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By J. B. DILWORTA

Ix estimating the investment-value of a mining-property or plant, the value of which decreases with operation, it is often necessary to know the sum which must be set aside periodically from earnings either to renew the plant at the end off its life, or to return the capital involved when the earning-power of the investment has ceased. In such cases it is manifestly incorrect simply to divide the total amount to be retired by the number of periods (usually years) during which the investment shall be active, as the sums periodically withdrawn have a certain interest-earning power varying with the length of time they are held and with the opportunities afforded for their investment. But though the interest may be considered to accumulate regularly year by year, yet the rules and tables for compound interest do not apply, owing to the addition of a fixed amount of new money to the total at the beginning of each period. Briefly stated, the problem of sinking-funds is, to find the amount of money which must be periodically set aside at a certain rate of interest, regularly compounded, to yield a certain sum in a given, length of time. In most practical cases the interest is compounded and the fresh amount added at the same time-usually once a year-and on this basis the problem may be solved as follows

Nov 1, 1909

By Frank Firmstone

Discussion of the paper of John B. Dilworth, presented at the Pittsburg meeting, March, 1910, and printed in Bulletin No. 35, November, 1909, pp. 1041 to 1043. FRANK FIRMSTONE, Easton, Pa. (communication to the Secretary*) :-Mr. Dilworth's formulas and tables are of course correct, and the extinction will occur as calculated, provided the money periodically set aside for sinking-fund be really invested. and the interest compounded as assumed in the calculation. Actually, in almost all cases, such funds are used "in the business," in which case, in addition to the periodical charges for principal of the fund, additional charges must be made at the end of each period to cover the interest and compound interest on previous charges. The periodical charge for sinking-fund thus becomes a varying and continually increasing one until the date of extinction. On many accounts it seems more natural and convenient to make the extinction by a fixed periodical charge under the legal rule for partial payments, namely, that each payment should apply first to the interest due at the date of payment;: and any remainder, after this is satisfied, be deducted from the principal before the interest for the next period is calculated. The formula below is convenient for such calculations S, Principal to be extinguished. Q, Periodical payment or charge for sinking-fund. B, Balance unpaid at date of nth payment, but before that payment is made. r, Rate of interest per period per cent. n, Number of payments or periods. Then, B=S(1+r)n-Q(1+ r)n-(1+r) Received July 27, 1910.

Apr 1, 1911

By Robert M. Becker

The evaluation of in situ rock stresses from measurements of the change in diameter of a borehole that is stress-relieved by overcoring has become a common practice. Generally the stress evaluation has been based on isotropic relations whereas rock in varying degrees is anisotropic. A plane elasticity solution for a circular hole along one axis of an orthotropic medium has been adapted to evaluation of in situ stress. The necessary elastic parameters for this evaluation may conveniently be obtained from static tests on the overcore in conjunction with a consistent orthotropic thick-wall cylinder solution. The method and equations for the laboratory and field evaluations are summarized and illustrated.

Jan 1, 1968

By P. E. Cavanagh

"The Davis tube test has been used for many years as a laboratory method for determining the magnetic iron re-coverable from a magnetite iron orebody. This paper de-scribes a method for determining the recoverable iron from ores of the Labrador Trough type, with the usua1 flow sheet utilizing spirals followed by magnetic separation.The mechanical structure of a metamorphosed iron ore, resulting from recrystallization over long periods of time, is the basis for the laboratory method developed. Similarities between the structures of such recrystallized ores and the structure of annealed and recrystallized steel are noted.A laboratory technique to determine the size of the different grains of gangue and iron ore minerals is de-scribed and the application of this information to arrive at recommended grinding techniques and flow sheets is demonstrated. The use of the method to determine recoverable iron in such ores is compared to actual iron recovery in the pilot-plant and commercial concentrations of the same ore.The use of a specified lower limit of recoverable iron as determined by this method, in order to design open-pit limits, achieves practical results when compared to designing a pit based on an arbitrary lower limit of total soluble iron. The Ungava Iron Ore deposits are used in giving an example of the resulting pit design changes."

