Pure discrete spectrum and regular model sets on some non-unimodular substitution tilings.

Substitution tilings with pure discrete spectrum are characterized as regular model sets whose cut-and-project scheme has an internal space that is a product of a Euclidean space and a profinite group. Assumptions made here are that the expansion map of the substitution is diagonalizable and its eigenvalues are all algebraically conjugate with the same multiplicity. A difference from the result of Lee et al. [Acta Cryst. (2020), A76, 600-610] is that unimodularity is no longer assumed in this paper.

The Effects of Switching from Sevoflurane to Short-Term Desflurane prior to the End of General Anesthesia on Patient Emergence and Recovery: A Randomized Controlled Trial.

While sevoflurane and desflurane have been regarded as inhalation agents providing rapid induction and emergence, previous studies demonstrated the superiority of desflurane-anesthesia compared to sevoflurane-anesthesia in the postoperative recovery in obese and geriatric patients. We investigated whether a short-term switch of sevoflurane to desflurane at the end of sevoflurane-anesthesia enhances patient postoperative recovery profile in non-obese patients. We randomly divide patients undergoing elective surgery (n = 60) into two groups: sevoflurane-anesthesia group (Group-S, n = 30) and sevoflurane-desflurane group (Group-SD, n = 30). In Group-S, patients received only sevoflurane-anesthesia until the end of surgery (for >2 hours). In Group-SD, sevoflurane was stopped and switched to desflurane-anesthesia before the completion of sevoflurane-anesthesia (for approximately 30 minutes). We assessed the intergroup differences in the times to get eye-opening, extubation, and a bispectral index of 80 (BIS-80). Group-SD showed significantly shorter times to get eye-opening (438 ± 101 vs. 295 ± 45 s; mean difference, 143 s; 95% confidence interval [CI], 101-183; p < 0.001), extubation (476 ± 108 vs. 312 ± 42 s; mean difference, 164 s; 95% CI, 116-220; p < 0.001), and BIS-80 (378 ± 124 vs. 265 ± 49 minutes; mean difference, 113 s; 95% CI, 58-168 p < 0.001) compared to Group-S. There was no between-group difference in postoperative nausea, vomiting, and hypoxia incidences. Our results suggested that the short-term (approximately 30 minutes) switch of sevoflurane to desflurane at the end of sevoflurane-anesthesia can facilitate the speed of postoperative patient recovery.

Pure discrete spectrum and regular model sets in d-dimensional unimodular substitution tilings.

Primitive substitution tilings on {\bb R} whose expansion maps are unimodular are considered. It is assumed that all the eigenvalues of the expansion maps are algebraic conjugates with the same multiplicity. In this case, a cut-and-project scheme can be constructed with a Euclidean internal space. Under some additional condition, it is shown that if the substitution tiling has pure discrete spectrum, then the corresponding representative point sets are regular model sets in that cut-and-project scheme.

Gröbner-Shirshov bases for non-crystallographic Coxeter groups.

For the group algebra of the finite non-crystallographic Coxeter group of type H4, its Gröbner-Shirshov basis is constructed as well as the corresponding standard monomials, which describe explicitly all symmetries acting on the 120-cell and produce a natural operation table between the 14400 elements for the group.

On the Penrose and Taylor-Socolar hexagonal tilings.

The intimate relationship between the Penrose and the Taylor-Socolar tilings is studied, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach produces both types of tilings together, clarifies their relationship and offers straightforward proofs of their basic properties.

Multidimensional period doubling structures.

This paper develops the formalism necessary to generalize the period doubling sequence to arbitrary dimension by straightforward extension of the substitution and recursion rules. It is shown that the period doubling structures of arbitrary dimension are pure point diffractive. The symmetries of the structures are pointed out.