This article is focused on considerations based on experimental studies concerning changes of selected parameters of identical compact fluorescent lamps (CFLs) intended for use in buildings during their operation. The studies constituted a long-term experiment whose goal was an evaluation of selected operating parameters of the CFLs in terms of meeting the requirements set out in the specified regulations as well as the issue of marking the lamps with the energy efficiency class. The measurements were performed with the authors’ experimental setup consisting of original equipment designed and made especially for the purpose of the measurements. The studies covered registration of the luminous flux as well as selected electrical parameters such as active power, current and the power factor during the so-called “start-up time” and operation time equal to 100 h, 500 h, 1000 h, 2000 h, etc. with a 1000 h step. The studies were finished with the moment of natural burnout of the CFLs tested. The results showed that the biggest drawback of CFLs is lack of preservation of the required time to reach 60% of the stabilized luminous flux just after short time of lamp operation. Similarly when assessing the conformity of the parameters declared by the manufacturer that have been verified, it can be stated that they are true only at the initial stage of lamp operation.

This article presents methods and algorithms for the computation of isogenies of degree ℓn. Some of these methods are obtained using recurrence equations and generating functions. A standard multiplication based algorithm for computation of isogeny of degree ℓn has time complexity equal to O(n2 M (n log n)), where M(N) denotes the cost of integers of size N multiplication. The memory complexity of this algorithm is equal to O (n log (n log (n))). In this article are presented algorithms for:

• determination of optimal strategy for computation of degree ℓn isogeny,
• determination of cost of optimal strategy of computation of ℓn isogeny using solutions of recurrence equations,
• determination of cost of optimal strategy of computation of ℓn isogeny using recurrence equations,

where optimality in this context means that, for the given parameters, no other strategy exists that requires fewer operations for computation of isogeny.

Also this article presents a method using generating functions for obtaining the solutions of sequences (um) and (cm) where cm denotes the cost of computations of isogeny of degree ℓum for given costs p; q of ℓ-isogeny computation and ℓ-isogeny evaluation. These solutions are also used in the construction of the algorithms presented in this article.