Jan 1, 1968

By Frank F. Aplan, Edward C. Dowling, Richard R. Klimpel

Several series of time-instantaneous samples were taken on a cell-by-cell basis in the flotation circuits of the Pinto Valley, AZ copper concentrator. These samples were used to calculate mass flow rates throughout the circuit using standard, deterministic metallurgical formulae and also a variety of more statistically oriented techniques. Because of the magnitude of the errors associated with the individual cell samples, the standard metallurgical formulae are not sufficient. Consequently, it is necessary to utilize some type of statistical technique capable of distributing the individual cell sample errors in such a way so as to provide a physically useful mass balance for the entire circuit. This paper explores the use of linear and least squares programming as one technique to providing credible mass balance calculations. For linear programming this was done by distributing the error using two different criteria involving specific linear programming formulations: least absolute sum minimization (which assumes an underlying double exponential distribution error structure) and minimax (which minimizes the maximum absolute deviation and assumes an underlying rectangular distribution error structure). These results were then compared to the more standard formulation of minimization of the sum of least squares which assumes an underlying normal distribution error structure. The least absolute sum approach was particularly attractive due to its simplicity of use and the ease in which repetitive calculations can be done with no user intervention.

Jan 1, 1990

By Yumi Nakashima, Setsuo Maeda

Vibration magnitude and frequency of the z-axis vehicle seat are time-variant, which are influenced by not only vehicle vibration characteristics themselves but also road surfaces, speeds and the human body. There is little in the current reporting about evaluating and analyzing automobile seat vibration that focuses on the time-variant. Yaguchi et al.1 has proposed a method to evaluate automobile seat vibration that is based on judgments using a subjective mental state. Their method focuses on the time-variant magnitude of the peak frequency on a power spectrum density. However, their method has no consideration of all the frequency contents of the discomfort, nor comparison between different peak frequency vibrations. Suzuki2 has emphasized that the vehicle vibration should be judged by a series of vibration stimuli to evaluate, because the vehicle vibration is time-variant, which isn’t a matter of the relationship between a single vibration stimulus and a subjective response. He clarified that the human sensation to the vehicle vibration discomfort changes every moment showing the relationship between the frequency-weighted r.m.s. acceleration calculated every 5 seconds and the category judgment to vehicle vibration discomfort every 5 seconds. However, his study doesn’t show what parameter connects to the subjective final judgment to vehicle vibration. Therefore, we applied the method similar to ISO100563 considering the time-variant to the vehicle seat z-axis vibration evaluation. The new method for the vehicle seat vibration considering the time-variant was examined on the hypothesis that the final subjective evaluation must be conducted from the judgment summarizing a series of vibration stimuli. Methods The vibration bench system, which reproduces the movement of a vehicle floor, was used for the experiment with the single-axis (vertical direction) four-post road simulator system, which is usually used for a car, as shown in Fig.1. The experiment was done on the right side of the vibration bench using the floor vibration which was 5.5 minutes, 0.822 m/sec2 (Wk) over the range 0.5-20Hz with 4 male subjects (age ave21.5, SD0.5, weight ave75kg, SD7.91kg, height ave166.8cm, SD5.2cm) and 4 suspension seats. As Fig.2 shows, subjects evaluated the degree of discomfort every 5 seconds to each seat vibration measuring the seat z-axis vibration acceleration. [ ]

Jan 6, 2006

By T. W. Wlodek

Abstract A simplified method of fatigue testing full-dimension, as-rolled, non-machined, mining drill rods is very desirable to the mining and steel industries in the classification of steels available on the market, through the evaluation of their fatigue limits and endurance strength. In this paper one such simplified method is presented and analysed. The preliminary results show many advantages of this method, such as simplicity and constancy of loading. The type of loading applied more or less simulates the working conditions of the outside fibres of the mining drill rods. Additional advantages of this method are the possibility of testing under dry and wet conditions, its quietness, and its ease of operation. Specially designed adaptors and specially applied techniques of fixing and preparation of samples make possible the breaking of a quarter-octagon hollow drill rod in a free length of uniform section in a rotating beam machine. At first glance this seems to be difficult to achieve. In the first preliminary test three different lots of steel were used. S-N curves under dry conditions were determined. These curves permit of the classification of the drill rods on the basis of the fatigue limit and endurance strength of the outside fibres of the metal, which is dependent to a greater or lesser extent on the effect of surface decarburization, surface imperfections, and special surface treatments. The average slope of the S.N curve in the damaging zone, and the fatigue limit in equal tension-compression rotating bending, were determined for SAE 1080, chromium-molybdenum and nickel-chromium-molybdenum mining drill rods. INTRODUCTION The fatigue limit and the endurance strength of mining drill rod steels are of interest to both the mining and the steel industries. These industries are greatly interested in lowering the cost of mining by reducing the consumption of these steels per ton of ore exploited.

