Dynamic response of a growing inclusion in a discrete system

The propagation of a semi-infinite line defect, contained in an infinite square-cell lattice is considered. The defect is composed of particles lighter than those in the ambient lattice and it is assumed this defect propagates with constant speed. Dispersion properties of the lattice are related to waves generated by the propagating defect. In order to determine these properties, the Wiener–Hopf technique is applied. Additional features, related to localisation along the defect are also identified. Analysis of the dispersion relations for this lattice, from the kernel function inside the Wiener–Hopf equation, is carried out. The solution of the Wiener–Hopf equation is presented for the case when an external load is applied corresponding to an energy flux at infinity.     

Functional connectivity between task-positive and task-negative brain areas and its relation to working memory performance

Functional brain imaging studies have identified a set of brain areas typically activated during cognitive tasks (task-positive brain areas) and another set of brain areas typically deactivated during cognitive tasks (task-negative brain areas). Negative correlations, or anticorrelations, between task-positive and task-negative brain areas have been reported at rest. Furthermore, the strength of these anticorrelations appears to be related to cognitive function. However, studies examining anticorrelations have typically employed global regression or similar analysis steps that force anticorrelated relationships to exist between brain areas. Therefore the validity of these findings has been questioned. Here we examine anticorrelations between a task-negative region in the medial frontal gyrus/anterior cingulate cortex and dorsolateral prefrontal cortex, a classic task-positive area, using an analysis that does not include global regression. Instead, we control for whole-brain correlations in the group-level analysis. Using this approach, we demonstrate that the strength of the functional connection between the medial frontal cortex and the dorsolateral prefrontal cortex is related to cognitive function and that this relationship is not an artifact of global regression.     

Line intensities of acetylene: New measurements in the 1.5-μm spectral region and global modelling in the ΔP=10 series

Using the Fourier transform spectra of the acetylene molecule recorded near 1.5-μm, the intensities of 111 lines belonging to seven hot bands of the main isotopologue ¹²C₂H₂ have been retrieved by means of a multispectrum fitting procedure. Considering the density of lines in the spectra, and the fact that the measured bands are the weakest observed, the accuracy of the measurements is around 10%. At first stage, an empirical treatment of these data has been performed, leading to the vibrational transition dipole moment squared and some Herman–Wallis coefficients. Then the measured line intensities of this work and collected ones from the literature have been treated simultaneously within the framework of the effective operator approach.     

Constructing the Co cyclic Structures for Crossed Copro duct Coalgebras

In this paper, we construct a cocylindrical object associated to two coal-gebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct c...     

Quantum topology phase diagrams for molecules,clusters, and solids

The need to make more quantitative use of the total electronic charge density distribution is demonstrated in this short perspective. This is framed in the perspective of the ground breaking early work of Bader and coworkers, along with mathematicians who captured the essential nature of a molecule in a suitably compact form in real space. We see that this simple form is the Poincaré–Hopf relation for molecules and clusters and the Euler–Hopf relation in solids. Thom's theory of elementary catastrophes combined with the Poincaré–Hopf relation provides the inspiration for the new quantum topology. An alternative use of the Poincaré–Hopf relation, molecular recognition, is discussed. Quantum topology is then used to create a topology phase diagram for both molecules and solids. The author adds their perspectives of the huge potential of the quantum topology approach by demonstrating the ease with which new theoretical ideas can be generated. © 2013 Wiley Periodicals, Inc.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.