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By E. Guerrini, M. Maccagni, J. Nielsen

"The solution for the treatment of the EAFD has not yet been fully achieved. Some of this dust has still not found an appropriate final destination. Large consortium treatment plants are quite expensive both in terms of investment and operating cost. Meanwhile, the tolling expenses for steel production companies are becoming very important, causing them to look for alternatives. Some steel plants are looking to close their production loop by internal treatment of their dust. Some years ago, Engitec began studying the coupling of the EZINEX® Process, an ammonium chloride electrolysis to recover the zinc contained in the EAFD, with the INDUTEC® Process, a pyro process based on an induction furnace that can convert EAFD into a C.Z.O. similar to the Waelz oxide. The combination of these two processes provides an alternative to the existing treatment options and is particularly interesting for relatively small capacities. In this paper, we would like to give the latest update about these two processes and their possible integration INTRODUCTION Zinc is contained in numerous wastes and secondary raw materials that can be thought of as high zinc concentrate mines. This is a very interesting source of Zn that is typically easily exploitable. Unfortunately, only a portion of these materials are currently processed to recover the metal value, while stabilized or unstabilized landfilling is often the final destination. Pyrometallurgical processes are mainly used to convert the zinc into crude zinc oxide (CZO). The various processes are very similar and characterized by the fact that the zinc bearing materials are usually submitted to a thermal treatment [1] in which the zinc is reduced, vaporized and re-oxidized producing CZO. This material not only contains zinc oxide, but also relatively high concentrations of heavy metals. Many potential CZO sources, such as electric arc furnace dust (EAF), galvanizing ashes, brass foundry and converters fumes also contain chlorides, fluorides and alkali metals that will transfer to the CZO. The classic example is the Waelz oxide [2]. This CZO is an intermediate product that must be transformed into zinc salts or zinc metal. Until now, the conversion to zinc metal is done through two main processes: the sulphate leaching and electrowinning system and the Imperial Smelting Process (ISP). ISP is facing a crisis for technical and economic reasons that has led to the closing of most of the existing plants. In any case, before being fed to one of these two processes, the CZO must be treated to eliminate or reduce some of the contained impurities. In particular, the halides are most harmful to these processes."

Jan 1, 2018

By M. McClintock

"High Pressure Grinding Rolls (HPGR) is increasingly being chosen for comminution circuits for its energy-efficiency for hard rock mining operations. Despite HPGR’s growing popularity, geo-metallurgy programs are still prohibitively expensive because of large sample requirements. Traditionally, sizing HPGR application requires a significant amount of sample, in the order of 1 to 10 tonnes, depending on the level of study and complexity of the resource. Therefore, engineering and design of HPGR circuits typically are reliant on few composites that are required to be representative of the resource and mine plan. Three bench scale HPGR test methodologies were developed in 2015 at NBK Institute of Mining Engineering at the University of British Columbia (UBC) capable of defining the energy size breakage relationship of pilot HPGR. These methodologies were developed to allow bench scale testing for different levels of study from PEA (Preliminary Economic Assessment) to detailed design and operations. The Piston Press test defines the energy size reduction relationship by measuring specific energy consumption and corresponding feed and product size distributions. The advantage of Piston Press testing is the small sample requirement of 5 to 10 kg. Small sample requirements allow multiple samples to be tested across a deposit. Piston Press testing allows extensive geo-metallurgy programs that can determine ore variability and inform in optimization and production planning. To date, the Piston Press methodologies have been validated on a pilot-scale HPGR unit located at UBC. Recently, testing was conducted to calibrate and validate the Piston Press test against full-scale HPGR on a gold sulphide ore deposit. The program included the collection of operational data with the respective HPGR feed and recycle sample. Sample collected was used both for Piston Press testing and HPGR piloting. This paper discusses the test-work and results as carried out during this program, using the aforementioned methodologies."