Jan 1, 1951

By Denby B

The ever increasing demand on land use has led to large areas of land being considered for development, which because of past mining activities are covered by substantial depths of fill materials. This paper examines the problem faced with the development of land infilled with open cast mining backfill, in predicting the behaviour of the fill upon development. To be able to design foundations suitable to withstand the movements that occur within open cast backfills or design a backfilling operation that produces land suitable for a proposed after development, a means of predicting backfill settlement is required. Factors critical to this prediction are the timing of backfilling operations, the compactive state of the backfill and the inundation of the backfill. The analysis of a considerable quantity of data collected from the monitoring of backfilling operations and backfill movement at a range of open cast coal sites located within the UK has given the authors a better understanding of how open cast backfills behave in terms of long-term creep settlement, collapse settlement and how these are effected by backfill scheduling. This knowledge has been encoded into a program running under Microsoft Windows that enables a user to make settlement predictions for a point, a given section or area or for the whole site. Differential settlements, critical to any development design, can also be determined between any two points taking into consideration the heterogeneous nature of open cast backfills. The program was tested with data from an open cast coal site in the UK. Compaction monitoring during the placement of the backfill material enabled a model of the backfill to be constructed taking into account backfill properties and scheduling. This model, taken as input into the program, enabled future backfill settlement predictions to be made. A comparison is given between these results and actual settlements obtained from a short-term settlement monitoring scheme.

Jan 1, 1995

By Paul W. McGann

This paper presents a methodology for long-range studies of petroleum supply, to meet projected demands, that involves modifications of procedures used previously. This paper continues a series of papers on this general topic in the AIME, the most elaborate recent one being that by Warren Davis given in February 1958. The procedures considered here begin with the assumption that the governmental framework of regulations and taxes remains fixed- but that price changes. After .these procedures have been reviewed, the effects of changing certain governmental controls, will be considered in order to judge their potential effects on future supply. This is an essential step because controls cannot be expected to' remain static in a situation changing as much as the petroleum. industry and because such changes are within-the scope of alternative ways of adjusting to impending problems. The first procedure begins with: a) trends in drilling success, b) relation between field income from oil and gas and footage drilled, c) declines in capacity from production, d) trends in capacity of new and producing wells, e) all monetary values are in constant 1958 dollars, and f) target amounts of domestic crude petroleum production. 'From these components projections are obtained of: 1) numbers of future producing wells required, 2) footage drilled, 3) new wells drilled, 4) crude oil found, 5) capacity of producing wells, 6) completion costs, 7) finding costs, 8) production costs, and 9) average wellhead crude oil price consistent with the footage-field income relationship.

Jan 1, 1960

By Gordon M. Yocom

A PROPER consideration of the subject of this paper should include economic aspects as well as the technical phases of the metallurgy, production, and properties of the product. The metallurgical phases of the processing and properties of the product will be considered only from practical aspects and within the scope of the writer's experience with tonnage production. The Bessemer process was invented 85 years ago and became important because it put steel manufacture upon a larger and less costly basis. In America the Bessemer production has declined for many years and has not maintained its proportionate place with the rapid advances of the open hearth. The achievements in the open-hearth field were attained by the greater number of technical people attracted to that branch of the industry. The antipathy of technical students for the older and less popular Bessemer field gradually weakened the forces defending it and retarded the development of new and better methods. In Europe the economic advantage of the basic Bessemer process has not been overlooked and the tonnage usually is greater than that of the open hearth. The acid process has been the subject of renewed attention in America during the past few years and those who are more familiar with it are striving to show that the method is too valuable to abandon. A considerable tonnage of Bessemer-blown metal, in both molten and ingot forms, used in connection with the open-hearth practice makes it an important auxiliary unit to the industry. This practice aids in modifying the price level of heavy remelting scrap in addition to speeding up the open-hearth operation. The use of Bessemer steel has continued not only because of periodic economic advantages but also because of certain inherent qualities of machinability, weldability and stiffness, which are valuable for many applications. The properties of stiffness and rather high reaction to cold-work require some modification in order to meet the demands of modern methods of processing, which involve cold-reduction and cold-forming. At least one factor contributing to the stiffness of this steel is the relatively high phosphorus content of the acid product. The phosphorus content of the Thomas or basic Bessemer steel of Europe is considerably lower than the normal acid product in America. The American industry has continued the use of the acid process chiefly for the reason that the available ores are more easily adapted to this process from both metallurgical and economic standpoints. In European practice the basic process is necessary with the highly phosphoric ores available and it is sustained to some degree by the sale of the rich phosphate slag as a by-product. The basic process was used in this country at several plants many years ago, but was abandoned for economic reasons. A part of the past history of these trials is given here because the author believes it has not been published and it has some bearing on the subject of this paper. The information is authentic to the extent that

