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kn — 2 Scalar Matrix and Its Functional Equations by Mathematical Modeling
Published in Michael Ruzhansky, Hemen Dutta, Advanced Topics in Mathematical Analysis, 2019
Pasupathi Narasimman, Hemen Dutta
The stability problem of various functional equations and mappings such as the Cauchy equation, the Jensen equation, the quadratic equation, the cubic equation, the quartic equation and various versions on more general domains and ranges have been investigated by a number of authors Jun and Lee (2001); Kannappan (1995); Ravi and Arunkumar (2006); Ravi et al. (2007, 2009a,b).
Variables, functions and mappings
Published in Alan Jeffrey, Mathematics, 2004
The roots of this special quartic equation may be found by first setting x2 = z, to reduce it to a quadratic equation in z, and using the formula for the roots of a quadratic to determine the roots z1=−b+b2−4ac2aandz2=−b−b2−4ac2a.
A screw theory approach to compute instantaneous rotation axes of indeterminate spherical linkages
Published in Mechanics Based Design of Structures and Machines, 2020
Juan Ignacio Valderrama-Rodríguez, José M. Rico, J. Jesús Cervantes-Sánchez
About 15 years ago Foster and Pennock (2003) presented a graphical technique that was able to find all the instantaneous centers of indeterminate linkages and improved substantially the approach proposed by Klein. A few years later, Di Gregorio (2008a) introduced an analytical technique that generated a system of equations involving both, closure equations of the planar linkages and locations of the indeterminate instantaneous rotation centers, so that He was able to find the location of the indeterminate rotation centers. In 2009, Kung and Wang (2009) employed graph theory to obtain a graph associated with the instantaneous centers of a linkage. This graph allowed Kung and Wang to formulate a system of iterative equations, whose unknowns are the coordinates of the indeterminate instantaneous rotation centers. The solution of the problem is reduced to solving a quadratic equation and then a quartic equation.