Search Documents

By D. R. Pyke

Many of the gold deposits in the Timmins• area show a close spatial association to ultramafic metavolcanics. Available analytical data suggest that ultramafic rocks contain significantly higher gold contents than other major rock types. In addition, recent analyses by Keays (1975) suggest that talc-carbonate alteration of ultramafic rocks releases significant quantities of gold. It is proposed that the ultramafic volcanics formed the principal source of gold for the deposits in Timmins, and that the gold was derived from the ultramafic flows when they were extensively carbonatized. Carbonatization of the ultramafic rocks and emplacement of the auriferous quartz-carbonate veins was probably coincident with the last major period of deformation in the gold camp. Delineation of hitherto unrecognized ultramafic volcanics could be an important guide to the discovery of further gold deposits.

Jan 1, 1976

By AIME AIME

THE John Fritz Medal Board of Award, at its annual meeting on Jan. 21, 1921, awarded its gold medal and diploma to Sir Robert Hadfield for the invention of manganese steel. On June 1, announcement was made that the Board of Award had awarded its gold medal and diploma to Charles Prosper Eughe Schneider for "achievement in metallurgy of iron and steel; for development of ordnance, especially the 75-mm. gun, and for notable patriotic contribution ' to the winning of the war." The award to Sir Robert Hadfield is for the year 1921; the award to Mr. Schneider is for 1922. The latter was made at this time in order that the medal might be presented by the group of American engineers now visiting England and France.*

Jan 1, 1921

By E. Kenneth Siroky

The concept of ultrasonic measurement was originally applied to marine operations. Sonar . . . standing for Sounding, Navigation and Ranging, was developed for military uses. Today Sonar has become very important to the fishing fleets and marine construction industries where its applications cover a wide range of uses our company, in addition to the inair ultrasonic equipment as discussed in this paper, is also deeply involved in marine sonar and works primarily with oceanographic research and fishing industries. Ultrasonics, by simple definition, are sound waves beyond the audible range of the human ear and are generally accepted to be waves over 20,000 cycles per second. When applied to level measurement, the principles of ultrasonics are basically quite simple. A sound pulse is initiated at a point in time and the time interval for the echo from that pulse to return can be interpolated into distance. The speed of sound in air under standard conditions is approximately 1,100 feet per second, or if converted into more meaningful information as related to distance measurement, the time required for sound to travel one foot round trip is 1.78 milliseconds. An early application for ultrasonic level monitoring equipment was in large grain elevators. Prior to ultrasonics, the common practice of inventory measurement was to have an employee walk around the top of these large grain elevators, which are often over 100 feet above ground level, and drop a weighted rope or chain down into the silo to determine the level of the grain. Needless to say, this was a slow process and could be extremely unsafe, especially during windy and snowy weather conditions. An alternate

Jan 1, 1971

By S S Solomons

In 1991 the uranium spot market price dropped to approximately US$7/Ib U308, a historical low in real terms and the short-term outlook for the industry in the next five years was grim. At this time the Ranger operation was producing uranium concentrate at its design capacity of approximately 3 000 tonnes/year. The loss of two major long-term contracts owing to price and reduced power utility demand due to excess inventories meant that the company could not match production to sales. Continuance at this production level would have resulted in a rapid buildup of product inventory and the tie-up of significant cash reserves. After analysing various options, an innovative operating strategy was devised such that production and sales were approximately balanced without a significant impact on the unit production cost or a long term effect on the plant or operation. A campaign mining/milling operation commenced and approximately 40 per cent of the workforce were retrenched. Multi-skilling of all employees was a critical aspect of ensuring a successful outcome. This paper examines the strategy and reports on the success of the operation two years after the restructuring exercise was effected in November 1991.

