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By R. Stanevich

Studies by the National Institute for Occupational Safety and Health (NIOSH) and the Bureau of Mines (BOM) have demonstrated that: (1) 90% of diesel particulate is less than one (1) micrometer in aerodynamic diameter; (2) more than 90% of the respirable mass in electric coal mines was greater than one (1) micrometer in aerodynamic diameter; and (3) in coal mines using diesel equipment, average diesel concentrations can represent up to 53% of the MRE respirable coal dust standard. For mines approaching the 2 mg/m3 standard, compliance may be easier to attain by controls directed at diesel exhaust particulate as opposed to coal dust control. First, however, a Simple instrument is needed to measure diesel exhaust particulate concentrations. This paper describes such a sampler, its construction, and use. While results from this sampler are primarily utilized to identify control areas, NIOSH is also using the sampler for estimating worker exposures in epidemiologic studies.

Jan 1, 1988

By S. S. Peng

This paper presents a computer program package for predicting surface movement and deformation caused by under-ground coal extractions. It is capable of: predicting final surface movement and deformation over underground openings; predicting dynamic surface movement and deformation process associated with underground lingual mining operations; processing and bookkeeping subsidence survey data; recommending subsidence parameters for those new coal mines where no subsidence data are available; and deducting subsidence parameters from collected subsidence data.

Jan 1, 1986

By David H. Searle

This paper will discuss the common trends existing in various Canadian jurisdictions for the closure and reclamation of mines. Included will be a discussion of the requirement to post security as well as its form and how security is calculated and refunded. Reclamation can no longer be left to the end of mine life. Progressive reclamation must occur throughout mine life and must be part of the mine plan from the beginning.

May 1, 2006

Computers and other microprocessor technology lead the world of technological change. Nevertheless, the real advances in the world at large are not necessarily in the computer industry, but in the industries whose economics benefit most by the advances that this computer revolution makes possible. The minerals industry has always been in the forefront of this advance. Technological change in the era preceding the industrial revolution, and the mining industry's part in it, provides an instructive lesson for what is happening today. Strong parallels can be drawn for predicting future advances. With each technological advance allowing more efficient production comes a re-alignment of economics - absolute and relative changes to prices, to quantities demanded, and to other market characteristics. This re-alignment applies not only to the mineral industry, but also to the world at large. Adaptability, rather than technical advancement per se is the key to survival and growth in a changing world. 'Adaptability' as a concept is easy to support. As an operational philosophy it is not so easy to implement. As a goal for planning, it is much harder to quantify. A fixed scenario of a future world may provide helpful guidelines, but a scenario that demands adaptability to an uncertain future world is much less definite. Of course, everyone else in the world is also uncertain about the future, and they are making their plans using different assumptions. This virtually guarantees that our future will turn out different to our expectations. This is in part what Hayek (1945) calls the 'knowledge' problem. Until now, most of the planning and technical research undertaken in the world has ignored this problem. This ignorance is a luxury that we can no longer afford. The paper looks at the history of technological change and highlights the characteristics of successful technological revolutions. 'Adaptability' to unforeseen circumstances is the key to success in this environment. The paper examines the knowledge problem from the perspective of the mineral industry, and suggests a number of directions for maximising the returns from application of computer technology in this important area.

Jan 1, 1995

By James Rowland, Isaac Zlochower, Richard Mainiero, Michael Sapko

The National Institute for Occupational Safety and Health (NIOSH) carried out exploratory laboratoryscale studies to identify factors that may contribute to nitrogen oxides (NOx) production associated with non-ideal detonation of blasting agents. Explosive admixture with drill cuttings, loss of fuel oil in ammonium nitrate and fuel oil (ANFO) from wicking, ammonium nitrate dissolution with water, degree of explosive confinement, ANFO density, and critical diameter were identified as contributing factors to increased NOx production under the laboratory test conditions. Experiments were also conducted to examine the effectiveness of various additives in reducing the NOx production from ANFO, emulsion, and ANFO/emulsion blends. Aluminum powder, coal dust, urea, and excess fuel oil in ANFO formulations were tested and were found to reduce both the nitric oxide (NO) and nitrogen dioxide (NO2) production. Fumes measurements were obtained in the NIOSH underground closed chamber from the detonation of 4.5-kg (10 lbs) charges in schedule 80 seamless steel pipe and from detonations in light weight galvanized steel stove pipe. Some exploratory tests were also conducted with 0.8-kg (1.8 lbs) charges of pulverized ANFO initiated with 0.08-kg (0.18 lbs), 50/50 (Pentolite) boosters (in the NIOSH 12-ft (3.7-m) diameter steel sphere) to measure the degree of fumes production associated with post-detonation oxidation. Ammonium nitrate, emulsion and Pentolite boosters were also detonated in an oxygen-poor environment.

