Search Documents

By G. Danko, R. Tiwari, J. Knowles

Many excavation and loading tasks require equipment operators to simultaneously coordinate the motion of multiple machine links, in order to achieve complex tool trajectories. Efficiency, ore selectivity, and machine wear, are all affected by the skill level and attentiveness of the operator. A software-based kinematics reconfiguration system designed to assist operators with various tasks has been implemented on a small experimental excavator using our new differential control architecture. Kinematics transformation and feedback control algorithms are being developed and tested using computer simulation, and the results implemented on the experimental excavator. Several task-specific kinematics transformations, including a virtual revolute-to-Cartesian machine reconfiguration and computer-assisted bucket steering and stabilization have been successfully tested. Progress, challenges, results, expected benefits, and planned work are described.

Jan 1, 2006

By W. L. Connell, O&apos

The properties of some heavy liquids which can be used in sink-float separations are discussed with major emphasis being given to the halogenated hydrocarbons. Data are presented on density, viscosity, thermal characteristics and the effects of moisture and temperature on the corrosiveness of the liquids towards various materials of construction. The toxicity of these materials, the hazards involved in handling them, and the procedures for handling them safely are also discussed. True liquids have certain advantages over colloidal suspensions for sink-float separation of minerals which makes their use especially advantageous when close separations, fine particle sizes or water-soluble minerals are to be treated. For best separating results, the medium should have an easily controlled, uniform, stable density. Here, true liquids have the advantages of allowing closer control of density and of not requiring agitation to maintain a uniform den- sity in the equipment. Low viscosities are desired in a separating liquid so that rapid separations of fine material can be made. Many liquids have lower viscosities than the colloidal suspensions at operating gravities of 1.4 to 5.0. For economic reasons and to prevent contamination of the product, the separating medium must be easily and completely removed from the ore. Normally, true liquids must be more completely removed than the cheaper suspensions and thus cause more problems in this area. The fact that the medium should not react with the minerals, air, water or the common materials of construction limits the choice of liquids which can be used, but many are available which are sufficiently stable. A more serious objection to the use of true liquids is that many of them present a toxic hazard to operating personnel and users of the product. Most true liquids are toxic to some extent, but modem knowledge of toxicity allows us to recognize the hazards inherent in handling them and enables us to design around them. Three types of true liquids are available for this use: 1) Halogenated hydrocarbons cover the gravity range from 1.2 to 3.3. They are generally more volatile and less viscous than the other liquids.

Jan 1, 1963

By W. J. Young, K. B. Macneill, C. N. Smith

"A BRIEF HISTORY OF THE MURRAY BROOK MINERAL DEPOSITDuring the mid-1950's intensive exploration activity in northern New Brunswick followed the discovery of the world class Brunswick base metal deposit. Using the prototypes of modern airborne geophysical and geochemical exploration techniques many mineralized areas in the Bathurst-Newcastle area were quickly identified. This base metal - silver camp is situated within the metavolcanic - metasidementary rocks of the Tetagouche Group which forms a roughly circular caldera-chaped voloanio complex of Ordivician age.One of the early results in the exploration history in the camp was the discovery of the Murray Brook Deposit by Kennco Explorations, (Canada) Limited. During routine ground checking of geophysical anomalies, most of which turned out to be graphitic schist, the discovery of some copper bearing float was made by the exploration team. This encouraged the company sufficiently to carry out a regional stream sampling program which lead to a large anomaly associated with a hematitic gossan. Diamond drilling of a weak Slingram anomaly over the gossan zone resulted in the discovery of massive sulphide lenses. This was followed in 1956-7 with an intensive drilling program. The result was the delineation of a potential ore body containing an estimated 23 million tons with an overall grade of 0.44% copper, 0.86% lead, 1.95% zinc, 25.73 g/tonne (0.91 oz/ton) silver, 0.28 g/tonne (0.01 oz/ton) gold. Within this package were higher grade zones of copper and lead-zinc mineralization approaching ore grades.A thick blanket of gossan was present and is reported to have caused the drillers considerable trouble as they attempted to penetrate it to get to the underlying sulphides. The gossan, consisting of iron oxides and silica fragments sits on top of the massive sulphides and attains a remarkable thickness of 45.5 meters (150'). Early work had suggested that the gossan was enriched in gold and silver. If this were the case and if the precious metal could be leached out with cyanide, then mining and recovering those values might be economic.With this in mind Northumberland Mines Limited optioned the property from Kennco in 1985. Preliminary leach tests indicated that indeed the gold in particular leached readily. Subsequent drilling of the gossan (using triple core barrel technology for better recovery of the easily ground core) indicated 1,536,363 tonnes (1,690,000 tons) with an average grade of 1.05 g/tonne (0.037 oz/ton) gold and 42.13 g/tonne"

