Supercomputing applications to the numerical modeling of industrial and applied mathematics problems

2007 ◽  
Vol 40 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Juan A. Acebrón ◽  
Renato Spigler
Keyword(s):  
Numerical Modeling ◽  
Applied Mathematics ◽  
Mathematics Problems

XX.—Studies in Practical Mathematics. II. The Evaluation of the Latent Roots and Latent Vectors of a Matrix

1938 ◽  
Vol 57 ◽  
pp. 269-304 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Applied Mathematics ◽  
Dynamical Theory ◽  
Mathematics Problems ◽  
Principal Axes ◽  
Practical Mathematics ◽  
Latent Roots

In many branches of applied mathematics problems arise which require for their solution a knowledge of the latent roots of a matrix A, sometimes only the root of greatest modulus but often the second and other roots as well, and the corresponding latent vectors. A few examples, among many that might be cited, are problems in the dynamical theory of oscillations, problems of conditioned maxima and minima, problems of correlation between statistical variables, the determination of the principal axes of quadrics, and the solution of differential or other operational equations. It is important, therefore, to have a choice of methods for obtaining latent roots and latent vectors without undue labour, and the object of the present paper is to augment the existing store of such methods.

scholarly journals A MATHEMATICAL MODEL FOR SUMMING ROTARY MOTIONS

2020 ◽  
pp. 32-45
Author(s):  
Igor' Popov ◽  
Keyword(s):  
Applied Mathematics ◽  
Analytical Description ◽  
Practical Aspect ◽  
Straight Line Segment ◽  
Planetary Gears ◽  
Mathematics Problems ◽  
Straight Line ◽  
Automation And Control ◽  
Rotational Motions ◽  
And Control

In this work, using the means of applied mathematics, problems are solved related to the field of automation and control of technological processes, namely, the analytical description of superpositions of rotations that occur during the operation of numerous mechanisms. The practical aspect of the topic is determined by the fact that in mechanisms such as planetary gears, cutter drives in machines for cleaning pipes of large diameters, etc. summation of rotational motions is realized, and the shape of the hodograph is useful information in the design of such devices. The prerequisite for consideration is the principle of summation of rectilinear uniform movements. The aim of the work is to determine how things are in a similar situation when adding rotational synchronous movements. It was found that just as the result of the addition of two uniform rectilinear mechanical movements is also a uniform rectilinear movement, the result of the addition of two uniform unidirectional circular movements is also a uniform circular movement. The hodograph when two uniform oppositely directed circular motions are added is an ellipse. In a particular case, the ellipse can degenerate into a straight line segment. When two asynchronous rotations are added, hodographs in the form of a cochlea are possible, which is similar to Pascal's cochlea.

Applications: Gears, Ratios, And The Bicycle

1989 ◽  
Vol 82 (6) ◽  
pp. 466-468
Author(s):  
Daniel Timothy Gerber
Keyword(s):  
Applied Mathematics ◽  
Textbook Author ◽  
Mathematics Problems ◽  
Mathematics Course

Inevitably a teacher will encounter students who see “no reason” to study mathematics beyond the basics. When asked why they are enrolled in a higher mathematics course, students usually mention college requirements. It then becomes the responsibility of the textbook author and the instructor to generate interest in mathematics. Authors generally include applied mathematics problems in their texts; however, students find such problems more interesting when they can directly acquire the information needed for solution. This approach is certainly a teaching advantage if the instructor is willing to bring props into the classroom. In this spirit, I have used a ten-speed bicycle to illustrate gear function because it is familiar to most students.

scholarly journals Advanced Mesh-Based and Particle-Based Numerical Methods for Engineering and Applied Mathematics Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-2 ◽  
Author(s):  
Cheng-Tang Wu ◽  
Lihua Wang ◽  
Bernard Bonello ◽  
Leevan Ling ◽  
Ninshu Ma ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Applied Mathematics ◽  
Mathematics Problems
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