Jan 1, 1994

By J Hudson

Autogenous (AG) and Semi Autogenous (SAG) grinding mills are the conventional selection for large-scale grinding circuits. It is accepted that these forms of comminution are not the most energy efficient available. This efficiency combined with escalating energy prices, steel prices and the requirement to process larger, lower grade deposits has necessitated that better comminution techniques are found to challenge the dominant position of AG/SAG mills in the grinding circuit. Recent advances in high pressure grinding rolls (HPGR), particularly in terms of roll surface protection have meant that, depending on the application, an economic alternative is available to the large diameter AG/SAG mills. Mining companies now recognise the potential benefits of HPGR and so they need proper assessment in the design of new or upgrade of existing grinding processes. Of course, the answer to the question AG/SAG or HPGR is not straightforward and the impact of the grinding process on the whole metallurgical process needs to be evaluated. Clearly this is a complex decision to make and requires substantial metallurgical knowledge, test work, and objective analysis. The perceived downstream processing benefits will differ between different plants depending on the ore type and processing conditions. The optimal design of the comminution circuit requires that a robust methodology is followed to objectively characterise the ore, size the equipment and determine the downstream processing benefits. The paper gives a brief comparison of the capital and operating costs for both grinding systems, and then outlines the appropriate test work that is required to make an informed decision.

Jan 1, 2006

By G. K. Zaharlev

With a productive output growing at an annual rate of 8%, the Soviet mining industry should emerge as the world's leader in total mineral output during the 1980's. (The Soviet Union's share in the world's total mineral output in 1973 was estimated at 22 to 23%.) According to estimates by Soviet mining experts, the mineral potential of the Soviet Union will sustain the current 8% annual growth rate in the future.

Jan 12, 1974

ShouSteel Mining Ltd., a subsidiary of ShouSteel (Group) Co., was founded in 1959 and is located in QianAn City in Hebei Province, China. ShouSteel?s pelletizing plant uses iron ore as a raw material combined with limestone, dolostone, or olivine, with bentonite as a binder. After mixing the raw materials and forming them into small, spherical balls, ShouSteel then fires pellets in kilns for hardening. The company sells the finished pellets as raw materials for blast furnaces used to produce industrial metals such as iron. ShouSteel?s handling capacity is approximately 24.5 Mt/a (27 million stpy) of ore. The company?s production capacity is 3.2 Mt/a (3.5 million stpy) of oxide pellets and 560 Mt (650 million st) of sinters. Until recently, ShouSteel Mining had not replaced its electronic scales in its series of ingredient chambers. Because of the wear and tear on these older scales, the weighing system began to encounter regular problems. The company experienced a high failure rate from the integrator, an unstable signal, weak anti-interference ability and low accuracy. ShouSteel also found that spare parts required during repairs were consistently high in cost and that system calibration was becoming increasingly frequent.

Jan 1, 2012

By W. D. Fogwill, P. J. Clarke

"The Dawn Lake uranium deposits are located 340 km north of La Ronge, Saskatchewan, in the Athabasca Basin between the Midwest Lake and Rabbit Lake deposits. Four zones of uranium mineralization, called the ""11, 14, 11A and 11B Zones,"" lie within the Athabasca Sandstone, at the sub-Athabasca unconformity and in the basement.At Dawn Lake, approximately 100 metres of Helikian Athabasca Group clastic sediments overlie Aphebian Wollaston Group pelitic and calcareous metasediments and pegmatites. Uranium with some nickel, cobalt and copper, occurs near the sheared stratigraphic contact between calc-silicate gneiss and graphitic, pyritic pelite. The mineralization lies in an area of low magnetic susceptibility which is thought to represent a rock sequence lying stratigraphically high within the Wollaston Group. There is no obvious vertical displacement of the unconformity by faulting, despite considerable brecciation, shearing and slickensides seen in the basement rocks. This suggests horizontal displacement on steeply dipping wrench faults as the main tectonic control along the 11, 11A and 11B trend.Below the Athabasca unconformity, the Wollaston Group rocks are altered to fine-grained mixtures of clays, chlorite and silica commonly called regolith. Along the mineralized trend post-Athabasca fracturing and (or) compaction have occurred through this clay-rich alteration zone, causing the steeply-dipping primary foliation to become contorted. This ""crenulated"" horizon can reach depths of 35 metres below the unconformity and is thickest along fault zones in the calc-silicate rocks. The ""crenulite"" is a distinctive unit which at Dawn Lake is commonly found above pods of ore located deep below the unconformity.Much of the mineralization in the 11A and 11B Zones occurs above, beside and below the thickest part of the crenulated zone, although the crenulated rock itself contains negligible amounts of carbonate, pyrite and uranium. Intense vuggy alteration and collapse breccias are found in calc-silicate rocks deeper and to the west of the 11A and 11B mineralization. There are at least two ages of uranium deposition in the basement zones, shown by small bright cubes of ""pitchblende /"" overgrown and replaced by duller botryoidal ""pitchblende II. ""Sooty pitchblende and yellow secondary minerals are the result of still younger reworking.The geological setting of mineralization, along the contact between carbonate-rich calc-silicate rock and pyritic pelite, suggests that the uranium was concentrated at a pH/Eh boundary located between deeply weathered, carbonate-rich and sulphide-rich basement rocks."