Jan 1, 2002

By P Shenon

THE Elk City district is in north-central Idaho about 60 miles east of Grangeville and near the headwaters of the South Fork of the Clearwater River (Fig. 1). At the height of its boom in the early sixties, Elk City had a population of more than 2000 people.1 Published estimates of the placer production from the district range from $10,000,000 to $18,500,000. Although the first quartz-vein location was made as early as 1870, very little gold was extracted from quartz ores until after the completion of the American Eagle mill in 1902. Between 1902 and 1932 a total of from $750,000 to $1,000,000 was taken from about six properties.

Jan 1, 1934

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.' They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

By Mo Jadbabaei, Scott Harrison

There is very limited information available regarding the air pressures, flow rate, and velocity profiles in blast hole air drilling applications. Currently, many people are using incompressible flow correlation to calculate the bailing velocity. In this article, air pressure, flow rate, and velocity profiles are calculated using compressible flow theory. The airflow at the bottom of the hole is simulated using the jet flow theory. The concept of choking condition is introduced, and it is concluded that the velocity at the nozzle exit cross section cannot exceed sonic velocity. The minimum pressure required for achieving choked condition at the nozzle cross section is calculated. Choked and overchoked flow conditions at the nozzles are examined, and the maximum achievable cleaning power is correlated to the nozzle size and pressure.

Jan 1, 1999

By John A. DesLauriers, Hans J. Broennimann

INTRODUCTION The early record of tunnel excavating machines in hard rock tunneling has not been one to particularly brag about. We have all heard the stories of major difficulties when trying to break hard rock with machines at promised advance rates of several times that of conventional drill and blast. Unfortunately, sometimes this has not happened. It has been through this trial of the past generations disappointments that today's TBM's have evolved to their present high level of performance in a wide range of ground conditions. Today's machines offer much increased reliability and durability. This translates into high availability to the tunnel contractor. Although there still are occasional disappointments being reported, the state of the art is that reliable and predictable machine excavation of rock now is both a reality and well founded expectation. The most recent editions of Atlas Copco's MINI/MIDI Fullfacer, we feel, make a strong contribution to the reliable performance of todays TBM's---especially in small-size rock tunnels. This report will, 1.) explain the equipment and effect of rock both on the cutting technique and machine performance; 2.) list advantages of the non-circular shape, during and after construction; 3.) list applications in civil and mining industries; 4.) discuss North American experiences, performance and costs; 5.) list advantages over drill and blast and; 6.) discuss briefly lease arrangements.

Jan 1, 1979

By G. W. Thomas

A simplified mathematical model of underground conduction heating in a system of limited permeability is presented. The model applies to underground retorting of oil shale, or to reservoirs containing extremely heavy oils. We assume that heat is introduced at a constant rate into a horizontal fracture which communicates between wells. The radial temperature distribution along the fractured surface is approximated by a step-function. Heat transfer away from the fracture is assumed to be by vertical conduction, and all convection effects are neglected. The model also takes into account the possible temperature dependence of thermal conductivity. A general expression for calculating the growth of the step-function temperature distribution with time is derived. The use of this expression and solutions to the one-dimensional heat equation make it possible to construct isotherms. Expressions for calculating .oil recovery, well spacing and heat efficiency are also given. An example calculation is presented for the conduction heating process in oil shale. Finally, the effect of the heat transfer coefficient between the gas and the fracture boundaries is investigated. INTRODUCTION Thermal recovery processes of oil recovery fall into the four general areas of hot fluid injection, forward combustion, reverse combustion and conduction heating. The first three of* these processes have been rather extensively studied in the past decade from both the experimental and theoretical points of view. As a result, it is possible to make reasonable engineering predictions and analyses of these processes. Little attention has been devoted, however, to the conduction heating process other than to note its possible utility.I To a certain extent, conduction heating cannot be divorced from the other regimes cited above, insofar as these provide the source of heat energy. In the conduction heating process, heat is introduced (either by combustion in the forward or reverse mode or by hot fluid injection) into a small fraction of the total reservoir thickness. This fraction may be either a streak of high permeability or an interwell fracture. Heat penetrates by conduction into the adjacent, less permeable regions of the oil-bearing rock, where the direction of conduction is essentially perpendicular to the streak or fracture. The heated product then drains by gravity or is gas driven to production wells. Conduction heating is probably most applicable to systems containing immobile bitumens such as tar sands and oil shale deposits and perhaps to low-permeability reservoirs containing highly viscous crudes. The mechanism also acts in combination with other thermal processes where fingering or overriding of a bed occurs. It seems probable that in at least one field test, conduction heating of this type was very influential.2 In this presentation we give a first approximation to some of the quantitative aspects of conduction heating. Marx and Langenheim3 treated a similar problem where they focused attention upon the injection interval, which spanned the total reservoir thickness. In their model, conduction heat losses to the bounding media imposed a practical limit on the calculated heated area. In the present study, however, we shall confine the injection interval to a small fraction of the reservoir thickness and assume it has no heat capacity. We therefore direct our attention to regions outside the injection interval into which the conduction of heat is beneficial. In particular, we will endeavor to locate specific isotherms in the media bounding the injection interval. Furthermore, we will construct our model to allow the thermal conductivity to vary arbitrarily with temperature. Thus the model will be applicable to underground retorting of shale where variations in thermal conductivity may be important. THEORY We consider the rock matrix to have no or, at best, a very limited permeability; consequently a

