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George Pacheco
Applied Mathematics for Mining. Intelligent Path To Successful Engineering.
Applied Mathematics for Mining. Intelligent Path To Successful Engineering.
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MINERAL NEWS
Mining Activity

Please access: http://keystoneminingpost.com/Company/Consulting/VisualCS/InfoOverviewMinNews.aspx to follow up-to-date news regarding mining and metal production.

The news contain information regarding the Andes Plateau mineral activity including eight mineral producing countries. These weekly updates contain valuable data with specific detailed description of mining activity in the country.
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WHY SMALLTALK?

Smalltalk is a pioneer in programming language development. Constructed in the 1970s by those clever folks at Xerox PARC in California. Smalltalk was the first major OOP language, and still widely regarded as the best. Over the past four decades, it has been highly influential in the design of other important languages, such as Objective-C, Ruby, Groovy, Scala, and Dart. Today, Smalltalk is still used to write industrial and financial applications (rather like a secret weapon that confers a competitive advantage). It is alive and well, particularly in the Pharo incarnation and it is emerging as a contender in client-side web development.

The beauty of Smalltalk lies in its simplicity and elegance, as well as its novel concept of a “live” development environment, where every object is active and you can examine it and change it at will. Ironically, this “novel” concept was created more than four decades ago! As a result, Smalltalk is eminently readable, almost like English, but it still manages to be succinct.
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COMPLEX NUMBERS and FUNCTIONS
Trigonometric and Hyperbolic Functions

Complex numbers, complex functions and complex analysis in general are part of an important branch of mathematics. They find wide application in solving real scientific and engineering problems.

In mathematics, a complex number is a number of the form z = x + iy, where:
- is the complex variable
- x and y are real numbers
- is the imaginary unit, with the propertyi2 = -1.

The real number x is called the real part of the complex number, and the real number y is the imaginary part. Real numbers may be considered to be complex numbers with imaginary part set to zero. That is, the real number x is equivalent to the complex number x + 0i.

In order to test the functions defined under sine/cosine/tangent, new methods have been written and executed. Please check: http://keystoneminingpost.com/Company/Consulting/VisualCS/TrigonometricFct.aspx
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Prospecting Concepts
AREA SELECTION

Area selection is a crucial step in professional mineral exploration. Selection of the best, most prospective area in a mineral field, geological region or terrain will assist in making it not only possible to find ore deposits, but to find them easily, cheaply and quickly.

Area selection is based on applying the theories behind ore genesis, the knowledge of known ore occurrences and the method of their formation, to known geological regions via the study of geological maps, to determine potential areas where the particular class of ore deposit being sought may exist.

SELECTION PROCESS
This process applies the disciplines of basin modeling, structural geology, petrology and a host of geophysical and geochemical disciplines to make predictions and draw parallels between the known ore deposits and their physical form and the unknown potential of finding a 'look-alike' within the area selected.
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Chacaltaya
Ski Resort

The World’s Highest Elevation Ski Resort is Chacaltaya, Bolivia at 17,785-Feet.
Chacaltaya ski resort was originally created to allow good winter snow skiing from November to March every year. It’s very sad, however, that this ski resort doesn’t run any longer. Due to andean glacial loss the glacier completely melted away. If you had a chance to visit this resort please give us your insight.

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ENVIRONMENT
Fauna diversity in the tropical Andes

The tropical Andes is home to an estimated 35,000 species of vascular plants, accounting for about 10 percent of all the world's species. The plateau harbor thousands of bird species that is unequaled in the world. In addition, there are nearly hundreds of mammal species in the tropical hotspots. If you had a chance to explore the andes plateau wild life, study and/or just interested in this topic I would like to hear your comments.
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OVERVIEW
Numerical Integration in Smalltalk

Numerical integration is intrinsically a much more accurate procedure than numerical differentiation.

The basic problem considered by numerical integration is computing an approximation to a definite integral,

I = ∫ah f(x)dx

The need for a numerical integration arises for two reasons: First, the function to be integrated may be such that the integral is too complicated to evaluate or may even be impossible to obtain analytically. Secondly, the function may be described only by a data array of values, so that a numerical approximation is the only approach available. I chose three methods of integration approximation: Trapeze, Simpson and Romberg to illustrate progress of function evaluation in each situation. The function to integrate:

f(x) = 1 / x
is specified as a block closure to be implemented in Smalltalk:

f := [:x | 1 / x]


Please check: http://keystoneminingpost.com/Company/Consulting/VisualCS/ComparisonMethods.aspx
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9/12/17
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IMPLEMENTATION
Complex Matrix Manipulation

As in the case of implementing a real matrix (Number Matrix Manipulation) a more complex matrix structure can be derived where matrices again can be added, multiplied and decomposed in many ways.

I show how to implement various complex matrix operations including matrix addition, subtraction, multiplication, transformation and determinant. A complex matrix can be created using either 2D complex array or by directly defining its matrix elements.

For interaction see: http://keystoneminingpost.com/Company/Consulting/Smalltalk/AlgebraComplexMatrix.aspx
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VECTORS AND MATRICES
Linear Algebra

Linear algebra concerns itself with the manipulation of vector and matrices. The concepts of linear algebra are not difficult, and linear algebra is usually taught in high school.

The concise notation introduced in linear algebra for vector and matrix operations can be directly adapted to object-oriented programming. Science and engineering often encounter many physical quantities that are vectors, including velocity, acceleration, force and momentum as well as solving linear equations with multiple variables.

These basic techniques have been applied to a wide variety of fields, from operations research to mineral engineering.

Please see: http://keystoneminingpost.com/Company/Consulting/Smalltalk/AlgebraMathOperators.aspx
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Smalltalk Sample Code

For a complete listing please see: http://keystoneminingpost.com/Company/Consulting/Smalltalk/Algebra.aspx
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