Jan 1, 2018

By Steven Wright, Sharif Jahanshahi, Shouyi Sun

"While there is a large industry based on recovering platinum group metals (PGM) from complex sulphide ores containing Cu and Ni, there is little information on the thermodynamics of the matte phase formed on smelting the ore and in particular the behaviour of Pt in the matte.The equilibrium between metallic platinum and industrial mattes was studied in a series of experiments where a small quantity of matte (5g) and platinum foil of 150 µm thickness (0.5 g) were equilibrated in magnesia crucibles at 1400°C under conditions where the oxygen and sulphur partial pressures were fixed.The chemical composition of the phases was determined from EDS analysis using a scanning electron microscope. Line scans were initially used to confirm that the foils had attained a uniform composition across their thickness. The composition of the matte was determined from analysis of an area of matte including the small metallic droplets and dendrites.The results of the equilibrium study are presented in terms of how the oxygen and the sulphur pressure affect the distribution of Pt, between the matte and the alloy foil (Lmatte/alloy). Other variables investigated were matte chemistry, i.e., the Fe content and the temperature. The activities of platinum in the mattes were calculated using a regular solution model describing the activity-composition relationship in the alloy."

Jan 1, 2003

By T. Damyanov

Spherical grinding media (balls) are the most widely used media for comminution of ores by grinding. A modelling simulation study of the behavior of two grinding media in the grinding process was conducted to determine the possible advantages of the new shape milling bodies called tetraballpebs. Tetraballpebs are in the shape of tetrahedrons with spherical convex walls. A three dimensional CAD model of the mill drum with a diameter of 1200 mm was used. A continuous operating mode was simulated in terms of the 3D contact elements of the model (milling bodies and mill drum). Simulation tests were carried out in a typical grinding mode and at a typical rotational speed of the drum mill (75 per cent of the critical speed in cataracting mode). Studies carried out with both grinding media include equal number of milling bodies with the same weight and volume. Having thus ensured a uniform mass of the grinding media and same number of milling bodies, and constant other conditions and process parameters, conclusions can be drawn about the influence of the shape of the milling bodies on the grinding process. A kinematic analysis of the system using CAE (computer-aided engineering) model parameterization was conducted. The controlled parameters are: ? Power draw; ? Kinetic energy of each milling body; ? Motion of milling bodies inside the drum Keywords: grinding, grinding simulation, balls, tetraballpebs, DEM, CAD-CAE

Sep 1, 2012

By Sharma K. K.

India is the third largest producer with accounting to fifth largest reserves base of coal in the world. Indian coal has high ash content (15-45%) and low calorific value. The basic processes being used in India at different places for coal washing adopts old techniques. Much of the valuable part is being lost during washing processes. With enhancement of the available techniques and use of new processes like flotation process indicates better recovery of carbon values during washing stage. The same will increase the reserve base, improve economy of operation and alleviate environment related problems. In the above backdrop this paper portrays the case study of an existing coal processing plant in India. The case study includes the modifications being incorporated in the existing process to enhance the product value. The existing practices and the future trend of process technology that could be adopted to meet the requirements in this country are also discussed. Keywords: washing, dense media cyclone, magnetite media, flotation

Sep 1, 2012

By G. Demi

The biggest chromium mineral processing plant in Albania is Bulqiza plant. It has been in operation for more than 20 years, treating low-grade chromium ores grade 20 ? 26 % Cr2O3 and producing chromium concentrates grade 48 ? 50 % Cr2O3. About 2 million tons of tailings with 13 % Cr2O3 content are stocked in a dam close to the plant. Mineral processing of low-grade chromium ores with less than 16% Cr2O3 content is unprofitable because the mining expenses are high comparing with the current market prices of chromium concentrate. Recycle and enrichment of existing tailings is profitable, because there are no underground mining expenses in this case and because that this kind of raw material does not need expenses operation of crushing and grinding. The existing plant is in operation for more than 8 years treating existing tailings as raw material. Grade of concentrate in the value 40 % Cr2O3 and Cr2O3 recovery in the value 30-35% in the plant are considered low. The main reason of low concentrate grade and recovery is high content of particles under 100 microns, the slimes, in raw material. In the paper is described the study carried out to improve enrichment of the tailings, as well as analyses of existing process, raw material and products. It is concluded that majority of lost is present in the slimes which are not separated in existing spiral separators and shaking tables. Basing in the study is composed the new flow sheet of recycling and concentration of the tailings to produce chromium concentrate grade 41 ? 42 % Cr2O3 and recovery 60 %, decreasing in this way the concentrate production cost two times. In the paper are presented the tests and results of concentration of particle size fraction under 100 microns, using gravimetric, magnetic and flotation methods, as well as equipment and machines suitable for slimes treatment and concentration.