Jan 1, 1941

By J. A. H. Church

My paper entitled "Spontaneous Combustion of Coal in Mines;" read some time ago before this Branch, consisted chiefly of extracts from the British Blue Book dealing with the same subject. Fallowing my article, Mr. de Hart submitted a paper dealing with the application of existing methods of working in Alberta to the conditions obtaining in our bituminous mines. I must confess that the perusal of his paper did not enlighten me either as to what might be a method preferable to those in vogue or even to Mr. de Hart's ideas on the subject, nor did the ensuing discussion of Mr. de Hart's paper afford any great clarification of the problem. The outstanding idea, supplied by Mr. Dick, seemed to be that a retreating system could not be employed, as no operator would feel justified in risking the capital necessary to driving to the boundary when the whole might be jeopardized by a fire breaking out in the waste. That a fire would break out in the waste of any adit-level working seemed to be conceded by all, and with that I agree; that an ignited waste could not be safely sealed off by means of stoppings in a coal barrier-pillar appeared to be the contention of Mr. Dick, or perhaps he attributed this idea to the Mines Branch-anyhow, it seemed to loom over the discussion like a miasma. With this aspect I do not agree, as ? reliance is placed wholly on stoppings in the thick seams of South Staffordshire, even in fiery mines. In the thick coal at Exhall colliery, or elsewhere in Warwickshire (34 feet 4 inches) containing hard and soft coal in layers, a fire assuming serious proportions is sealed off. By the way, retreating long-wall methods are employed. In Fifeshire, sealing off fire in the Dysart mine has been accomplished successfully. The seam averages about 20 feet thick.

Jan 1, 1924

By Amir Karami, Derek Kinakin, Catherine Schmid

The Mathews Stability Graph Method (Mathews et al., 1981) has been used by geotechnical engineers and mining engineers for over 40 years to estimate the performance of longhole open stopes in underground mines. The method is widely used and accepted by practitioners because it is relatively simple to use and can be modified to account for observed performance at a given mining operation. While the simplicity of the method increases its accessibility and utilization, it does not intrinsically account for variability in the various inputs, including rockmass quality, structure, stress, or stope orientation. This paper presents a modified approach for the Stability Graph Method, whereby Python scripts are used to process available geotechnical datasets and combine them with actual or potential distributions of Q parameters, induced stress, structure, or stope orientation. The resulting Stability Numbers are then plotted as a contoured distribution on the Stability Graph.  This allows the practitioner to quickly incorporate large datasets into the analyses, while also developing an understanding of how variability in rockmass quality, induced stress, structure, or stope orientation could affect stope stability.  This paper presents the fundamental principles of the Stability Graph method, the Python script and workflow, and two case studies to demonstrate the utility of the tool.

Oct 1, 2024

By Daniel Hodouin, Claude Bazin

"A graphical method to assess the size reduction by grinding is presented and illustrated with data collected from laboratory grinding tests and industrial grinding circuits. The method lies between the graphical comparison of size distributions and the population balance model. The method is easy to apply and provides a quick way to compare grinding mill performances under various operating conditions and processed ores. The application of the method to industrial mills shows that a grinding mill operation could present an invariant behaviour that can be exploited for simulation purposes.INTRODUCTIONThe size reduction of particles by grinding has been studied for decades and several books were published on the subject. Most of the recent studies focus on the modelling of the ball, semiautogenous and autogenous grinding mills operation (Napier-Munn et al., 1996) because accurate simulators can be used for design, optimization and control. Although the development of realistic simulators is progressing, the trial and error method is still used by many operators to identify optimum operating conditions for a grinding machine.Laboratory tests allow the characterization of the material submitted to grinding and the analysis of various operating conditions, such as ball size or shape, mill speed and slurry concentration of solids, on particle size reduction. Similar tests can be conducted in a plant, but results are often difficult to analyze due to errors associated with sampling and sensor accuracy. This paper presents a graphical method to assess the degree of size reduction carried out by a grinding machine. The paper consists of three sections. The first section describes the method and the following sections illustrate the method with data taken from laboratory and industrial grinding machines."

