In coding theory, Gray isometries are usually defined as mappings between finite Frobenius rings, which include the ring Zm of integers modulo m and the finite fields. In this paper, we derive an isometric mapping from Z8 to Z4 2 from the composition of the Gray isometries on Z8 and on Z4 . The image under this composition of a Z8-linear block code of length n with homogeneous distance d is a (...

in this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the gray-scott model, in which spot patterns have been observed. we focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. a complete bifurcation study of these solutions is presented. the main mathematic...

We discuss non-relativistic scattering by a Newtonian potential. We show that the gray-body factors associated with scattering by a black hole exhibit the same functional dependence as scattering amplitudes in the Newtonian limit, which should be the weak-field limit of any quantum theory of gravity. This behavior arises independently of the presence of supersymmetry. The connection to two-dime...

We discuss non-relativistic scattering by a Newtonian potential. We show that the gray-body factors associated with scattering by a black hole exhibit the same functional dependence as scattering amplitudes in the Newtonian limit, which should be the weak-field limit of any quantum theory of gravity. This behavior arises independently of the presence of supersymmetry. The connection to twodimen...

Drawing on existing literature, this research offers a theoretical delineation of the gray zone conflict, that is, conflict below threshold armed conflict. It begins by identifying characteristic features attributed to propose definition concept. then situates within framework International Relations theory Realism before setting out main lines strategic action used. Lastly, it examines various...

Although holism has long been a central theme in anthropology, current perception is that anthropological discourse is being pulled apart along its biologyculture seams. Despite reservations among sociocultural theorists, Darwinism remains the only body of theory that purports to link sub-disciplines of anthropology. The importance of holism in anthropology is reconciled here with disciplinary ...

A new methodology based on Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) and Graph Theory is presented for characterizing the anatomical connections between brain gray matter areas. In a first step, brain voxels are modeled as nodes of a non-directed graph in which the weight of an arc linking two neighbor nodes is assumed to be proportional to the probability of being connected by ner...