuit could also be used to estimate downstream flotation circuit performance because the general aim in this study is to The aim of the study is to investigate optimum operating variables and achieve p(80) size of 57 µm and 64 % of -36 µm particle in hydrocyclone overflow stream, which is optimum for that porphyritic copper ore for best concentrate recovery after flotation process in specific copper ore comminution circuit by using modelling and simulation techniques. Sampling survey was carried on the fine ore bin in order to perform Bond work index test and determine work index value (Wi). Thereafter mass balancing, using the size distribution data and tonnages, models for ball mills and hydrocyclone were developed. Finally, the circuit performance were investigated by computer simulations via JKSimMet software."

Jan 1, 2018

By John Ralston, Stephen Grano, Yongjun Peng, Daniel Fornasiero

"A specially designed mill which allowed the control of pH throughout grinding was used to study the effect of grinding conditions on galena flotation and galena separation from pyrite. The changes occurring on the mineral surface during grinding were investigated by EDTA extraction and ToF-SIMS measurements.Galena flotation and galena separation from pyrite were strongly dependent on the type and amount of oxidation species produced on galena and pyrite surfaces under different grinding conditions. Iron oxidation species depressed both galena and pyrite flotation, whilst lead oxidation species activated pyrite flotation but had little effect on galena flotation. Optimum galena flotation and galena selectivity against pyrite were achieved by selecting grinding conditions that enabled lead and iron oxidation production to be controlled.Grinding conditions had a large effect on the flotation of the galena particles of different sizes. Flotation of fine galena particles (-10 µm) was depressed by iron oxidation species derived from the grinding media. Chromium grinding medium decreased the production of iron oxidation species and therefore increased the flotation of fine galena particles."

Jan 1, 2003

By Khoi Nguyen, Luke Keeney

"Hardness" is an important yet diverse material physical property and is a key parameter in the mining industry in fields such as comminution, geotechnical and blast modelling. Several laboratory and field based measurement techniques exist to measure hardness (e.g. Point Load Testing, Vickers, Brinell, A*b, BMWi, UCS), all are designed for specific applications. Current tests are generally destructive and require specific sample preparation procedures which results in high cost tests that are not conducted in adequate quantities to map hardness across an ore body. The EQUOtip rebound hardness tester is a device that has been developed for application in ore body hardness domaining within the AMIRA P843 GeMIII Research Project. The rebound hardness test is non-destructive and suitable for application on half and whole diamond drill core. Data acquisition protocols and a data processing software application (EQProcess) have been developed to facilitate routine collection of comparative hardness information. This paper outlines the data acquisition and processing methodology and provides application examples of defining relative hardness domains in different geological deposit styles.

Jan 1, 2014

By P. Somasundaran, G. Anastassakis, Z. Pan, D. R. Nagaraj

Gums are often used as depressants for talceous gangue minerals in the flotation of nickel and platinum bearing ores. However, the mechanisms of gum adsorption on talc are not clearly established. In this work, adsorption of guar gum at the talc-solution interface is investigated using spectroscopic and allied techniques. Guar gum adsorption on talc is not affected significantly by changes in solution conditions such as pH and ionic strength. Electrokinetic studies showed that guar gum decreased the negative zeta potential of talc but did not reverse the charge. Fluorescence spectroscopy studies conducted to investigate the role of hydrophobic bonding using pyrene and dansyl probes showed no evidence of the formation of hydrophobic domains at talc-aqueous interface. Urea, a hydrogen bond breaker, reduced the adsorption of guar on talc to the same extent as that for guar/alumina system, in which hydrogen bond plays an important role. All of the above results suggest that one of the main driving forces for guar adsorption on talc is hydrogen bonding rather than electrostatic or hydrophobic force.

Jan 1, 2003

By Reuter M. A., R. D. van der Weijden, W. F. C. van Wageningen

"Copper(II) can be recovered or removed from acidic copper sulfate solutions as cuprite or metallic copper powder by reduction with carbohydrates. The copper powder characteristics, such as size and shape of particles, determine the tendency to adhere to reactor walls and to agglomerate. In order to make this process suitable for a commercial scale pipe reactor, process conditions and the reactor configuration were varied in order to influence the copper characteristics in a positive way. The aim was to achieve proper particle throughput in the pipe reactor and to obtain a well defined copper powder.In this paper the effect of both, chemical and physical parameters on the shape and size of particles were systematically studied in a number of autoclave experiments. These parameters include mixing, Cu(II) concentration, pH, temperature, seeding, use of additives and reactor materials. Additionally, Monte Carlo simulations of copper growth inside a Kenics static mixer were made. Results show that the use of additives and the use of static mixers influence particle characteristics the most."