Jan 1, 1986

By N. Ginouse, S. Reny

"In the mining industry time is critical as production depends on the speed of the mining cycle. During the mining process, the time required to re-open access for the next phase of an underground heading is a key point that strongly depends on the ability of the selected ground support technique to promptly ensure the safety of workers. Fiber reinforced dry-mix shotcrete has been proven to be an efficient and well adapted technique, able to produce a ground support material with the required energy absorption or flexural toughness in a single application phase. In this context, this paper demonstrates the possibility of significantly speeding up the mining process by using a new fiber reinforced dry-mix shotcrete. The new fiber reinforced dry-mix shotcrete is capable of developing flexural toughness in only 24 hours that is equivalent to what is typically achieved after 28 days using current fiber reinforced drymix shotcrete technology.INTRODUCTIONShotcrete is often used for ground support when using the drill and blast method or other tunnelling methods. But before re-opening access for the next phase of the underground heading, the applied shotcrete is required to reach a minimum compressive strength and in case of fiber reinforced shotcrete, a minimum flexural toughness (energy absorption) in order to ensure the safety of the workers going into the heading. Combined with bolts, the use of conventional fiber reinforced shotcrete becomes an interesting method for ground support as it is applied very soon after excavation and works to stabilize ground movements (Bernard E. S., 2009). In this case, the toughness development of fiber reinforced shotcrete becomes an important feature of the material when looking to speedup the mining cycle. However, early re-entry criteria in underground openings are difficult to ascertain as the load carrying capacity of fiber reinforced shotcrete is usually assessed after 7 or 28 days. For this reason, re-entry criteria varies from one mining area to another and are usually based on compressive strength requirements. For example, in northern Ontario, Canada, one of the current practices in the mining industry consists of allowing safe re-entry once fiber reinforced shotcrete has developed a compressive strength of higher than 4 MPa (Dufour, O’Donnell, & Ballou, 2003). Flexural toughness requirements on fiber reinforced shotcrete are also typically based on evaluation after 28 days."

Jan 1, 2015

By W. Blake, J. Whyatt

Sixty years of rock bursting in the Coeur d'Alene district has taught painful lessons and led to a number of practical advances in controlling rock-burst hazards. This paper summarizes these lessons, concentrating on practical measures that have been successfully adopted to reduce hazards. These lessons are explained in the context of district mining history and current understanding of rock-burst phenomena. Overall, the paper provides the practicing mine engineer with an appreciation of rock-burst hazards and an overview of practical measures that can be used to control these hazards in the context of Coeur d'Alene district experience.

Jan 1, 2003

"Conveyed coal flows have been diverted on the basis of real time ash analysis since the 1980s. Many coarse particle separation methods are available through screens, jigs, heavy media separation, particle sorters, to name a few, however bulk diversion requires a representative, continuous analysis to ensure diversion decisions can be made with confidence. Sensors also need to be able to provide measurements at useful time increments so that small tonnages can be diverted for maximum selectivity. Particle separation typically requires high capital costs and there are limitations either in throughput tonnage or particle size or both. Few techniques are able to provide robust and representative analysis of conveyed flows in a useful time basis. Prompt Gamma Neutron Activation Analysis provides multi-elemental analysis of conveyed bulk materials and has been proven in the minerals industry since 2003. This paper outlines the success of this technology in minerals applications in iron ore, phosphate rock and most recently in copper-gold ores, including its use in bulk diversion.INTRODUCTION Naturally occurring quality variability, or heterogeneity, in mineral deposits enables separation and recovery of the valuable components through mining and processing operations. There are distinct advantages in processing the minimum quantity of material to achieve the highest possible yield. Unfortunately, declining ore grades has resulted in larger scale operations and a subsequent loss in selectivity for mining operations. As limits are approached on the practical size of equipment, there is more motivation to investigate alternative solutions. Mining companies are subject to increasing social resistance to growing waste disposal requirements in addition to higher energy and transport costs. Major savings are available by reducing the quantities of material processed where pre-concentration can be effectively applied at early stages in the process. One of the simplest ways to pre-concentrate is to measure the bulk material and reject waste soon after mining so that minimal expense is incurred and that only higher quality material is sent to processing operations. This bulk sorting can occur within the mining operations and has major benefits through energy and other consumables savings. This paper discusses the application of real time analysis technologies suitable for bulk sorting within the minerals industry. Technology that has proven representative for conveyed material bulk analysis and its successful applications to date is explained. Analysis using a sensing technique is only one component of a successful bulk sorting process; the importance of effective diversion systems and a bulk sorting strategy are also discussed. The bulk sorting stage may be one component of a system that could include additional downstream technologies such as particle based sorting systems on a diverted stream."

