Explicit solutions for recurrences
... EXAMPLE Compound interest describes an investment in which the interest rate is applied each period to the previous base and added to that base to produce the new principal. That is, Pn = P(n–1) + rP(n–1) = (1+r)P(n–1). The resulting recurrence generates a geometric sequence. Pn = P0(1+r)n for n per ...
... EXAMPLE Compound interest describes an investment in which the interest rate is applied each period to the previous base and added to that base to produce the new principal. That is, Pn = P(n–1) + rP(n–1) = (1+r)P(n–1). The resulting recurrence generates a geometric sequence. Pn = P0(1+r)n for n per ...
Functions - Cihan University
... airport mapping, each person gave only one reason for the trip, but the same reason was given by several people. This mapping is a many-to-one mapping, so it is a function. • The mapping in example 2, rounded whole number onto unrounded number is NOT a function, since, for example, the rounded numbe ...
... airport mapping, each person gave only one reason for the trip, but the same reason was given by several people. This mapping is a many-to-one mapping, so it is a function. • The mapping in example 2, rounded whole number onto unrounded number is NOT a function, since, for example, the rounded numbe ...
DECOMPOSITION OF RATIONAL NUMBERS INTO ODD UNIT
... the least common multiple of a finite collection of odd numbers is necessarily odd, since none of the numbers in the collection have 2 as a factor and hence their least common multiple can only contain primes which are not 2. (2) We caution all readers that the open question asked does not simply as ...
... the least common multiple of a finite collection of odd numbers is necessarily odd, since none of the numbers in the collection have 2 as a factor and hence their least common multiple can only contain primes which are not 2. (2) We caution all readers that the open question asked does not simply as ...
5 COMPUTABLE FUNCTIONS Computable functions are defined on
... EXAMPLE 4 The function f (n) = n + 3 is computable. The input is W = 1n+1 . Thus we need only add two 1’s to the input. A Turing machine M which computes f follows: M = {q1 , q2 , q3 } = {s0 1s0 L, s0 B 1s1 L, s1 B 1sH L} Observe that: (1) q1 moves the machine M to the left. (2) q2 writes 1 in the b ...
... EXAMPLE 4 The function f (n) = n + 3 is computable. The input is W = 1n+1 . Thus we need only add two 1’s to the input. A Turing machine M which computes f follows: M = {q1 , q2 , q3 } = {s0 1s0 L, s0 B 1s1 L, s1 B 1sH L} Observe that: (1) q1 moves the machine M to the left. (2) q2 writes 1 in the b ...
Functional decomposition
Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. In general, this process of decomposition is undertaken either for the purpose of gaining insight into the identity of the constituent components (which may reflect individual physical processes of interest, for example), or for the purpose of obtaining a compressed representation of the global function, a task which is feasible only when the constituent processes possess a certain level of modularity (i.e., independence or non-interaction). Interactions between the components are critical to the function of the collection. All interactions may not be observable, but possibly deduced through repetitive perception, synthesis, validation and verification of composite behavior.