The chairman said that the share capital remained unaltered, and the debenture debt had only been decreased by the yearly amortisation.
"The World in Chains" by John Mavrogordato
What is the cost for amortisation in the long mortgages on property in the country?
"Readings in Money and Banking" by Chester Arthur Phillips
Contrariwise, when a burst of renewals falls due, in excess of the current rate of amortisation, a boom sets in.
"The Accumulation of Capital" by Rosa Luxemburg
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In discussing the eﬃciency of combinatorial generation, we say that an algorithm is constant amortised time [44, §1.7] if the average amount of time required to generate an ob ject is bounded, from above, by some constant.
Generating All Partitions: A Comparison Of Two Encodings
In Section 2.1 we develop and analyse a simple constant amortised time recursive algorithm to generate all ascending compositions of n.
Generating All Partitions: A Comparison Of Two Encodings
To establish that Algorithm 2.1 generates the set A(n) in constant amortised time we must count the total number of invocations, IA2.1 (n), and show that this value is proportional to p(n).
Generating All Partitions: A Comparison Of Two Encodings
This algorithm, although concise and simple, can be easily shown to be constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
RecDesc uses what Ruskey refers to as a ‘path elimination technique’ [44, §4.3] to attain constant amortised time performance. A slight complication arises when we wish to use RecDesc to generate al l descending compositions.
Generating All Partitions: A Comparison Of Two Encodings
Using Theorem 2.2 it is now straightforward to show that RecDesc generates all descending compositions of n in constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
To show that the algorithm is constant amortised time we must demonstrate that the average number of invocations of the algorithm per ob ject generated is bounded, from above, by some constant.
Generating All Partitions: A Comparison Of Two Encodings
Ruskey demonstrates that RecDesc is constant amortised time by reasoning about the number of children each node in the computation tree has, but does not derive the precise number of invocations involved.
Generating All Partitions: A Comparison Of Two Encodings
Thus, for any value of n we are assured that the total time required to generate all partitions of n will be proportional to the number of partitions generated, implying that the algorithm is constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
There are, however, several constant amortised time algorithms to generate descending compositions, and in this section we study the most eﬃcient example.
Generating All Partitions: A Comparison Of Two Encodings
Zoghbi & Sto jmenovi´c also provided an analysis of AccelDesc, and proved that it generates partitions in constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
Thus, since the number of iterations of the internal loop is constant whenever dq ≥ 3 (the case for dq = 2 obviously requires constant time), the algorithm generates descending compositions in constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
The preceding paragraph is not a rigorous argument proving that AccelDesc is constant amortised time.
Generating All Partitions: A Comparison Of Two Encodings
By analysing these algorithms we were able to show that although both algorithms are constant amortised time, the descending composition generator requires approximately twice as long to generate all partitions of n.
Generating All Partitions: A Comparison Of Two Encodings
Less emphasis was placed on reducing the cost of constructing ﬁxed KBs, since it was felt that this cost could be amortised over several pro jects if idas was successful.
Automatic Generation of Technical Documentation
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