Jan 1, 2018

By Andy Boeckmann

Engineers and owners widely recognize the benefits of foundation reuse - cost savings, reduced construction schedules and reduced environmental impacts, among others. Yet for many projects with existing foundations identified as reusable, reuse is an idea that is discussed at length before cold feet prevail. To address this disconnect, Deep Foundations Institute (DFI) formed the Foundation Reuse Task Force in 2021, which intends to promote reuse, leveraging experience among DFI members and collaborating across pertinent committees. Indeed, the task force includes about 40 members drawn from the Subsurface Characterization for Deep Foundations, Sustainability and Testing and Evaluation committees. One of the first orders of business for the task force was to create a database of successful reuse projects, developing short summary documents highlighting the database projects and recruiting reuse-focused presentations for the ITS Money program. Solid progress has been made on each front: the case history database includes 12 cases so far; the first three summary documents were recently published to DFI's website and foundation reuse projects have been well represented among the past year's ITS Money program. The reuse case history summary documents are available at www.dfi.org/foundation-reuse- case-histories; each of the three is also discussed below. The summary documents demonstrate the feasibility and benefits of foundation reuse. The documents are therefore a useful tool for foundation engineers to share with owners, structural engineers and anyone else who may be hesitant to pursue foundation reuse. The task force continues to welcome new members and anyone interested in joining can contact Andy Boeckmann. The task force is also eager to highlight additional reuse success stories. Anyone with case history information to share is also encouraged to contact Boeckmann.

Jul 1, 2022

By C. M. Young

Bituminous coal piled in heaps or bins frequently undergoes a process of spontaneous heating as the result of the absorption of oxygen. It seems probable that the first absorption of oxygen by coal which has not previously been exposed to the air may occur as a condensation or a combination of oxygen in some form which does not result in the production of carbon dioxide, but slow combustion soon begins. The absorption of oxygen is accompanied by an increase of temperature, and this by an increased rapidity of absorption; hence the dangerous condition proceeds from bad to worse, until the kindling point is reached, unless the process is interrupted. A dangerous rise of temperature can be prevented by excluding oxygen, by increasing the bulk of coal in proportion to its surface exposed, or by circulating enough air to dissipate the heat produced. The storage of coal, in practice, varies from almost complete exclusion of oxygen, by storing under water, to such freedom of access as exists when the coal is stored in open piles. Oxygen available for absorption by coal is supplied by the air in the interstices between lumps and by additional air which may enter the pile through circulation. The size of the coal largely affects both of these supplies; for if the fragments are small the spaces between them constitute a small percentage of the total volume, and little oxygen will be available unless the circulation of air brings in a fresh supply, while with large fragments the percentage is relatively large; circulation also is much easier through a pile of coarse lumps. In the case of lump coal, although a large amount of air may be present, the exposed surface is comparatively small and there is little opportunity for the absorption of oxygen to be so rapid as to cause dangerous heating. Attempts have been made to prevent heating by allowing a sufficient circulation of air to carry off the heat generated; obviously this method cannot be applied to fine sizes nor mixed sizes. When storing coal at the University of Illinois, an attempt has been made to use so much fine coal and to pack it so thoroughly as to prevent circulation of air, while also reducing the original air in the pile so as to prevent heating. This method has been fairly successful, but in some