Jan 1, 1993

IN the irregularly shaped ore-bodies of the North Mount Lyell mine by overhead stoping, the method of filling the is a special feature.The situation of the mine two miles from the smelter and mill at an devation of 1000 ft. above the latter, precluded the economical use of granulated furnace or the mill tailings, even if these materials were as suitable for the purpose as the rock nowquarried at North Lyell methods at Mount Lyell have already been described in Proceedings of the Institute.*The breaking the ore in large dome-shaped stopes is still the rule, but the slope or "rill" is much flatter now than formerly. Owing the greater fluidity of the filling now in use, it is sometimes necessary to resort to square-sets, both at the ground floor and above, the roofs and walls are generally enough to permit stoping without timber, except for ground and occasional stacks on the rills.Sufficient area of ground floor has been beaten out to start overhead stoping, the dome back is partly formed, with its apex a rise which connects with the mullock-pass reticulation.(Sce 1 showing this reticulation in diagrammatic form.)

Jan 1, 1927

By Donald Leroux, Dave Scott, Giovanni Di Prisco

"The Lady Loretta lead-zinc deposit in Northwest Queensland, Australia contains an average of 5.9% lead, 17.1% zinc and 97 g/t silver. Ore mineralization is mostly comprised of fairly complex intergrowths of pyrite, sphalerite and galena. Starting in 1998, Noranda Inc., the major joint venture partner of the project, conducted extensive metallurgical test work, which culminated in July - August 2000 in a series of Pilot Plant tests. A common thread to all the metallurgical work has been the deportment of a large portion of silver into non-payable metallurgical products. Average silver distribution from four Pilot Plants shows a distribution of silver in lead concentrate of 28%, whereas silver in zinc concentrate was 49%, and 23% in the final tails.The consistently poor silver recovery as well as the fairly unusual silver distribution, particularly in zinc concentrate, was considered an issue to be thoroughly investigated. A mineralogical plan was devised to determine if these particular metallurgical results were somewhat related to the nature and mode of occurrence of silver carriers. Work was performed to determine discrete silver-bearing minerals and/or silver contained in solid solution in a suite of commonly occurring sulphides. Ore microscopy, SEM methods, Electron Microprobe and Ion Microprobe analyses were all used to answer these questions, and to find the silver carriers, so a metallurgical plan could be devised to improve silver recovery.INTRODUCTIONPotential economic exploitation of the Lady Loretta deposit in Queensland, Australia is driven by revenue derived from zinc and lead flotation concentrates and co-product silver recovery in lead. Relatively low recoveries of payable silver to lead concentrate, and high silver distribution to zinc concentrate necessitated an investigation into the natu"

Jan 1, 2002

"AQUILA Mining Systems Ltd. is a Canadian company that designs and develops monitoring, control and navigation systems for the surface and underground mining industries. In 1992, AQUILA Mining Systems began the development of technology for monitoring, controlling and positioning mobile mining equipment. In 1993, AQUILA completed its first field test with GPS receivers onboard ablasthole drill, and thus demonstrated the viability and strategic relevance of this technology in surface mining. Since then, AQUILA has installed GPS-based technology on drills and shovels in several Canadian mines. This paper will review the development of these systems and discussthe benefits the mining industry could realise through their production implementation."

Jan 1, 1997

By A. Adu-Acheampong

The Mid-Tennessee Zinc (MTZ) mines, comprised of the Gordonsville, Elmwood, and Cumberland sites, last operated 4 years ago and are undergoing rehabilitation to begin production in 2008. The mines utilize a random room-and-pillar mining method that results in complex ventilation networks. Upon decommissioning, the mechanical ventilation units were removed and disposed of and several shafts sealed. In an effort to re-open the mines and operate in compliance with imminent Mine Safety Health and Administration (MSHA) diesel particulate matter (DPM) regulatory limits of 160TC µg/m3, a new ventilation system was required. The new ventilation system was developed primarily based on the diesel equipment required to meet production. Particular emphasis was placed on the DPM, diesel equipment utilization, main fan sizing, and fan locations to enable the mines to meet MSHA?s ventilation requirements in a cost efficient manner.

