Exercises on linear forms in the logarithms of algebraic numbers
... Let α1 , . . . , αn be algebraic numbers. Let b1 , . . . , bn be non-zero integers. Deduce from Matveev’s result a lower bound for the quantity ...
... Let α1 , . . . , αn be algebraic numbers. Let b1 , . . . , bn be non-zero integers. Deduce from Matveev’s result a lower bound for the quantity ...
1 Sequences, Series, how to decide if a series in convergent
... errors come confusing series with sequence, so train yourself to always ask “is this a statement about a series or is it a statement about a sequence?” The series a1 +a2 +· · · is called an infinite series because it is formed from an infinite sequence. It has nothing to do with whether the sum a1 + ...
... errors come confusing series with sequence, so train yourself to always ask “is this a statement about a series or is it a statement about a sequence?” The series a1 +a2 +· · · is called an infinite series because it is formed from an infinite sequence. It has nothing to do with whether the sum a1 + ...
the maximization of a serial system`s reliability
... system reserves, j = 1, 2, …, N. In the case of a single restriction problem it is sufficient to introduce just one multiplier for creating the free restrictions Lagrange auxiliary function. Knowing that max{Rs(x)} is equivalent to min{- Rs(x)}, the Lagrange function can be written as follows: N N ...
... system reserves, j = 1, 2, …, N. In the case of a single restriction problem it is sufficient to introduce just one multiplier for creating the free restrictions Lagrange auxiliary function. Knowing that max{Rs(x)} is equivalent to min{- Rs(x)}, the Lagrange function can be written as follows: N N ...
Step Functions
... circles indicate that the points (1, 1), (2, 2), (3, 3), and so forth, do lie on the graph. Notice that the domain of the greatest-integer function is the set of real numbers, but the range is the set of integers. If your graphing utility has the int, or floor function, it will graph the greatest-int ...
... circles indicate that the points (1, 1), (2, 2), (3, 3), and so forth, do lie on the graph. Notice that the domain of the greatest-integer function is the set of real numbers, but the range is the set of integers. If your graphing utility has the int, or floor function, it will graph the greatest-int ...
1 Super-Brief Calculus I Review.
... subinterval), times its length, which is the circumference of the circle of radius 2πxk . So the volume of each chunk is approximately 2πxk · f (xk ) · ∆x. When we add Pnup the volumes of each of the n chunks, we get an estimate for the volume of the solid, given by V ≈ k=1 2πxk f (xk )∆x. Then to o ...
... subinterval), times its length, which is the circumference of the circle of radius 2πxk . So the volume of each chunk is approximately 2πxk · f (xk ) · ∆x. When we add Pnup the volumes of each of the n chunks, we get an estimate for the volume of the solid, given by V ≈ k=1 2πxk f (xk )∆x. Then to o ...