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The great innovation in Pascal's calculator was that it was designed so that each input wheel is totally independent from all the others and carries are propagated in sequence. Pascal chose, for his machine, a method of re-zeroing that propagates a carry right through the machine. [ 17 ]
Solving the above for k fo and k bo in terms of the equilibrium concentrations c oe and c re and the exchange current density j o, the current density j as a function of applied potential E may now be written: [5]: § 8.3
The equation arises not by analyzing the individual positions and momenta of each particle in the fluid but rather by considering a probability distribution for the position and momentum of a typical particle—that is, the probability that the particle occupies a given very small region of space (mathematically the volume element) centered at ...
John Herschel, Description of a machine for resolving by inspection certain important forms of transcendental equations, 1832. In applied mathematics, a transcendental equation is an equation over the real (or complex) numbers that is not algebraic, that is, if at least one of its sides describes a transcendental function. [1]
When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical independence is the same as linear independence. The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent. For example ...
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$1 million prize for the first correct solution to each problem.
Each original site expands with an expansion velocity v, and establishes additional sites that survive for a lifetime L. The result is a more complex set of 3 equations. [73] Reappearance factor The Drake equation may furthermore be multiplied by how many times an intelligent
This is a linear Diophantine equation or Bézout's identity. + = + The smallest nontrivial solution in positive integers is 12 3 + 1 3 = 9 3 + 10 3 = 1729.It was famously given as an evident property of 1729, a taxicab number (also named Hardy–Ramanujan number) by Ramanujan to Hardy while meeting in 1917. [1]