Bounding right-arm rotation distances

Rotation distance quantifies the difference in shape between two rooted binary trees of the same size by counting the minimum number of elementary changes needed to transform one tree to the other. We describe several types of rotation distance, and provide upper bounds on distances between trees with a fixed number of nodes with respect to each type. These bounds are obtained by relating each restricted rotation distance to the word length of elements of Thompson's group F with respect to different generating sets, including both finite and infinite generating sets.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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The effect of counterpoise correction and relaxation energy term to the internal rotation barriers: application to the BF3 ...NH3 and C2H4 ...SO2 dimers

The relevance of the fragment relaxation energy term and the effect of the basis set superposition error on the geometry of the BF3⋯NH3 and C2H4⋯SO2 van der Waals dimers have been analyzed. Second-order Møller-Plesset perturbation theory calculations with the d95(d,p) basis set have been used to calculate the counterpoise-corrected barrier height for the internal rotations. These barriers have been obtained by relocating the stationary points on the counterpoise-corrected potential energy surface of the processes involved. The fragment relaxation energy can have a large influence on both the intermolecular parameters and barrier height. The counterpoise correction has proved to be important for these systems

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is suppressed. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass.

Loop bifurcation and magnetization rotation in exchange-biased Ni/FeF2

Exchange-biased Ni/FeF2 films have been investigated using vector coil vibrating-sample magnetometry as a function of the cooling field strength HFC . In films with epitaxial FeF2 , a loop bifurcation develops with increasing HFC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with HFC until only a single positively shifted loop is found. Throughout this process, the negative and positive (sub)loop shifts maintain the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing HFC . The transverse magnetization shows clear correlations with the longitudinal subloops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single-crystal nature of the antiferromagnetic FeF2 , which breaks down into two opposite regions of large domains.

Forage preservation (grazing vs. hay) fed to ewes affects the fatty acid profile of milk and CPT1B gene expression in the sheep mammary gland

Background: Alterations in lipid metabolism occur when animals are exposed to different feeding systems. In the last few decades, the characterisation of genes involved in fat metabolism and technological advances have enabled the study of the effect of diet on the milk fatty acid (FA) profile in the mammary gland and aided in the elucidation of the mechanisms of the response to diet. The aim of this study was to evaluate the effect of different forage diets (grazing vs. hay) near the time of ewe parturition on the relationship between the fatty acid profile and gene expression in the mammary gland of the Churra Tensina sheep breed. Results: In this study, the forage type affected the C18:2 cis-9 trans-11 (CLA) and long-chain saturated fatty acid (LCFA) content, with higher percentages during grazing than during hay feeding. This may suggest that these FAs act as regulatory factors for the transcriptional control of the carnitine palmitoyltransferase 1B (CPT1B) gene, which was more highly expressed in the grazing group (GRE). The most highly expressed gene in the mammary gland at the fifth week of lactation is CAAT/ enhancer- binding protein beta (CEBPB), possibly due to its role in milk fat synthesis in the mammary gland. More stable housekeeping genes in the ovine mammary gland that would be appropriate for use in gene expression studies were ribosomal protein L19 (RPL19) and glyceraldehyde- 3- phosphate dehydrogenase (GAPDH). Conclusions: Small changes in diet, such as the forage preservation (grazing vs. hay), can affect the milk fatty acid profile and the expression of the CPT1B gene, which is associated with the oxidation of fatty acids. When compared to hay fed indoors, grazing fresh low mountain pastures stimulates the milk content of CLA and LCFA via mammary uptake. In this sense, LCFA in milk may be acting as a regulatory factor for transcriptional control of the CPT1B gene, which was more highly expressed in the grazing group.