Sep 1, 2012

By C. A. Acuña

Extensive literature exists on the motion of single bubbles and the behaviour of swarms of bubbles. This contribution describes work to track and reveal the motion of individual bubbles in a swarm. The technique is based on high speed cinematography and tracking of multiple moving objects. Image processing algorithms were implemented in Matlab to isolate and measure geometric proper-ties of the bubbles in image sequences recorded at 2 ms interval; and these properties were compiled into a data structure. To track a bubble, the geometric properties and a matching criterion were applied on consecutive pictures to identify the bubble. The bubble trajectory was reconstructed from the data structure for the matched objects. The methodology is briefly described. The new technique was tested for bubbles produced at slot-type spargers (i.e., approximately 2-D swarms) in the presence of two frother types ('strong' and 'weak'). Two observations are discussed: a) that bubble motion in a swarm describes a velocity-size relationship dictated by the dominant bubble size class; and b) that surfactant type influences bubble rise velocity for bubbles in the range 0.1 mm to 4 mm. The latter suggests surface viscosity rather than surface immobilization determines bubble rise velocity.

Jan 1, 2014

By S. M. Viduka

This paper presents a numerical investigation of solid separation in jigging device, which is a gravity separation method widely used in ore processing. Separation is recognized as being heavily dependent on fluid motion in the jig. This study explores the effects of the inlet time dependent velocity profile on jigging performance. Modelling of the liquid-solid system is performed through a combination of computational fluid dynamics (CFD) to simulate liquid flow and discrete element method (DEM) to resolve particle motion. The initial packing conditions consist of a binary-density particle system of 1130 particles each 1 cm in diameter. A variety of jigging profiles are implemented in jigging. The saw tooth pulsation profile is selected with three variations in both amplitude and frequency. The performance of each profile variant is compared in terms of solid flow patterns, separation kinetics, energy, and mean particle position. These quantitative comparisons demonstrate significant differences in the segregation rate, energy, and solid phenomena, helping find an alternative optimum operating setting for the system.

Sep 1, 2012

By P. Prusti

An air dense medium fluidised bed separator (ADMFBS) is the efficient process for dry beneficiation of coal. Magnetite powder is used as medium to make required pseudo-fluid density in the fluidised bed. The dynamics behavior of coal particle with reference to its position changes from ideal solution to pseudo-fluid condition in different bed densities depending on its shape, size and density. In this study, three set of projected areas of coal particles were taken. Each set contains four different shapes i.e., cubical, rectangular prism, spherical and triangular prism with different density starting from 1.3 to 1.8 gm/cc. It is observed that coal particles having density less than the bed density, floats in different positions in the dense medium fluidised bed. Higher projected area particles float in deeper height in comparison with smaller projected area. The difference in position of coal particles in the bed increases (nearly 1 to 4 cm) as the coal density approaches towards bed density irrespective of the different shapes. Different shapes of coal particles behave in different ways based on the operating parameters like bed density, coal density and projected area of coal particle. Empirical model equations are proposed to predict the position of coal particle of each shape in the air dense medium fluidised bed system. Keywords: ADMFBS, particle dynamics, projected area, shape

Sep 1, 2012

By Y. X. Yang

Porous silica was obtained by acid leaching of chrysotile. The porous silica had been characterized by chemical analysis, powder X-ray diffraction (XRD), Fourier transform infrared spectros-copy (FT-IR), and N2 adsorption-desorption techniques. It is shown in this study that the porous silica retains the nanofibrous morphology of the original chrysotile, and produces a high specific surface area (SBET) of 391. 8 m2/g and total pore volume of 1. 05 mL/g. The increase in SBET and the total pore volume of the porous silica reflect the formation of micropores of 1.2~1.5nm and meso-pores of 3.2~3.8nm in diameter inside the porous structure. The hysteresis loop of N2 adsorption-desorption curve indicates mainly slit-shaped pores. The porous silica is amorphous, but its structure is regular to some extent. The structural unit of silica from chrysotile is a SiO4 tetrahedron and six-member silicon-oxygen rings with the tetrahedral positioned alternately up and down in the six-member rings.

