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To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
η-reduction (eta reduction) expresses the idea of extensionality, [24] which in this context is that two functions are the same if and only if they give the same result for all arguments. η-reduction converts between λx.f x and f whenever x does not appear free in f.
The first half of the 20th century saw the gradual development of the mechanical calculator mechanism. The Dalton adding-listing machine introduced in 1902 was the first of its type to use only ten keys, and became the first of many different models of "10-key add-listers" manufactured by many companies.
In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [1] Every output random variable from the simulation is associated with a variance which limits the precision of the simulation results.
The process of row reduction makes use of elementary row operations, and can be divided into two parts.The first part (sometimes called forward elimination) reduces a given system to row echelon form, from which one can tell whether there are no solutions, a unique solution, or infinitely many solutions.
A cycloidal drive or cycloidal speed reducer is a mechanism for reducing the speed of an input shaft by a certain ratio. Cycloidal speed reducers are capable of relatively high ratios in compact sizes with very low backlash. [1] The input shaft drives an eccentric bearing that in turn drives the cycloidal disc in an eccentric, cycloidal motion ...
In computational mechanics, Guyan reduction, [1] also known as static condensation, is a dimensionality reduction method which reduces the number of degrees of freedom by ignoring the inertial terms of the equilibrium equations and expressing the unloaded degrees of freedom in terms of the loaded degrees of freedom.
For example, a torque multiplier with a rating of 3:1 will turn its output shaft with three times the torque, but at one third the speed, of the input shaft. However, due to friction and other inefficiencies in the mechanism, the output torque is slightly lower than the theoretical output.