For the interval, and the corresponding in Remark 2.2, we define = : , and exist,.
Now, on using Corollary 2 corresponding to (8) (see Remark 3), the mapping T admits a unique fixed point, which also remains a unique solution of the problem described by (27).
The majority of darker cells - corresponding to late December - remarks the abundance of outlying activity close to the Christmas holidays, probably generated by the increasing presence of tourists and by the disruption of the typical workday patterns.
For every (k in mathbb {I}_{ell }), let (x_{beta _k}) be the corresponding root vector as in Remark 2.14.
Remark 2.2 The corresponding result for second-order continuous periodic problems has been proved in Theorem 1 of [17] by the proof using the same strategy as above.
Remark 2.5 The corresponding results (see, for example, Theorem 1 of [17], Theorem 1 of [18] and Theorem 3.5 of [19]) are improved in the following senses: (1) For the Krasnosel'skiĭ-Mann-Opial type iterative solution of x + A x = f, we study simultaneously the existence, uniqueness, convergence, convergence rate estimate, and the stability.
In particular, we consider the periodic and antiperiodic boundary conditions as in [[15], Remark 6.17] and the corresponding M -function.
Unfortunately, it would also require the solution of the Master equation (and of the corresponding backward equation) which, as we remarked before, is not computationally feasible.
After summarizing the reflective design of the tools, the chapter explains each of the tools, including its inference system and its corresponding Maude implementation, with examples and concluding remarks.
As explained in remark 1, section 2, the corresponding mereology need not be as strong as classical extensional mereology.