Jan 1, 2009

By M. B. Boyer, C. H. Herty, F. A. Hartgen, G. L. Frear

"DEFINITION OF VISCOSITYViscosity has been defined as the resistance experienced by one portion of a liquid moving over another portion, such as one molecular plane moving over an adjacent plane. A measure of viscosity is the force required to keep one plane in motion at Unit velocity, the other plane being considered stationary. Figure 1 illustrates the general idea that the surface friction between two adjacent areas will be greater the larger the molecules. Therefore it may be assumed that viscosity will be increased by molecular association or agglomeration, and likewise dissociation rill decrease viscosity. According to Maxwell (1)6 the unit of viscosity, the poise, is the tangential force per square centimeter of area of either of two horizontal planes 1 centimeter apart, one of which is fixed while the other moves with unit velocity, the space between being filled with viscous liquid of unit viscosity.The need for a satisfactory apparatus and experimental procedure for the determination of viscosity of high-melting materials at temperatures corresponding to those in pig-iron and steel making has been recognized during the past few decades. The condition of the slag during the smelting and refining periods in the iron- and steel-making processes exerts an important influence on the metal product obtained, this slag condition really meaning the state of viscosity or, vice versa, fluidity, which the slag attains under certain conditions."

Jun 1, 1934

By Sergio N. Monteiro

Polymeric matrix composites with dispersed hard particles are being as wear resistant tools in industrial polishing operations. In the present work, the microstructure of epoxy composites with different amounts of embedded diamond particles, up to 30 wt.%, was investigated for the effect on fracture characteristics. It was found that the introduction of diamond particles promoted an increase the porosity of the epoxy matrix. Moreover, the particle morphology associated with a non-uniform distribution within the matrix was responsible for the nucleation of cracks that caused rupture of the composites.

Jan 1, 2006

The proposed classification scheme is based on two primary parameters, one for petrographic composition and the other for rank, both being determined with microscopic techniques. The scheme has been applied to a wide range of Australian coals and found to provide a useful means of relating their inherent properties to properties such as volatile-matter yield, crucible swelling number, and calorific value, which will determine how these coals might be used commercially.

Jan 1, 1970

By Steve Kral

Competition from foreign coal producers could displace as much as 9 Mt/a (10 million stpy) of US coal bound for power plants located near waterways. But, according to a Maryland-based coal consultant, it could be worse. Theoretically, about 52 Mt (57 million st) of domestic coal could be vulnerable to imports by 1990, said Forrest Hill, of Hill & Associates of Annapolis. Hill was speaking to about 150 coal industry executives and experts at the third annual Coal Marketing Strategies Conference in November. Most were at the Denver, CO conference to pick up tips on how to sell coal in an oversupplied market. Imports threaten domestic markets Of the 200 utilities studied by Hill and his staff, 119 are situated near major waterways, he said. However, most of those waterways are not equipped to handle coal from the shipping lanes. Good news for US coal producers. But don't breathe too easily. Foreign coal still poses a major threat to domestic markets, Hill continued. The strength of the US dollar is an obvious factor. But easy access to US utilities located on waterways combined with low rates for ocean vessels give foreign producers another edge. And foreign mines are typically low cost producers. For example, Hill said Colombia's huge Cerrejon mine can deliver coal to an Illinois power plant for $47.87/t ($43.39 per st). That compares to $52.85/t ($47.95 per st) from a Kentucky coal mine. Also, Colombian coal producers can generate a cash flow even if the coal sells for $27.50/t ($25 per st). The main competition US producers face from abroad, as Hill sees it, comes from Australia, Canada, Colombia, Poland, South Africa, and, perhaps, from Venezuela. Domestic producers, however, do have some things going for them. Most US coal buyers, Hill said, "are not wild about the idea of buying foreign coal." A 10% price advantage or pressure from public utility commissions would be needed to force some of them to buy foreign coal, he said. Some of the utilities contacted said they would not commit to more than one-third of their stockpiles to a foreign source. Another advantage for US producers is that they have room in their long-term contracts to cut prices and still maintain a profit, Hill said. Railroads, too, have high profit margins written into their rate structures. They are also aware of the import threat. Therefore, they may reduce their rates accordingly to keep their markets. Marketing's role The energy price shocks of 1972 and 1976 caused major adjustments in world economics. Coal was no exception. High oil prices caused many utilities to look at less expensive coal. As the market improved, coal prices began to respond, said R. Gale Daniel, of Anaconda Minerals Co. But clean air legislation and the strengthening dollar caused havoc in the coal markets, he said. The price of oil crashed, taking with it predictions of record coal use. The result is an oversupply of coal that has led to price cutting. Now, coal marketing must be recognized in its "true leadership role," Daniel said. Marketing people must know when to use spot sales to balance production objectives and maintain cost-effective-

