Efficient computation of the Zassenhaus formula Casas, Fernando; Murua, Ander; Nadinic, Mladen
Computer physics communications,
November 2012, 2012-11-00, 20121101, Letnik:
183, Številka:
11
Journal Article
Recenzirano
Odprti dostop
A new recursive procedure to compute the Zassenhaus formula up to high order is presented, providing each exponent in the factorization directly as a linear combination of independent commutators and ...thus containing the minimum number of terms. The recursion can be easily implemented in a symbolic algebra package and requires much less computational effort, both in time and memory resources, than previous algorithms. In addition, by bounding appropriately each term in the recursion, it is possible to get a larger convergence domain of the Zassenhaus formula when it is formulated in a Banach algebra.
Advanced chemical peels: Phenol-croton oil peel Wambier, Carlos G.; Lee, Kachiu C.; Soon, Seaver L. ...
Journal of the American Academy of Dermatology,
August 2019, 2019-Aug, 2019-08-00, 20190801, Letnik:
81, Številka:
2
Journal Article
Recenzirano
Once considered the standard for deep facial resurfacing, the classical Baker-Gordon phenol-croton oil peel has largely been replaced by formulas with lower concentrations of phenol and croton oil. ...The improved safety profile of deep peels has ushered in a new era in chemical peeling. Wrinkles can be improved and skin can be tightened with more subtle and natural results. No longer does a deep peel denote “alabaster white” facial depigmentation with complete effacement of wrinkles. Gregory Hetter's research showed that the strength and corresponding depth of penetration of the phenol-croton oil peel can be modified by varying the concentration of croton oil. This second article in this continuing medical education series focuses on the main historical, scientific, and procedural considerations in phenol-croton oil peels.
This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of ...Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker–Akhiezer functions, and determine zeros and poles of the Baker–Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
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