Jan 1, 1965

By John F. McCoy

The U.S. Bureau of Mines (USBM) awarded? a contract to Foster-Miller, Inc. to develop guidelines for designing, constructing, stocking, and maintaining rescue chambers in underground mines. This report develops information and recommendations which could be used by a mine operator who desired to install a rescue chamber. Volume I covers the following major areas: atmospheric life support, configuration and construction, chamber location, power and lighting, equipment and supplies, communications, and psychological aspects and training. Volume II contains the following appendices: History of Barricading, Chamber Pressuriztion Considerations, Diffusional Infiltration of Gas, Compressed Air Storage, Location Examples, and Psychological Aspects.

Jan 1, 1983

By Horace Pops

Martensitic transformation has been studied during cooling and heating in ß-phase Cu-Zn alloys to which small additions have been made of Ni, Ag, Au, Cd, Ga, In, Si, Ge, Sn, and Sb. The start and finish of the martensitic reaction and the variation of transformation temperature with third-element content were determined by electrical-resistivity measurements from alloys which had either constant zinc contents or constant values of electron concentration. All of the third elements, except nickel, lowered the transformation temperature if the results were plotted along the lines of constant zinc contents in each ternary system. A significant difference in the rate of lowering of the transformation temperature per atomic percent of the third element was observed for elements which had the same nominal valence. No systematic variation of transformation temperature with the valence of the third element was observed. It is suggested that the observed increase in transformation temperature for nickel-bearing alloys is due to the transfer of electrons from the conduction band of the alloy to virtual bound states. However, electron concentration is not the most important factor controlling the instability of the 0 phase. The transformation temperatures of the ternary alloys can be predicted from the following approxilnate expression: Ms (°K) = +3280 - 80 Zn + 8 Ni - 30 Ag - 12 Au - 140 Cd -90 Ga- 145 In - 80 Ge -175 Sn - 120 Si - 150 Sb MOST binary ß -phase alloys based upon the noble metals copper, silver, and gold are unstable at low temperatures and transform spontaneously by a martensitic reaction. This transformation has been studied recently in the ordered bcc ß'-phase Cu-Zn binary al1oys1,2 where the transformation temperature is below the room temperature and decreases with an increase in zinc content. It has been reported that the transformation temperatures can be raised above room temperature by small additions of a third element such as silicon3,5 or gallium,4,5 but no quantitative study has been made. The transformation temperature of different binary alloys can be altered by third-element additions. For example, it was shown that nickel and copper may have a large effect on the Ms temperature of CU-Al6 and Au-cd7 alloys. The present investigation was made to determine systematically the influence of various third elements on the martensite-transformation temperature of Cu-Zn ß-phase alloys. Since these alloys have an electronic origin,' alloy compositions were chosen so that the transformation temperatures could be determined at constant zinc contents or at constant values of electron concentration. I) EXPERIMENTAL PROCEDURE Ten ternary alloy systems were obtained by adding nickel, the noble metals silver and gold, and some B-subgroup elements to a Cu-Zn matrix. These are arranged according to their rows and columns in the Period Table as follows: Each ternary alloy was prepared by melting and casting weighed quantities of high-purity metals (99.99+ pct) in sealed quartz tubes under a partial pressure of helium to make a 4-g ingot. The molten alloys were shaken vigorously and then quenched in water. Since the weight loss was negligible, the compositions of the ingots after casting and annealing were assumed to be the same as the nominal compositions. The ingots were homogenized after casting in helium-filled Vycor tubes for 24 hr at temperatures between 750" and 810 C and quenched into brine. Metallographic examination revealed that all alloys were homogeneous, poly crystalline ß-phase alloys, and that the grain size was in the range 1 to 5 mm. Electrical-resistivity measurements were made to determine transformation temperatures of the ternary alloys during continuous cooling or heating. Transformation temperatures of the ternary alloys can be determined by electrical-resistivity measurements since the resistance of the martensitic phase is much higher than that of the 0' phase. The technique has been described previously in connection with a study of Au-Zn alloys.9 The reproducibility of transformation temperature was approximately ±6°C. II)RESULTS A hysteresis was always observed in electrical-resistivity curves and was usually less than about 12°C.