Jan 1, 1986

By L. J. Prosser, A. T. Iannacchione

Unfortunately from 1991 through 1995, 44 miners were fatally injured in the stone industry. Of these 12 occurred at underground mines from a total work force of less than 2,000 miners. Nine of these 12 miners were fatally injured in falls of roof or rib. A safer environment for the miners can be achieved by evaluating the nature of the hazardous ground and by developing more efficient and effective ground control strategies. Roof and rib conditions in the underground stone industry were observed and assessed at 33 mines in Illinois, Indiana, Kentucky, Maryland, Missouri, Pennsylvania, and West Virginia [(Figure 1)]. Hazard assessment indicated that those ground failures occurring under moderate to substantial overburden (> 30 m [l00 ft]) were caused by stress concentrations and geologic structures. Ground failures near the surface are caused by solution (water) processes. Selection of the mining horizon and mine layout decisions tremendously influence ground stability.

Feb 24, 1997

By Nilce Alves Santos, Vânia Lúcia de Lima Andrade, Keila Lane Carvalho Gonçalves, Harold Wyslouzi1

"When confronted with the difficult decisions on advancing an exploration project to the feasibility and construction stages, it is important to know how various regions of the ore body will react in the milling and concentration processes. While bench scale test work is common and inexpensive, the results and information provided are somewhat limited due to the difficulty in accurately predicting the effects of recirculating middling streams or gradual changes in solution chemistry.Conventional Pilot Plants, processing 100 to 1,000 kg/hour of sample ore, provide the detailed engineering data required to develop a final process flowsheet and to size the equipment. They are, however, expensive to set-up and operate, and are really only viable for major projects that are well advancedIn the latter part of 1999, the Mineral Development Center at CVRD (MDC) purchased a new piece of mineral processing equipment which can run continuous flotation tests using drill core samples. To evaluate its performance, and to compare it with conventional testing methods, various types of flotation tests were carried out using two different types of copper ore. The limitations and advantages of open circuit and locked cycle bench tests, as well as the Mini Pilot Plant and the Conventional Pilot Plant were evaluated.Open circuit tests carried out at the bench scale only provide basic information. More complete and trustworthy information is obtained, in terms of the recirculation of flows and reaching a permanent and stable flotation regime, as the dynamics and complexity of the tests increases. The data obtained showed that the MPP’s metallurgical performance was equivalent to that of a conventional pilot plant."

Jan 1, 2002

By Fulvio Tonon

And Rabcewicz said ?tunnels should be driven full face whenever possible.? ADECO, which stands for ?Analysis of Controlled Deformations in tunnels,? now allows us to fulfll Rabcewicz?s dream in any stress-strain condition. In order to achieve that dream and its consequent control over cost and schedule, however, NATM must be abandoned for the ADECO. The paper presents the basic concepts in the ADECO approach to design, construction and monitoring of tunnels together with some case histories, including: full face excavation for Cassia tunnel (width of 22 m, height of 14 m) in sands and silts under 5 m cover below an archeological area in Rome, Italy; Tartaguille tunnel (face area > 100 m2) advanced full face in highly swelling and squeezing ground under 100 m cover where NATM led to catastrophic failure, France; and 80 km of tunnels (face area > 100 m2) advanced full face in highly squeezing/swelling ground under 500 m cover for the high-speed railway line between Bologne and Florence, Italy (turnkey contract).