Jan 1, 2014

By Evgeni Visariev

In Copper smelter Aurubis Bulgaria, the copper in slag from the Flash furnace and the Converters is recovered by flotation. The scheme of slag processing is crushing, two stage grinding (autogenous and ball) and flotation. Till 2010 the grinding cycle in the plant was in two stages ? the first stage was AG Mill 70?23 working with a classifier and the second stage was ball mill 3.6/5.5 working with a hydrocyclone. In 2010 a new AG Mill 65x78 with hydrocyclone was put in operation in order to increase throughput of the plant. The second stage of the grinding cycle is with the same ball mill. The Old AG mill processed 55-60 t/h slag with particle size -0.071 mm 75% or over 75 t/h with particle size -0.071 mm 35-40 %. The new AG Mill was designed for throughput 105 t/h with particle size -0.071 mm over 70 %. After the start up there were some problems with the equipment ? block up of AG Mill?s grate and pumps for feeding of the hydrocyclone. For optimization of the process a lot of general tests were made. One of the main problem was a wearing of the sand nozzles. Different materials (rubber, ceramic, metallic) for the sand nozzles were tested. The openings of the grate were changed. This paper presents: ? the optimal technological parameters of the old and the new working scheme; ? how the technological parameters of the new working scheme change when the hydrocyclone works with different nozzles; ? the effect of the change of the grate openings; ? the problems with the increase of the circulating load; ? a final decisions for improvement of the grinding cycle work. Keywords: spigot, wearing, classification, effectiveness, circulating load, autogenous, mill

Sep 1, 2012

By A. K. Suri

India plans to increase the nuclear power share in overall energy-mix to about 30% by 2032 using both indigenous and imported reactor technologies. In the immediate time-frame, it is envisaged to generate 10000 MW electricity by PHWR technology by 2020 using indigenous uranium resources. This necessitates setting-up of new uranium mills and augmenting the existing resource, mining and milling capacities. This paper describes the current status and future R & D needs towards achieving the targeted demand of yellow-cake. Keywords: uranium, hydrometallurgy, leaching, yellow cake

Sep 1, 2012

By Kr. J. Dedelyanova

Selective flocculation of iron minerals could improve the economics of high intensity magnetic separation as concomitant process. When the minerals are finely disseminated is necessary a finer grinding to be applied which generates a lot of slimes. The HIMS is not enough efficient for particles below 20 microns ? territory where the selective flocculation is already well known industrial practice, so the combination of these two methods of beneficiation can bring a higher grade at high recovery to be achieved. The dynamics and selectivity of the precipitation process is studied in batch tests with flocculant starch and dispersants sodium silicate and sodium hexametaphosphate. The influence of preliminary conditioning with nitrogen acid at pH 2 before flocculation is also investigated. Flowsheet including these two methods is tested and the distribution of iron is shown.

Jan 1, 2014

By G. Bonifazi

Mining activities belong to human history, they are lost in the mists of time. They usually impact on large portions of the territory, both directly (exploitation areas and logistic activities directly related to exploitation) and indirectly (exploited material handling, processing and storage areas). As a result, at the end of mine life cycle, dismissed areas usually cannot be directly re-utilized without efficient and well addressed rehabilitation actions. Main goal of the proposed approach was to analyze the results obtained when a set of procedures, based on the collection and the analysis of remote sensed data, is developed to evaluate the effect of rehabilitation of land contaminated by extractive industry activities and to perform a monitoring and registration of the environmental impact of such operations by the application and the integration of modern information technologies, as Earth Observation (EO) and Geographic Information Systems (GIS). The study was developed in the framework of the EU-Asia program of the European union (EXTRACT-IT Project-Contract No: CN/ASIA IT&C/006 (89870): Application of Information Technologies for the sustainable management of Extractive industry activities) and it was addressed to three different dismissed mine areas in India, Thailand and China, respectively. The results, in terms of methodologies selected, strategies applied and results obtained, are described with particular reference to Fuxin coal mine area in China.

