Two explicit guard functions Kj = Kj(δz), j = 1, 2, are obtained, which depend on the distance δz between z and the nearest point of the integer lattice in the complex plane, such that δzK1(δz) ≤ |σ(z)|e−π|z|2/2 ≤ δzK2(δz), z ∈ C, where σ(z) stands for the Weierstraß σ-function. This result is used to improve the circular truncation error upper bound in the qth order Whittaker-type derivative s...

PURPOSE This study evaluated the effect of light-emitting diodes (LEDs) on polymerization shrinkage and bottom-to-top hardness ratios of composites. MATERIALS AND METHODS Six LEDs (Elipar FreeLight, 3M ESPE, St. Paul, MN, USA; Versalux, Centrix, Shelton, CT, USA; Ultra-Lume LED2, Ultradent, South Jordan, UT, USA; Zap LED only, CMS-Dental/Soft-Core Texas, North Richland Hills, TX, USA; Zap dua...

We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q ≥ 2, has a base-b representation that consists of a length-l block of digits repeated n times, where n ≥ 2. Assuming the abc conjecture of Masser and Oesterlé, we completely characterize those triples (q, n, l) for which there are infinitely many solutions b. In all cases...

We give a geometric interpretation of Milnor's invariants ¯ µ(ijk) in terms of triple intersection points of Seifert surfaces for the three link components. This generalizes ideas from Cochran [Co] to links which are not algebraically split. We recall how to compute ¯ µ(ijk) from Milnor [Mi]. Given a link L, its link group π 1 (S 3 − L) has a Wirtinger presentation, generated by the arcs of the...