By William Reisz

Over the years as surface mining operations have become more sophisticated, angle drilling has become a more popular blast design technique, especially in areas where overburden and stripping ratios have increased. Another method of blast design is the staggered pattern, which greatly improves explosives distribution within the blast. While both methods present some engineering challenges, this paper will discuss how the two methods can be combined to enhance fragmentation, improve cast percentage, drill production ratios and highwall control. A practical engineering approach will be presented as well as a discussion on the discipline required to maintain a quality blasting plan.

Jan 1, 2002

During the latter part of 1937 consideration was given to the construction of a; local smelting plant for producing blister copper. Previously copper concentrates had been shipped to the United States of America. The proposition had the advantages of a saving in cost of realization, quicker financial return and reduced dependence on overseas shipping.The smelter was designed by the existing staff, who had difficulty in obtaining data on small plants, particularly on the reverberatory furnace. Construction was started in March, 1938, and the reverberatory was blown in on January 16th, 1939. One roaster had been operating for several weeks prior to this date.While results and operating technique on this new departure in small-scale smelting are barely beyond the experimental stage, it is felt that the experience gained to this time should be recorded to help fill the obvious gap in published information covering plants of this type.At present there are three copper smelters operating in Australia; the other two plants are equipped with blast furnaces.LOCATIONThe new smelter is situated in a position convenient to the concentrator and to the power plant. The site is traversed on two sides by a brick flue, from an old smelter plant, which connects with a 250-ft. stack. This stack and portion of the old flue are used in connection with the...

Jan 1, 1939

By Rob Sloan, Simon Yu, Rob Robison, Mark Schmidt

"In 2000-2009, Highland Valley Copper (HVC) tested new generation 660 mm cyclones supplied by various manufacturers in an aim to replace existing first generation 762 mm cyclones without success. Due to plant infrastructure limitations, new generation larger (838 and 800 mm) cyclones were not feasible. In 2010, an approach of testing hybrid 800 mm diameter cyclones was initiated by HVC. The hybrid cyclone consists of an 800 mm cyclone upper head section and the use of existing 762 mm cyclone conical sections. Three hybrid 800 mm cyclones were engineered and fabricated, targeting a throughput of 850-950 mtph and were installed in the E line cyclone cluster. Since starting operation on September 20, 2011, three hybrid 800 mm cyclones have been running at combined throughput ranges of 750 to 1050 mtph. Based on plant Daily Met Reports, the test hybrid cyclones demonstrated a decrease in misplacement of coarse copper bearing material to the cyclone overflow and better cyclone efficiency when compared to the existing 762 mm cyclones at the same throughput. The hybrid 800 mm cyclones also demonstrated significantly higher capacity per unit when compared to the existing cyclones. Based on the improvement demonstrated in the full plant trials, HVC decided to install the new hybrid 800 mm cyclones in all five grinding lines starting in July, 2012. A more detailed discussion of the full plant trials and initial results of the first complete retrofit of E line will be presented. INTRODUCTIONHighland Valley Copper Partnership (HVC) is Canada’s largest base metals mine and one of the world’s largest producers of Cu-in-concentrate. The mine, located in the central interior of British Columbia, is owned (97.5% interest) and operated by Teck Resources Ltd. In 2011, HVC produced about 210 million lbs. of Cu and 8 million lbs. of Mo. HVC’s Mill Modernization Project (MOP), which was budgeted for $475 M, is currently under intensive construction and is scheduled for commissioning in Q1 2014. The following description was valid at the time of writing this paper.The operation has been expanded a number of times since the startup of the original Lornex mill in 1972. The plant started up with two 9.75 m (32 foot) diameter primary SAG mills. It was expanded in 1981 with the addition of a 10.36 m (34 foot) diameter SAG mill. In 1988, the Highmont concentrator grinding mills and flotation section were moved and attached to the Lornex mill site. This added two10.36 m (34 foot) diameter AG primary mills to the Highland mill. This brought the total number of primary mills to five referred to as Line A, B, C, D and E: three SAG mills (A, B and C) each with two ball mills in parallel and two AG mills (D and E) each with one ball mill. Each AG mill line is equipped with one short head pebble crusher. Ball mill circuits are classified using 8 clusters of ten Linatex 762 mm cyclones to reach a target P80 330 micron (equivalent 43% +100 mesh), before the cyclone overflow product advances to the bulk flotation circuit."