Jan 1, 2014

By S. Titkov

At present, Russia is engaged in processing, 3new plants of hard-to-process potash ores with increased content (up to 10 - 12%) of insoluble impurities (insoluble residue ? I.R.). This required additional research to improve the process of potash ores flotation. Based on the study of the effect of dispersive properties of frother and its flow rate on the efficiency of aliphatic amines with different length of the hydrocarbon radical (as sylvite collector) there was showed the possibility to apply high molecular amine with length of hydrocarbon radical C20 ? C26 by normal temperature of circulated plant salt solution (saturated solution KCl ? NaCl ? H2O). There was designed and tested in plant conditions the modified amine collector with the length of the hydrocarbon radical C16 - C26, improving flotation of Sylvite under normal temperature of circulating salt solutions at potash flotation plants. There was made the study of the influence of the hydrocarbon radical length of alkylmorpholine on the Halite flotation from intermediate products of sylvite recleaner flotation with different content of I.R. (silicate-carbonate slimes), at normal and elevated temperature of salt solution. On the basis of the application of modified alkylmorpholine for Halite flotation, there was developed the process of further beneficiation for the intermediate products of sylvite recleaner flotation from potash ores with increased content of insoluble impurities, which can eliminate the circulation of the intermediate products in the process flow sheet of sylvinite ore processing and increase the KCl recovery into the finished product. Keywords: flotation, potash, halite, alkylamine, alkylmorpholine

Sep 1, 2012

By G. C. Li

Gold extraction using iodide leaching from refractory carbonaceous gold ores was studied. Thermodynamic analysis of iodide leaching chemistry had been carried out. Eh-pH diagram of Au-I2-I--H2O leaching system showed that the coordinating active forms from iodides were I3- and I-, while the major coordinate compound formed during iodide leaching was AuI-. For leaching parameters optimization, technological parameters such as I2 concentration, I2 :I- ratio, oxidation assisting agents, liquid/solid ratio, and leaching duration were studied. The leaching results showed that the average Au leaching rate reached 91% and 92% for oxidized ore and roasted primary ore respectively. Leaching process proceeded in weekly acidic or neutral slurry at ambient temperature; the leaching duration was 4 hours. After that gold was extracted from the pregnant liquor by activated carbon adsorption ? desorption ? electrowinning process. Gold recovery was over 93% in the adsorption process, while the gold recovery in electrowinning process was about 95%, provided that the initial gold concentration is 40mg/L or larger. For iodine regeneration it is enough to add hydrogen peroxide in excess into the filtrate after gold electrowinning, all the iodides existing in the solution in any forms would be precipitated in the form of elemental iodine.

Jan 1, 2014

By H. R. Manouchehri

"In all electrical beneficiation methods, the difference in electro-physical properties of the contributed mineral particles, essentially frictional charge, electrical conductivity and dielectric constant properties are exploited to achieve separation. The composition of the raw material determines what kind of either corona charging, conductive induction, or triboelectric separation method should be employed. The process is versatile and is influenced by different parameters related to mineral characteristics, surrounding ambient conditions and electrical and mechanical attributions of the separating device. Electrical separation is surface based beneficiation method which is mainly affected by the surface and surface changes of the minerals. Therefore, it is essential to understand how the electrophysical properties of the minerals can be changed/modified. During electrical/electrostatic separation process, both charge magnitude and its polarity that developed on the particles and therefore, their electrical beneficiation potential is essentially defined by surface phenomena. Therefore, it is essential to understand how the main electro-physical parameters can be changed/modified with applied surface treatment/pretreatment methods to promote separation. Surface treatment of minerals is carried out by different means, including chemical conditioning, irradiation, thermal treatment, etc. This paper discusses and analyze the electrical separation process, electrophysical properties of the minerals with special focus on the effect of surface pretreatment/treatment methods to affect electrical beneficiation potential of the minerals. The surface treatment methods vary in a wide range from simple surface cleaning to more complicated chemical conditioning and doping. The knowledge of the solid-state physics and chemistry leads to improve the beneficiation potential of different mineral systems by choosing suitable treatment method(s). Despite the complexity and multiplicity of the charging mechanisms, difficulties in separating fines it seems to be beneficial make our attempts to further investigate and develop the process as dry, low cost beneficiation process, especially nowadays when environmental concerns, as well as energy and water consumptions are main concerns for mining industry."