Jan 1, 2003

By Wenqing Qin, Yunfan Wang, Ximei Luo, Fen Jiao

In order to investigate the effect of nanobubbles on adsorption of surfactant on mineral surface, the nanobubbles on the surface of calcite with -37µm fraction in the sodium oleate system were controlled by pressurization and decompression to mixing vessel. Subsequently, the adsorption amount of sodium oleate on the surface of calcite were detected by ultraviolet spectrum at different stirring times and different pressures. At the same time, the nanobubbles on the calcite surface were imaged with atomic force microscopy (AFM). In addition, a homemade vacuum Hallimond tube device was used for the flotation of single mineral, and the grade and recovery of minerals in concentrate was used to determine the influence of the nanobubbles on flotation. The experimental results showed that a large number of nanobubbles were found on the calcite surface by AFM under the dissolved oxygen difference (DOD) condition of -4 mg/L. And a large difference in adsorption capacity of sodium oleate on the surface of calcite was observed under different air pressure conditions. It indicated that the ambient pressure had a certain effect on the adsorption of sodium oleate on the calcite surface, and this effect did not depend on the constant low pressure or constant normal pressure, but depended on the changing process of pressure. The single mineral flotation experiment results indicated the recovery of calcite under decompression condition (formation condition of nanobubbles) was 1.5-2 times that under constant normal pressure, and the flotation time is much shorter. Moreover, the recovery under constant normal pressure was greatly influenced by flotation time. In this paper, only one aspect of the effect of nanobubbles on mineral flotation was preliminarily explored. It was confirmed that after vacuum-pumping, the adsorption of sodium oleate on calcite surface could be increased, the flotation time also was greatly reduced and the recovery of calcite was increased.

Jan 1, 2018

By M. L. Liu

This work reports the results about the determination of mean activity coefficients and relative partial molar free energies for copper sulfide mineral bioleaching solutions by potentiometric method at 25ºC. The experimental potentiometric data were obtained by combining a solid state membrane-cupric ion selective electrode (Cu2+ ISE), containing a KNO3 filling solution, and an Ag/AgCl electrode. The measurements were performed in different series of copper sulfide mineral bioleaching solutions. The non-ideal behavior of the system was described on the base of the Pitzer ion-interaction model for mixed salts. Meanwhile, the relative partial molar free energies of bioleaching solution were investigated. The determination of the thermodynamic properties offers a basic data for the study of copper sulfide mineral bioleaching solutions.

Jan 1, 2014

By J. Leite

In a small-scale mining in Brazil?s northeast, scheelite were exploited since 1940?s using a traditional gravity concentration flowchart (composed by jigs and shacking tables) that operates with low efficient for fine particles. Tailing of this plant was submitted to chemical, mineralogical and size characterization. Results pointed 50% smaller than 74µm with a grade of 0.11% WO3. The particle?s size is an important operational variable to heighten recuperation by shacking tables. Tests using Falcon SB40 centrifuge concentrators and shacking table were realized, optimizing their operational variables. Based on the tests results a new flowchart was proposed for concentrating and tailings recovery.

Sep 1, 2012

The value creation with kaolin clays depends on removing the colored impurities which manifests in to higher brightnessone of the most sought after properties on applications such as paper coating, paint and others. The processes for removing impurities include magnetic separation, froth flotation and selective flocculation. While the flotation and selective flocculation processes exploit the physico-chemical differences between the surface properties, the magnetic separation uses the bulk magnetic susceptibility differences between the diamagnetic clay and ferro- and para-magnetic nature of the impurities. The major advantage with magnetic separation remains high yield and no or low reagent usage. However, the magnetic separation technology suffers from low separation efficacy when finer colored impurities (<1 µm) are encountered in the feed. Use of stronger magnetic intensities during magnetic separation showed limited success; nonetheless the adverse effect due to finer size range remains a dominant effect even at 5 Tesla magnetic field. Furthermore, the presence of diamagnetic colored impurities irrespective of their sizes can not be removed. Cytec Industries has recently developed a ?bolt-on? chemical enhancement technology for magnetic separation that essentially embraces the best product performance attributes of flotation and selective flocculation while keeping the chemical usage to a minimum level and using the readily available magnetic separation equipment. The paper will outline the technology and illustrate optimization work at pilot plant magnet on a wide variety of crude accommodating the process needs and plant limitations. The major advantages of chemical enhancement technology to magnetic separation include: 1) simple extension to existing magnetic separation technology, 2) ability to produce comparable product in quality with cost effectiveness compared to flotation and selective flocculation, 3) removal of impurity minerals over wide size range, 4) removing non-magnetic impurities, 5) providing robust process with high process yield and 6) operation-friendly nature. Furthermore, chemical enhancement technology for magnetic separation has also emerged as a platform for re-moving impurities at low levels in other mineral systems as well.

