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	<title>The Mathematica Journal</title>
	<link>http://www.mathematica-journal.com</link>
	<description></description>
	<lastBuildDate>Fri, 17 Feb 2012 13:50:22 +0000</lastBuildDate>
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		<title>Motion of a Spinning Top</title>
		<description><![CDATA[Both approximate and exact solutions for the motion of a spinning top are constructed with the help of quaternions.
Quaternion Algebra
A quaternion is a four-dimensional quantity consisting of a scalar, say , and a three-dimensional vector , collectively denoted . Addition of two quaternions is component-wise,




(1)



(we do not need to add quaternions in this article). Their [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/motion-of-a-spinning-top/</link>
			</item>
	<item>
		<title>Evaluation of Gaussian Molecular Integrals</title>
		<description><![CDATA[This article discusses the evaluation of molecular overlap integrals for Gaussian-type functions with arbitrary angular dependence. As an example, we calculate the overlap matrix for the water molecule in the STO-3G basis set.
Introduction
Computational quantum chemistry makes extensive use of various integrals (and their derivatives) of the general form [1, 2, 3]




(1)



where  is an unnormalized [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/evaluation-of-gaussian-molecular-integrals/</link>
			</item>
	<item>
		<title>The Return of the Riemann Surface</title>
		<description><![CDATA[My favorite subject&#8212;Riemann surfaces&#8212;is revisited through the eyes (functions) of Mathematica 6. Old friends will appear in a new light(ing) and new acquaintances with untreated surfaces will be made.
Introduction
This is my first column since Version 6 came out a few months ago. Version 6, after being in the works for many years, provides a wealth [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/the-return-of-the-riemann-surface/</link>
			</item>
	<item>
		<title>Classic Puzzles in Wolfram Demonstrations</title>
		<description><![CDATA[Sudoku, today&#8217;s most well-known grid-solving puzzle, was originally invented by Howard Garns in 1978. Almost 30 years later, its popularity suddenly exploded. This column presents logic puzzles of various sorts and challenges readers to solve the puzzles in two ways: by hand and with Mathematica. Solvers are invited to send their code to edp@wolfram.com.
Fifteen Classic [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/classic-puzzles-in-wolfram-demonstrations/</link>
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		<title>Dynamic Integration of Interpolating Functions and Some Concrete Optimal Stopping Problems</title>
		<description><![CDATA[This article describes a streamlined method for simultaneous integration of an entire family of interpolating functions that uses one and the same interpolation grid in one or more dimensions. A method for creating customized quadrature/cubature rules that takes advantage of certain special features of Mathematica&#8217;s InterpolatingFunction objects is presented. The use of such rules leads [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/dynamic-integration-of-interpolating-functions-and-some-concrete-optimal-stopping-problems/</link>
			</item>
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		<title>Making Holes and Windows in Surfaces</title>
		<description><![CDATA[In this article, we demonstrate , a program which removes points from any  or  picture whose coordinates satisfy a stated condition. We also demonstrate  and , programs which make an entire or a specific portion of an opaque surface into a transparent mesh. We use these programs to view the region of [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/making-holes-and-windows-in-surfaces/</link>
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		<title>Graphing on the Riemann Sphere</title>
		<description><![CDATA[We give a procedure to plot parametric curves on the sphere whose advantages over classical graphs in the Cartesian plane are obvious whenever the graph involves infinite domains or infinite branches.
Introduction
Graphing a curve in the Cartesian plane can be done only in a restricted &#8220;window&#8221; . If the function to be plotted has a large [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/graphing-on-the-riemann-sphere/</link>
			</item>
	<item>
		<title>Airfoil Aerodynamics Using Panel Methods</title>
		<description><![CDATA[Potential flow over an airfoil plays an important historical role in the theory of flight. The governing equation for potential flow is Laplace&#8217;s equation, a widely studied linear partial differential equation. One of Green&#8217;s identities can be used to write a solution to Laplace&#8217;s equation as a boundary integral. Numerical models based on this approach [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/airfoil-aerodynamics-using-panel-methods/</link>
			</item>
	<item>
		<title>MathCode: A System for C++ or Fortran Code Generation from Mathematica</title>
		<description><![CDATA[MathCode is a package that translates a subset of Mathematica into a compiled language like Fortran or C++. The chief goal of the design of MathCode is to add extra performance and portability to the symbolic prototyping capabilities offered by Mathematica. This article discusses several important features of MathCode, such as adding type declarations, examples [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/02/mathcode-a-system-for-c-or-fortran-code-generation-from-mathematica/</link>
			</item>
	<item>
		<title>Exploring Reflection and Transmission Coefficients in Elastic Media</title>
		<description><![CDATA[Reflection and transmission (scattering) of plane waves at a planar boundary between two elastic half-spaces are important fundamental processes in seismology. Such plane waves may be compressional (P) or shear (S) in an elastic medium. In this article we apply Mathematica to computing the complex algebraic expressions describing the reflection and transmission amplitudes, phases, and [...]]]></description>
		<link>http://www.mathematica-journal.com/2012/01/exploring-reflection-and-transmission-coefficients-in-elastic-media/</link>
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