Jan 1, 2018

By Shenxu Bao, Ying Bian, Xiang Liu, Liuyi Ren, Yimin Zhang, Chun Liu

Efficient enrichment of high-carbon low-grade mica stone coal containing vanadium is a key problem in the mineral processing field, and the mature beneficiation process is yet to be developed and applied. In this paper, a special mineral mica type of stone coal containing vanadium from Tongshan, Hubei Province, China was selected as the research object. Chemical analysis results show that this mineral contains V2O5 0.71%, SiO2 49.28%, C 13.44%, and CaO 6.26%. Scanning electron microscope (SEM) shows that vanadium generally exists in all kinds of mica minerals in 20 µm to 50 µm fractions. Mica stone coal containing vanadium must be ground to a particular fineness (approximately 45 µm). To reduce acid consumption during vanadium extraction from stone coal through acid leaching, a pretreatment process was proposed to enrich micas by using shaking table and flotation methods. A new combined technology process was implemented, resulting in a 0.96% improvement in the vanadium grade of raw materials in the succeeding process. Vanadium losses were controlled to 4.57% through the pre-concentration process, which reduced the burden of the subsequent procedure. The content of high acid consuming minerals was also diminished, such that approximately 6612 CNY was saved from producing 1 t V2O5. Therefore, stone coal containing vanadium should be pre-concentrated by using an appropriate combined process to reduce costs.

Jan 1, 2014

By L. Tong

Stirred milling of laterites offers possibilities for improving liberation and selective size reduction of soft nickel-bearing minerals in laterites. Batch grinding tests were performed in a Netzsch LME4 stirred mill on a siliceous goethitic (SG) nickel laterite sample (-2000 µm particle size) to evaluate the effect of operating conditions such as stirrer speed, grinding time, pH, solid content, water salinity and charge volume. The target was to produce a -38 µm fraction in the milling product with high nickel recovery and grade. Addition of dispersant (sodium hexametaphosphate) was also optimized with respect to the rheology of the slurry. In terms of stress intensity, the optimum grinding conditions for selective size reduction were: 1000 rpm, 50 per cent charge volume. At higher stress intensity (2000 rpm), Ni recovery in the -38 µm product was higher, but Ni grade was low, due to the breakage of the harder siliceous particles. Decreasing the yield stress by modifying slurry pH or adding dispersant improved the rheological properties of the pulp, but had no great influence on Ni upgrade in the fine product. Modifying water salinity by adding 2 M NaCl had also little effect. The breakage of the +38 µm particles in the feed determined Ni upgrade greatly. Ni grade in the -38 µm product decreased with grinding time, suggesting that the Ni-bearing minerals break first, while the harder siliceous minerals have a lower breakage rate. The breakage rates with respect to sample mass for Ni, Mg and Si indicate that: Mg > Ni > Mass > Si. The optimum grinding time for the highest Ni upgrade was 0.25 min. The Ni grade increased from 0.88 per cent to 1.35 per cent (upgrade 54 per cent), with 24 per cent Ni recovery. Keywords: fine grinding, stirred media mill, nickel laterite, slurry rheology

Sep 1, 2012

By B. Peszko

There are many measuring methods of grain sizes. Taking into consideration the fine grained materials, one of the existing techniques is measurement of grain size by the Coulter Counter method. This method is based on the measuring the changes of electrolyte resistance during grains flow through the calibrated diaphragm. This method is relatively simple to apply, significantly precise and the results are given quickly. However, the problem is that the measurements are limited by the size of diaphragm. Because of this situation, measurement of grain sizes by this instrument is possible in range from 10% to 60% of diaphragm diameter. This limitation causes the necessity of re-placing diaphragm in case when the measured grain size distribution concerns the material of large size range. In purpose of determining the total grain size distribution, the synthesis of some partial distributions, given for individual grain fractions (with different diaphragm applied), is required. This is possible to do by calculating the mixture of distribution functions, created from the partial distribution functions. Two materials were selected to research: quartzite and glass, which were comminuted in cylindrical crusher, additionally grinded, screened and then analyzed by Coulter Counter for five grain fractions: 0~125 µm, 0~80 µm, 0~56 µm, 0~40 µm and 0~25 µm. For each fraction, five different partial distributions were given (in case of glass ? four), which are the basis for the creating the joined grain composition. To assure the adequacy of the given distribution function, it is necessary to obtain the possibly best approximation of partial distributions. In the work, both the parametric and non-parametric methods of density approximations of investigated random variable. For each grain fraction the approximations were done by three traditional distribution functions: RRB, GSA and log-norm distribution functions and three methods of non-parametric approximation: Gauss kernel, Epanechnikov kernel and orthogonal Fourier series method. As the criterion of the certain distribution function acceptance, the value of the residual deviation was assumed, given by the formulae:

Jan 1, 2014