Jan 1, 1918

By J. W. Davis

In the last few years major industrial companies have begun to realize the importance of Reliability as an enterprise strategy that, properly implemented, will improve financial performance. Typical results of an effective Enterprise Reliability Strategy include a 20% -50% reduction in maintenance cost accompanied by a 5% - 10%increase in real production capacity, with no capital investment in production equipment. One factor fueling the race to acquire and implement enterprise reliability is the pressure for companies to be increasingly cost-effective and competitive in global markets. In a recent study, Asset Productivity: The Next Wave, the Boston Consulting Group (BCG)stated that, “In order to compete for funds, companies must offer investor returns that are competitive with other opportunities. Alternative investments such as dot-com and others with non-traditional business models have raised the bar.” (APDF version of the study can be downloaded at www.bcg.com). BCG views asset productivity as the most powerful mechanism for increasing shareholder return. The author believes that the most effective way to increase Fixed Asset Productivity is to maximize asset utilization by increasing the Reliability of the Assets and the associated processes. Developing and implementing an ERS requires significant effort and knowledge. Most companies have difficulty finding a sufficient supply of these valuable commodities to implement an ERS Program internally. Many companies also struggle with figuring out how to get started and what direction to proceed.

Jan 1, 2003

By Gordon MacVean

THE adoption of rock dusting, as a safety measure, has made notable progress in the West Virginia coal mines since May, 1925. At that time there were but two mines in the State that were thoroughly rock dusted, mines No. 2 and No. 12 of the Boone County Coal Corp., at Sharpless. Since then it is probable that 75 per cent of the coal operators in the State have given consideration at one time or another to rock dusting. This growth of interest followed the meetings of the various mining institutes all over the country, during the summer of 1925, at which papers were presented, drawing the attention of the coal mining operators to the merits of this safety measure. Yet outside of the experience with rock dusting at the Old Ben Coal Corp., of Southern Illinois, and the Carbon Fuel Co., of Rains, Utah, there had been no actual occurrence in the coal mines of the United States, which could be taken as positive evidence of the efficacy of rock dusting in the prevention of the propagation of coal dust explosions. The U. S. Bureau of Mines, however, had run innumerable tests under conditions which closely approximated actual coal mining conditions and had clearly shown that rock dusting was effective.

Jan 1, 1926

By Charles Waidner

IN response to many urgent requests for a concrete realization of a series of standard temperatures that would be available to any one anywhere for the standardization of pyrometers and the reproduction of the standard scale of temperature for use in laboratories and industrial works, the Bureau, in 1916, made arrangements with several manufacturers to prepare a series of- pure metals that could best serve this purpose. After the necessary preliminary work of chemical analysis, as a check on the purity, together with exact determinations of melting or freezing points, the Bureau began, in 1917, the issuing of melting -point standards of tin, zinc, aluminum, and copper. At the outset, it was decided to secure metals of the highest purity and of American manufacture, and this was accomplished in a more satisfactory manner than anticipated. In the preparation of these temperature standards, the Bureau has had the hearty cooperation of several American companies, which have succeeded in producing metals highly satisfactory for the purpose and of as high a state of purity as could have been obtained anywhere. Each company that undertook the responsibility of furnishing a metal for this series of standards exercised most painstaking care to produce the best possible product as to purity and uniformity. A representative of the Bureau witnessed the actual preparation of each metal. The 300 and 400-lb. (136 and 181-kg.) samples making up the first series were all used up, with the exception of the aluminum, early in 1919. The Bureau has taken steps to replenish its stocks of metals serving as pyrometric standards and to the list has been added lead. The copper and lead are being ordered this time in 1-ton lots and the zinc and tin in 300-lb. (136 kg.) lots as before. The wide dissemination of these samples will be appreciated when it is noted that the metals are distributed by the Bureau inn quantities of 50 cu. cm. each, at $2 a sample and accompanied by a certificate which gives the melting point as determined by samples from the same lot. The manufacture and detailed description of chemical analyses, physical measurements, and precautions in use of these pyrometric standards, are described in detail in the Bureau Circulcar No., 66.