Jan 1, 1967

By N Cusworth, W R. Mackenzie

"In 2007, the authors presented a framework for the conduct of resource project feasibility studies and provided guidance on minimum standards and best practice (Mackenzie and Cusworth, 2007).This paper will present the authors’ observations in relation to feasibility studies undertaken to support investments made during the unprecedented period of resource project capital investment since 2007. It will also provide comments on general trends in the mining industry’s approach to project assessment and update recommendations on best practice.CITATION:Mackenzie, W R and Cusworth, N, 2016. The use and abuse of feasibility studies – has anything changed?, in Proceedings Project Evaluation 2016, pp 133–148 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 8, 2016

Jan 1, 1915

By Joseph B. Perry, G. M. Kirwan

MagnEsitE is found in 22 California counties, but many of the deposits are too small or too impure to be of commercial value. Several of substantial size and quality were entirely exhausted by wartime operation. At present, three properties comprise the only known workable deposits in the state. Of these, the Western mine and the Patterson mine have been known and worked for many years, and have been described in considerable detail in various publications, therefore need only brief mention here, because of their proximity to the Bald Eagle mine. The latter, recently developed, is unusual in type of ore deposit, plant design and operation, as well as products made, and very little has been written concerning it. WESTERN MINE The Western mine, 32 miles south of Livermore, Calif., was formerly operated by C. S. Maltby. It has been a consistent producer for many years.l The ore is of amorphous variety, occurring along fracture zones in serpentine. The veins vary greatly in width, the average being perhaps 8 ft., with the maximum indicated in one early stope of 40 ft.; 2 ft. is considered the minimum for economical mining. The strike of the veins is predominantly north and south, with dip to the west varying from 40" to 75". Walls are well defined and as a rule firm and easily supported. Veins range in length from a few hundred feet to 1000 or more. Their maximum vertical extent is about 350 ft., but many run less. Early mining consisted of open-cut and glory-hole work on the larger outcrops. This was followed underground by a modified shrinkage system, the waste and low-grade horses being removed by hand sorting on the tramming levels and transported to surface dumps. Filled-stope mining is used now, in order to eliminate the handling of waste, which has

Jan 1, 1942

By F. Tailoka

Microporous membranes have been used to create a very fine dispersion of bubbles which greatly enhances the mass transfer of electroactive species to the electrode. Using this system, it has been shown that it is possible to electrowin copper as a coherent planar deposit, at high current densities, from copper chloride solutions.

Jan 1, 1990

By B. W. Gandrud, G. D. Coe

"INTRODUCTION The Bureau of Mines, United States Department of the Interior, with the cooperation of the University of Alabama and coal producers of Alabama, is making a series of washability studies to obtain technically and commercially important data from the productive coal beds of the State. Based on the system followed in these studies, this report consists of screen-sizing and sink-and-float data on the America and Pratt beds at Gorgas, Ala.SAMPLING AT THE MINESAlthough operations were discontinued in 1929, the accessible openings of the old Gorgas mines of the Southeastern Fuel Co. made possible the taking of samples from the America bed at three openings and from the Pratt bed at two openings. A sample was taken from the America bed at the Klondyke opening; a second was taken about 1 rile south of the Klondyke at the Musgrove America opening, and a third sample was taken about 1-1/2 miles south of the Musgrove-America at the Cricket Lodge opening. A sample was taken from the Pratt bed at Musgrove-Pratt No. 1, which is about 3/4 mile east of Musgrove-America, and a second sample was taken at Musgrove-Pratt No. 2, which is about 3/4 mile west of Musgrove-America. The samples ranged in weight from 1/2 ton to 1 ton and were equivalent to approximately a 2-ton sample from each bed. Figure 1 shows sections of the beds at the places sampled.In addition to the samples for washability study, a seam sample for analysis was taken at each of the places sampled. So as to give a representative seam sample for each of the two beds, these samples were combined in the laboratory in proportion to the thickness of the bed at the places sampled."