Jan 1, 2014

By Q. X. Li

The state discharge standard for arsenic-containing wastewater which is the first kind of pollution is less than 0.5 mg/L. In fact, in a certain company, the acidic arsenic-containing wastewater in non-ferrous smelting was as high as 860 mg/L, which is far beyond the state discharge standard. Obviously, the direct release of this wastewater without further treatment would result in great hazards to the ecological environment. To aim directly at the characteristics of acidic arsenic-containing wastewater, in this study, two steps of treatment including oxidation-flocculation and removal fluoride by mixing alkaline neutralization were suggested. Through analyzing various influencing factors in treatment effects, the optimum technical conditions were obtained. The sediments after treating were recyclable and the secondary pollutions can be avoided. Moreover, the results also show that, all indexes of the effluent after treating are lower than the First Grade Standard of Integrated Wastewater Discharge (GB 8978-1996). This novel method has advantages of short flow sheet, easy operation and low cost.

Jan 1, 2014

By Carlos G. Rudolp, Julio C. Videla, Mario Zuleta

"The present paper summarises the results of gravity pneumatic concentration of a borax ore with 17.5 % B2O3. The sample was extracted from the Tincalayu ore deposit located in the Salta Province of Argentina.The applied methodology was based on a former study (Zuleta, 1985). It consisted of sample characterization by means of physical and mineralogical determinations, chemical analyses as well as pneumatic table concentration tests. In this, a simplified concentrating flowsheet was utilized.A concentrate with 30.6 % B2O3 and 74.7 % recovery was obtained. The recovery was 8.8 % less than previously reported and that was of 30.6 % B2O3 with 87 % recovery. Nevertheless, the simplified flow sheet presented processes only two granulometric fractions, - 6.4 mm + 0.3 mm and - 0.3 mm, compared to the three granulometric fractions used in the previous study: - 6.4 mm + 1.4 mm; - 1.4 mm + 0.3 mm and . 0.3 mm. This would simplify industrial implementation."

Jan 1, 2003

By Peter Ay, Florian Logsch, Satyanarayana Narra

"The traditional lignin separation process from the precipitated suspension creates severe filtration problems by plugging of the filter medium due to the small particle size (20 to 60 µm) of the suspended lignins. The plugging causes further problems in the successive processing of the filter cake. A new lignin separation process has been developed at the Brandenburg University of Technology (BTU) Cottbus as a part of the Research and Development and Demonstration (R & D & D) project "LignoBioFuel". The new developed process separates lignin in the form of granules with diameters ranging from 100 µm to 300 µm. The restrainment of the granule’s size in their successive treatments is expected to result in higher filtration efficiencies and reduction in plugging of filter mediums. To evaluate the filtration efficiency, the filtration resistance of the produced granules as well as the conventional suspensions has been investigated. The results show that there is a 60 to 80 % filtration efficiency increase and around 60 % reduction in plugging of filter mediums with the lignin granules in comparison to the conventional suspensions. Furthermore the successive processing of lignin granules was easier due to their porous structures removing the impurities such as adherent acids and salts. The purity of the separated lignin was measured with their sulphur (reduced from 7 % to 2.7 %) and ash (reduced from 46 % to 0.5 %) contents. The newly developed process has displayed better results in comparison to that of the conventional process. The new process displays high potentials in optimizing and improving the present state of the art treatments and is promising several ecological, economical and environmental improvements."

