The limit case of a domination property

The domination number γ(G) of a connected graph G of order n is bounded below by(n+2-e(G))/ 3 , where (G) denotes the maximum number of leaves in any spanning tree of G. We show that (n+2-e(G))/ 3 = γ(G) if and only if there exists a tree T ∈ T ( G) ∩ R such that n1(T ) = e(G), where n1(T ) denotes the number of leaves of T1, R denotes the family of all trees in which the distance between any two distinct leaves is congruent to 2 modulo 3, and T (G) denotes the set composed by the spanning trees of G. As a consequence of the study, we show that if (n+2-e(G))/ 3 = γ(G), then there exists a minimum dominating set in G whose induced subgraph is an independent set. Finally, we characterize all unicyclic graphs G for which equality (n+2-e(G))/ 3= γ(G) holds and we show that the length of the unique cycle of any unicyclic graph G with (n+2-e(G))/ 3= γ(G) belongs to {4} ∪ {3 , 6, 9, . . . }.     

Origins of intersubject variability of blood oxygenation level dependent and arterial spin labeling fMRI: implications for quantification of brain activity

Accurate localization of brain activity using blood oxygenation level-dependent (BOLD) functional magnetic resonance imaging (fMRI) has been challenged because of the large BOLD signal within distal veins. Arterial spin labeling (ASL) techniques offer greater sensitivity to the microvasculature but possess low temporal resolution and limited brain coverage. In this study, we show that the physiological origins of BOLD and ASL depend on whether percent change or statistical significance is being considered. For BOLD and ASL fMRI data collected during a simple unilateral hand movement task, we found that in the area of the contralateral motor cortex the centre of gravity (CoG) of the intersubject coefficient of variation (CV) of BOLD fMRI was near the brain surface for percent change in signal, whereas the CoG of the intersubject CV for Z-score was in close proximity of sites of brain activity for both BOLD and ASL. These findings suggest that intersubject variability of BOLD percent change is vascular in origin, whereas the origin of inter-subject variability of Z-score is neuronal for both BOLD and ASL. For longer duration tasks (12 s or greater), however, there was a significant correlation between BOLD and ASL percent change, which was not evident for short duration tasks (6 s). These findings suggest that analyses directly comparing percent change in BOLD signal between pre-defined regions of interest using short duration stimuli, as for example in event-related designs, may be heavily weighted by large-vessel responses rather than neuronal responses.     

2-D self-assembly of the bis(phthalocyaninato)terbium(III) single-molecule magnet studied by scanning tunnelling microscopy

The presence of alkoxyl chains on the single-molecule magnet [(Pc')2Tb(III)] and its planar character favour its 2-D self-assembly on HOPG with the molecular plane parallel to the graphite surface, enabling us to control and/or predict the orientation of the preferential magnetization axis on the surface.     

Enzyme dynamics and tunneling enhanced by compression in the hydrogen abstraction catalyzed by soybean lipoxygenase-1

A fully microscopical simulation of the rate-limiting hydrogen abstraction catalyzed by soybean lipoxygenase-1 (SLO-1) has been carried out. This enzyme exhibits the largest, and weakly temperature dependent, experimental H/D kinetic isotope effect (KIE) reported for a biological system. The theoretical model used here includes the complete enzyme with a solvation shell of water molecules, the Fe(III)-OH- cofactor, and the linoleic acid substrate. We have used a hybrid QM(PM3/d-SRP)/MM method to describe the potential energy surface of the whole system, and the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) to calculate the rate constant and the primary KIE. The computational results show that the compression of the wild-type active site enzyme results in the huge contribution of tunneling (99%) to the rate of the hydrogen abstraction. Importantly, the active site becomes more flexible in the Ile553Ala mutant reactant complex simulation (for which a markedly temperature dependent KIE has been experimentally determined), thus justifying the proposed key role of the gating promoting mode in the reaction catalyzed by SLO-1. Finally, the results indicate that the calculated KIE for the wild-type enzyme has an important dependence on the barrier width.     

A unified synthetic approach to trachylobane-, beyerane-, atisane- and kaurane-type diterpenes

A general synthetic approach to the polycyclic carbon skeleton of biogenetically related trachylobane, beyerane, atisane, and kaurane diterpenes from carvone is described. The skeleton of these diterpenes is prepared from a common intermediate, that is, 25, readily prepared from carvone using an IMDA reaction and an intramolecular diazo ketone cyclopropanation of an unsaturated ketone as key steps. The tetracyclic diterpene ring systems are obtained from this key trachylobane-type intermediate through the regioselective reductive cleavage of the cyclopropane ring, after adequate modification of the functionalization around the tricyclo[3.2.1.0^2,7]octane moiety.     

Gas-Phase Synthesis of Ethyl tert-Butyl Ether (ETBE) on H-ZSM-5 Catalyst in Continuous Fixed-Bed and Fluidized-Bed Reactors

The gas-phase synthesis of ETBE from ethanol and isobutene has been carried out over a H-ZSM-5 catalyst in two types of continuous-flow catalytic reactors, fixed-bed and fluidized-bed. We have studied the influence of temperature, molar ratio ethanol/isobutene and weight hourly space velocity on the yield of ETBE.     

The $$\varvec{N}$$ N -soliton,fusion, rational and breather solutions of two extensions of the (2+1)-dimensional Bogoyavlenskii–Schieff equation

Nonlinear Dynamics - The aim of this work is to analyze and explore the dynamics of two extensions of the Bogoyavlenskii–Schieff equation. The Hirota bilinear method is applied to the...