Jan 1, 2004

By Jordan Scheremeta, Sudhir Tripathi, Mahfooz Alam

Injection leaching can improve leach ore recovery by displacing retained solutions, enhancing ore wetting, and creating new flow paths for efficient solution collection. This paper presents a method to assess the feasibility of injection leaching in finer-grained, potentially contractive ores (from a geotechnical slope stability perspective) using limit-equilibrium (LE) slope stability analysis and static deformation modeling. LE models were carried out by assigning peak undrained strengths to the heap leach ore material, and modeling the excess pore pressure induced during the injection leaching process using spatial function in Slope/W. Static deformation modeling was completed using the software Fast Lagrangian Analysis of Continua (FLAC) to evaluate the potential for deformations due to the excess pore pressures induced during the injection leaching process. A constitutive model was used to represent the geomechanical behavior of the leached ore material, which enables the prediction of deformation and potential stability issues resulting from excess pore-pressure induced during injection leaching process. The two-pronged approach provides a practical method to assess geotechnical impacts and guide data-driven decisions in injection leaching operations.

Feb 22, 2026

By G. Watson, S. Sawyer

A Method to Calculate Hydrodynamic Loads on Underground Bulkheads Bulkheads are structures built in openings in underground mines to impound water, preventing the water from entering the active mine workings. These structures not only have to be designed to withstand the static, hydraulic pressure, but also the dynamic or seismic pressure, which would be generated by an earthquake. Bulkheads can be considered underground dams. Unlike dams on the surface, bulkheads are often subjected to hydraulic heads that exceed the heights of the bulkheads. Theodor von Karman in 1933, and Westergaard earlier, developed the equation by which the hydrodynamic pressures on surface dams could be calculated. Civil engineering handbooks of today contain this equation. In this paper, using the methodology developed by von Karman and Westergaard, the authors have developed an equation by which the hydrodynamic forces on bulkheads could be calculated when the hydraulic head exceeds the height of the bulkhead.

Jan 1, 2007

By Ruilin Yang

"Blast vibrations are essentially a strain/stress wave propagating in rock or structures inthe vicinity of a blast. However, blast vibration has always been quantified in terms ofpeak particle velocity (PPV) or acceleration (PPA), and a meaningful relationshipbetween blast vibration and strain/stress has not been established. The determination ofthe dynamic strain from blast vibration may improve quantification of blast damage andselection of a blast vibration limit for critical structures or high walls. Dynamic strainrelates to rock mechanics or material strength more directly than peak particle velocity(PPV). This paper documents a method to calculate the three-dimensional dynamic straintensor from recorded blast vibration signals. The method is based on determination of thedisplacement gradient at a point of interest for each time instance during the vibrationduration. The method to calculate dynamic strain is applicable to generic seismicwaveforms including near and far field blast vibration from a production blast withmultiple blast holes. In order to minimize measurement errors the specifications of thespacing between monitors and the sampling frequency of the vibration recording aredescribed."

Jan 1, 2012

A simple method of designing effective fill drainage systems for slurry backfill is presented. By using the proposed method, it is easy to calculate and predict the expected fill drainage rates or to provide additional drainage systems to accelerate the fill drainage. The fundamentals of hydraulic fill and an efficient method to determine its permeability is also explained. The safety in hydraulic filling and bulkhead stability depends totally on achieving effective drainage regime for the fill. This paper provides the basis for creating such efficient drainage regimes. The recent fatal fill bulkhead failures in Australia were the result of poor drainage from the respective fill masses, and therefore it is more important to provide suitable drainage arrangements to continue using hydraulic fill to the benefit of the mining industry. At present there is no procedure available to mine operators to estimate the expected bulkhead pressures to design a satisfactory bulkhead. Some mines are constructing bulkheads after their initial investigations carried out years ago. Other mines have simply borrowed the ideas from the pioneer mines and using in their areas. It is high time that we develop a rational approach to estimate the expected bulkhead pressures for the design of bulkheads. We need a simple model that could be understood and used by the mine operators on a day-to-day basis. This paper also presents a model to predict the bulkhead pressures for designing safe bulkheads.