Jan 1, 2013

By Isobel Yeo, Luca Cocchi, Sven Petersen, Nico Augustin, Sean Plunkett, Ingo Klaucke

Exploration for seafloor massive sulfides is currently mainly focused on investigation for active hydrothermal vent fields. However, most of the resource potential is thought to be related to inactive, large deposits that had enough time to accumulate sufficient tonnage. At the same time, ageing of these deposits will ultimately result also in burial acted by either sediments and/or volcanic deposits. We currently lack the technologies to explore for these deposits in a time- and cost-efficient manner. In the fall of 2012 we used a number of AUV-based technologies to explore and image a sulfide occurrence at the Palinuro Volcanic Complex in the Tyrrhenian Sea (Mediterranean Sea; Fig. 1) where sampling and drilling have documented a buried polymetallic barite-pyrite dominated site (Petersen et al., 2014). Sulfide mineralization is here covered by volcaniclastic and pelagic sediments and only red sediment staining and the presence of few tubeworm bushes indicated recent hydrothermal activity - black smoker venting is absent. We used AUVbased high-resolution bathymetry, sidescan sonar imaging, subbottom profiling, as well as magnetics to describe, in a quantitative way, the previously known sulfide-bearing areas as well as to successfully explore for new hydrothermal sites including large chimney structures (Figs. 2). Additionally chemical sensors (CTD, Eh, turbidity) investigated the water column for signs of hydrothermal activity in areas not previously investigated, but at the end, only weak anomalies were found in the southern part of the summit.

Sep 1, 2014

By M. Jacobs

Keywords: Smelting, converting, sulphide, sulphide smelting, platinum, platinum group metals, PGM, base metals, nickel, copper, matte, slag, furnace, electric furnace, Söderberg, electrode, granulation, converter, flash drier, sulphuric acid, acid plant, Ausmelt, Sirosmelt, pyrometallurgy, metallurgy, Anglo Platinum, South Africa Waterval Smelter complex is situated in Rustenburg, in South Africa?s North West Province. The smelter objective is to process wet concentrate to produce crushed, slow-cooled, sulphur-deficient nickel-copper matte rich in platinum group metals (PGMs), gold, and base metals for despatch to the Magnetic Concentration Plant at the Base Metals Refinery. Throughout its history, the smelter complex has been continuously upgraded in line with increasing production demand, changing feeds, environmental initiatives, and advances in available technology. The smelter receives filter cake and slurry from Anglo Platinum concentrators and joint ventures. Wet concentrate is fed through a flash drying process utilising coal-fired, fluidised bed hot-gas generators, to produce dry feed material for the electric furnaces and slag-cleaning furnace. For primary smelting, two electric furnaces are used, each with a rated capacity of 34MW. Furnace matte, containing the bulk of the base metal sulphides and PGMs, is tapped periodically into refractory-lined ladles and granulated using high-pressure water jets, then dried through electrically powered pneumo-driers to become the main feed to the Anglo platinum Converting Process (ACP). Slag is tapped semi-continuously, granulated, and treated through the slag mill. The ACP treats the combined matte output of Waterval, Polokwane, and Mortimer smelters. It is a top-blown furnace, with furnace matte, air, and oxygen being injected into the converter via a lance submerged in the slag. Converter matte is tapped and bottom cast into moulds, slow-cooled, crushed, and despatched to the refineries. Slag is granulated and dried for recycling to the slag-cleaning furnace. ACP slag is fed to the slag-cleaning furnace along with a reductant and a sulphur source. Slag-cleaning-furnace matte is granulated for processing by the ACP, while slag is granulated and processed in the slag mill. The slag mill and flotation circuit treats granulated slag from the electric furnaces and slag-cleaning furnace to recover entrained matte containing valuable PGMs and base metal sulphides.

Jan 1, 2006

By L C. Taylor, H U. Lesiste

This paper describes a method for estimating the density distribution in the soil cap as a function of distance from its top at the time of impact with the target. It provides an estimate of the density distribution in the soil on the center line of the soil cap at the time of target impact for a single depth of burial of the charge and two heights of target and shows that, for the heights of target and the depth of burial considered, the thickness of the soil cap first increases from the in situ value and then decreases. The distribution of soil density along the centerline of the soil cap changes significantly with distance from its original position. These results can be used for validating hydro-code computations and the soil models used in the computations.

Jan 1, 2011