and Applied Analysis 3 Next we present auxiliary statements which play important roles in proving the main results. Define F : 0,∞ → R by F x Φ x/q−1/q −Φ 1−1/x and h : Φ −∞ q ,∞ → R by h x x 1 − q1−α [ 1 − ( 1 ( q − 1 ) Φ−1 x )1−α] . 2.1 For y : q0 → R \ {0} define the operator L by L [ y ] t Φ ( y ( q2t ) qy ( qt ) − 1 q ) −Φ ( 1 − y t

The operation of 1–3 nm thick SOI MOSFETs, in double-gate (DG) mode and single-gate (SG) mode (for either front or back channel), is systematically analyzed. Strong interface coupling and threshold voltage variation, large influence of substrate depletion underneath the buried oxide, absence of drain current transients, degradation in electron mobility are typical effects in these ultra-thin MO...

This paper classifies morphisms from {0, 1} that map to ultimately periodic words. In particular, if a morphism h maps an infinite non-ultimately periodic word to an ultimately periodic word then it must be true that h(0) commutes with h(1).

It is known that there are recurrent words with constant abelian complexity three, but not with constant complexity four. We prove that there are recurrent words with ultimately constant complexity c for every c.

Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of r...