Jan 1, 2002

By Kugan Kuganathan

Pastefill is being increasingly considered as a viable fill by underground mine operators. Mount Isa Mines (MIM) chose pastefill to fill their deep copper mine (>1200m deep) after considering various other types of fill in the feasibility studies. During the development of pastefill at Mount Isa (1996 - to date) the Mining research of MIM developed two cost effective, reliable and simple testing methods and used. With the help of these tests the behaviour of MIM pastefill was studied thoroughly and the most optimum mix design for pastefill was achieved. The MIM's pastefill plant, the largest in the world with a capacity of 450rph continuous pastefill production and unique in the process used, has been built (1998-1999) to produce pastefill to the specification developed through extensive testing program using the Flow Cone and Mini Slump cone Tests. As a consequence, it is now possible to select the optimum pastefill mix designs and predict their flow behaviour in bore holes or pipe lines using only these tests. MIM Blended Tailings Pastefill (BTPF) uses 3-3.55 Portland cement and the cost of pastefill is much lower than the total tailings pastefill, that could be produced from the same tailings.

Jan 1, 2001

By Axel Preusse

In the Ruhr district, pipelines of public and private infrastructure are made of cast iron, steel, plastics or asbestos cement. Legal framework, technical regulations and normative standards define which pipeline materials may be used for the transmission of which kind of product Thus ground water endangering substances as well as inflammable or explosive products are only permitted to be transported in steel-made pipelines. Ground movements, due to underground mining, are transmitted via the soil to the pipeline and cause extra strain within the steel pipeline (Figure I). In extreme cases durable deformations may occur, characterized by an oval profile or a fold in the pipeline. To avoid or minimize damages, balancing elements are installed into the concerning pipeline, reducing the ground movements which might otherwise cause damages. [ ] The distance between the balancing elements is not arranged by random, but by a calculation method developed in a doctoral thesis [Spielberg, 1999] which represents the actual available standards in science and technology. The calculation method considers all relevant influencing variables with impacts on the movement behaviour of steel pipelines in mining areas, such as technical data of pipeline design (e.g. steel grade, wall thickness, weld seam quality), soil conditions (e.g. friction), laying depths of the pipelines, the operational impacts (working pressure, corrosion) and the mining impacts. As of today, mining has caused no damages to steel pipelines protected by this calculation method.

Jan 1, 2004

By Kanchan Mondal, Anthony (Sam) Spearing, Gopi Bylapudi, Joseph C. Hirschi

"The U.S. coal mining industry uses about 100 million rock anchors per year. ASTM F432 specifies the requirements for rock bolts on mines but does not address corrosion. Corrosion has been found to be an issue in Australian coal mines (Hebblewhite et al., 2003 and Villaescusa et al., 2007), where the problem has been researched and stress corrosion has been found to be a significant cause of rock falls. Corrosion is also a major concern for underground civil construction in the U.S. but has not been considered an issue or adequately researched in coal mines. Underground conditions are conducive to corrosion mainly because of water quality and humid conditions. There is a perception, however, that when bolts are fully grouted, adequate corrosion protection is offered to the steel. Research has shown that this is not necessarily the case, due to the formation of micro-cracks as the resin sets and with subsequent rock movement shearing the resin column. This paper outlines a method to determine the corrosion potential of bolts used in long-term excavations and suggests ways to mitigate such effects based on research conducted in the lab and on three mines.INTRODUCTIONResearch on rock anchor corrosion in mines has not been extensive enough in the past, and the effects of several factors in the mine atmosphere and waters are not clearly understood. One probable reason for this lack of research may be attributed to the time required for gathering meaningful data, which makes the study of corrosion quite challenging.Almost all the rock bolts used in coal mines are made from steel, hence the corrosion of iron needs to be understood. The corrosion of iron is an electrochemical phenomenon with the overall equation"

Jan 1, 2010