Jan 8, 1919

By Robert L. Zook

Coal refuse slurry impoundments are dams constructed of coarse coal refuse to impound fine refuse (slurry) and water (25-30% solids). Both products are waste from coal preparation plants. A number of these structures in West Virginia, Pennsylvania and Kentucky were investigated to determine embankment stability. During the investigation a variety of embankment designs were encountered. The investigation determined the soil and geological characteristics of the embankments and the sites. This was accomplished by a test drilling and monitor installation (observation wells and piezometers) program, geologic study, and large scale mapping which allowed sub-surface profiles of the embankments to be constructed. The laboratory testing program concentrated on textural classification of the coal refuse, permeability and determining strength parameters to be utilized in the stability analyses. For the stability analyses, the Modified Fellinius Slip Circle, Simplified Bishop Slip Circle and Analysis for Translational Failure -were utilized. In all stability analyses hydrostatic pressure and earthquake were considered. This investigation indicated that 62% of the embankments analyzed are in a stable condition. The coal seam mined, the type of roof rock, and the gradation of the refuse influence the degree of compaction obtainable and the permeability of refuse. The shear strength of coal refuse appears to be controlled by its composition, moisture content, degree of compaction, amount and grain size of fines present. This investigation demonstrated these em¬bankments should not be treated as pure state-of-the-art dams; consideration must be given to the particular properties of coal refuse and the total refuse disposal system. Refuse dim slurry impoundments generally lack the site se- lection phase that is standard practice with siting most other types of dams.

Jan 1, 1974

By A. K. Raina

Blast induced damage to the final wall of rockmass in any civil or engineering application is a major concern to the rock excavation engineers. There are at least four distinct techniques practised by blasting engineers to minimise the damage to the parent rock during blasting that are classified as contour blasting. One of the methods to achieve a smooth wall or rock surface in blasting is pre-splitting, where blastholes in the final row are mildly loaded with explosives and fired first in sequence before the rest of the holes in a round of blast to achieve a split in rockmass. Since blasting is one of the most adopted methods for achieving a final wall in a desired shape, while maintaining the rockmass integrity, the design of pre-split blast assumes importance. There are several variables that determine the final shape of the pre-split face including the rock type, the drill diameter, the explosive characteristics, the orientation of major joints with respect to drill hole, the linear charge density, the spacing of drill holes and inclination of the drill holes. This study attempts to determine the importance and sensitivity of variables in pre-split blasting using historical data from open excavations of a hydroelectric project in India. Keeping in view the multitude of variables, low correlation of independent variables with responses and high level of interactions between the variables that define the blast results, it was found suitable to use ANN to determine the importance and sensitivity of the variables involved. A new method to determine the blast induced damage to rockmass, namely, undamaged area (AUD%), is introduced. Half Cast Factor (HCF%) and AUD%were calculated for a high wall and trenches by digital image analysis technique using the Fragalyst software. Joint spacing and linear charge density emerged as most controlling variables in determining the final result of pre-blast. The relative importance of other variables assuming significance in the case of both the designed outputs is also discussed. A comparative analysis of HCF%and AUD%on the basis of results obtained from ANN analysis is also presented. A futuristic approach concept has also been introduced.

May 30, 2021

By Daniel G. DiCanio

This report describes a computer-based model for estimating the tangible costs of injuries and deaths from work-related accidents in underground coal mines. The study undertook to identify and quantify the elements of accident costs, including field visits to coal mines, insurance carriers, and public agencies. The mathematical models developed for each tangible element of accident cost are presented in Volume I of the report. A listing of the computer programs which comprise the model and instructions for using the programs are presented in Volume II. Statistical distributions of mining family characteristics, data on 95 miners killed in underground accidents, and other basic data used to develop the model are presented in Volume III. Application of the model to a data base of 9,286 accidents which occured in underground bituminous coal mines during 1974 yielded a total of $56,900,000 in tangible costs to industry, mining families, and public agencies. Loss of income to the families of miners injured or killed in these accidents accounted for 47 percent of the total.

Jan 1, 1976

A simulation of a capper concentrate smelter was built with a capacity of 450,000 tons per year. The system's components to simulate were three : a Reverbetory furnace, a Wiente ' s modified converter ( TMC ) and two cranes. The system was classified as dynamic, stochastic and discrete. In the simulation language choice it was concluded that the most advantageous one was GPSS/H. The model verification was done through the interactive Debugger that the language has and the statistical validation was done through the result variables of sane activities, that as a whole characterize the system (charged matte and charged concentrate to the TMC, skimming white metal and skimning slag). The validation was done comparing the simulation results of these variables with the ones obtained for those variables in a specific month in the smelter. The comparison consisted in a difference of means test and in all cases the equality was accepted with a 95% of confidence. The animation tool was PROOF, a general purpose animator, that is used after processing the simulation.

Jan 1, 1994