Jan 1, 2014

By Boris Albijanic, Hongjuan Chen, Bogale Tadesse

"During mechanical flotation of fine liberation sized complex rare earth ores, a large fraction of ultrafine valuable mineral particles are lost to tailings. Fine gangue mineral particles can be entrapped within the froth phase and be floated together with target mineral particles. Another common challenge in ultrafine rare earth mineral flotation is the formation of a sticky froth (excessively stable froth). Thus, the improvement of the flotation of fine and ultrafine rare earth bearing minerals through appropriate cell design and reagent selection is highly desirable. The aim of this study is to investigate the performance of a pico-bubble cavitation flotation column in improving selective recovery of ultrafine rare-earth elements (REEs) bearing minerals from complex and low-grade ores. In pico-bubble cavitation column, very small bubbles are generated which are capable of attaching to ultrafine particles and consequently modifying their surface properties. The overall effect of these processes should lead to improved flotation selectivity and recovery of ultrafine RE mineral particles. In this paper, the effects of a number of flotation operating variables on recovery and grade of REE minerals was investigated using a continuous pilot scale pico-bubble column flotation. At the flotation conditions used in this study, subtle monazite upgrade was observed while gangue Fe oxide was preferentially floated even in the presence of depressants. INTRODUCTION Rare earth elements (REEs) have unique properties such as superconductivity and catalytic activity, and are in high demand for a large number of cutting-edge technologies in the modern world including the production of mobile phones, fuel cells, displays, permanent magnets for wind power generation, high-capacity batteries, green energy devices, etc (Naumov, 2008). REEs tend to be intimately associated within many minerals, and are rarely found in high concentrations in deposits for economic extraction. Up to now, among over 250 minerals containing REEs, bastnasite (Ce), monazite (Ce, Th and La) and xenotime (Y) are the three main minerals that contain sufficient grade of REEs for commercial exploitation (Zhang and Edwards, 2012). The deposits that contain bastnäsite, monazite and xenotime usually have complicated mineral compositions, with various valuable minerals of fine embedded grain sizes in association with complex gangue minerals. In order to ensure liberation of the REEs minerals, fine grinding to less than 30 µm is necessary. This fine grinding leads to difficulty in recovering a large proportion of fine and ultrafine particles in separation processes such as flotation (Trahar and Warren, 1976). Consequently, highly liberated and ultrafine fine valuable REEs particles are lost into tailings during traditional mechanical flotation. Besides, the formation of extremely sticky and stable froth inhibits the drainage of hydrophobic particles. Thus, improving flotation of rare earth bearing minerals, particularly the ultrafine size range, is highly desirable."

Jan 1, 2018

Vanadium-titanium magnetite from Panzhihua was crushed with open and closed circuit process by high pressure grinding roller (HPGR). The particle size characteristics of the crushed product were analyzed and the micro-cracks generated by HPGR during the crushing process were studied. The results showed that, in crushed products, the reduction ratio increases and the size distribution becomes more uniform with increasing of the pressure on roller?s surfaces. The fine fraction content of crushing products from -3.2 mm classification closed-circuit by HPGR increases obviously compared with that by Jaw Crusher and particle size distribution is more uniform. Large amount of intra-crystalline cracks and cleavage cracks are generated in vanadium-titanium magnetite crushed by HPGR, which makes the specific surface area larger and Bond grinding work index (objective particle size is 0.074 mm) decreased by 14.05% than that by Jaw Crusher. And the liberation degree of monomer of the product crushed by HPGR increased compared with that by Jaw Crusher with the similar fineness of grinding. Keywords: iron ore, high pressure grinding roller, micro-crack

Sep 1, 2012

By P. Radziszewski

In comminution research, ore breakage and wear are usually studied independently of one another. Much of this is due to the fact that wear is usually a slow process compared to ore kage. However, the abrasion wheel test used to determine the abrasive wear contribution to total steel media wear provides the opportunity to study not only abrasive wear and friction but also ore breakage. In this paper, we will explore the use of the abrasion wheel wear test device to study abrasive wear, friction and ore breakage using standard Ottawa foundry sand. We will look into the feasibility of applying the work index as well as t10methodologies to this test set-up. We will also look at how the work index results evolve with abrasive wear and friction. We will then discuss the merits of pursuing the use of this abrasion wheel test for not only wear characterization but also breakage characterization.

Jan 1, 2014

By G. Unland

The sizing of crushers depends on the expected crushing forces. However, the crushing forces develop differently with every individual rock while it is compressed by the working surfaces of the crusher. For sizing, this compression process has to be characterized by the maximum crushing force. The maximum crushing force depends on the strength, shape and size of the rock, the amount and velocity of the imposed displacement of the working surfaces of the crusher on the rock and the conditions of the contact surfaces. From experience it is known that the strength of the material and, therefore, the crushing forces depend on the size of the specimen. This dependence is the so called size effect. The determination is based on compression tests. The force development is recorded during the compression of the specimen and for every individual test the maximum force is determined. The occurring maximum crushing forces of several rocks with the same diameter comminuted under the same conditions can be assessed by a mean value and a variance. The relationship between the mean values of the cross section related maximum crushing forces FAmax and the corresponding sizes d of the specimens can then be described by mathematical functions. They are derived from different approaches (phenomenological, statistical and statistical-physical methods). The phenomenological methods are subjective and yield functions depending on the assumptions of a person, whereas the statistical and statistical-physical methods are based on an evaluated function and the optimization of the parameters.

Jan 1, 2014