Jul 1, 1939

By Randy R. Williams, Brian W. Wilson, George M. Filz, Marina S. W. Li

"Detailed design of an extensive deep mixing (DM) scheme using the Cutter Soil Mixing (CSM) technique was completed for foundation support of mechanically stabilized earth (MSE) walls for Kitimat Liquefied Natural Gas (LNG) at Bish Cove, British Columbia, Canada. The design was based on the provision of soil-cement structures, constructed in highly variable subsurface conditions that consisted of thick deposits of fine-grained soils overlying granular soils, and required to meet project-specific performance criteria, to support the MSE walls. The design, consisting of rectangular CSM panels constructed to form barrettes connecting to a longitudinal wall of continuous CSM panels, was configured to manage the distribution of stresses and strains that could be developed within the soil-cement structure.The results from 2D finite element analyses were used to determine the necessary arrangement and properties of the CSM panels to accommodate localized areas of relatively high shear, tensile and compressive stresses within the soil-cement structure. The relationships between unconfined compressive strength and elastic modulus for fine-grained and granular soil-cement structures obtained from the Bish Cove data were compared with published references and were found to be significantly different in the higher strength range materials.BACKGROUNDDeep Mixing design was completed for the development of the Kitimat LNG Facility located in Bish Cove, British Columbia, for support of two relatively high MSE walls and associated bulk earthwork operations. Deep mixing was necessary to treat the very weak native deposits in-situ to meet project performance requirements and physical constraints without the need for significant excavation and disposal work. The DM design was undertaken on the basis of adoption of the CSM technique for in-situ ground improvement of the native foundation soils which consisted of very soft to soft fine-grained marine deposits and loose to compact sandy silt to silty sand, overlying dense sand and gravel (Fig. 1). The DM area is located immediately upslope of the Bish Cove beach area, and is “L” shaped in plan, approximately 300 m long by approximately 28.8 m wide (parallel to the beach area) and 165 m long by an average width of 21.0 m (perpendicular to the beach area). The depth of the DM ranged from about 5.0 m to 30.7 m with typically 2.0 m embedment into dense granular soils. Details of the design philosophy, including an overview of the DM design and the project background information are presented by Li et al. (2014a). Details of the construction aspects of the Kitimat LNG deep mixing are presented by Wilson et al. (2014)."

Jan 1, 2015

By C. Ceccarini, I. Salvadori, G. Oggiano

GENERAL BACKGROUND The first mention of the presence of bauxite in the mesozoic series of north-west Sardinia (fig. 1) is owed to Oosterbaan, a Dutch geologist, who carried out a geological survey of the area in the ninetten thirties. A more detailed study of the mesozoic series was attempted in the fifties by Pecorini and other, who concentrated particularly upon the stratigraphy of the bauxitic horizons, through examination of the various outcrops. In the sixties a pining company, Monte Amiata S.p.A., turned its attention to a section of the deposit outcropping near Olmedo and, considering it to be of some promise, carried out prospecting works consisting essentially of various trenches, some bore holes, a few adit and a. layout plan for the preparation and execution of trial exploitation. The results, although positive, did not convince the company's shareholders to continue the exploration. This report, which is intended as a new contribution to knowledge of the Sardinian bauxite deposit, takes into account the information acquired not only from a drilling prospection begun in 1979 in connection with the SOMIT-PROGEMISA joint venture, but also the results of structural studies and numerous chemical, mineralogical and

Jan 1, 1984

By Katherine Harding

Basic concepts of matrix algebra and manipulations of matrices are presented in such a way that little competence in mathematics is required. Examples are always included to illustrate concepts and techniques. The paper is divided into six sections. The first four sections are devoted to some of the more basic concepts of matrix algebra, whereas the last two sections are concerned with specific applications.

Jan 1, 1967