Diatomic molecules attached to complexed iron or cobalt centres are important in many biological processes. In natural systems, metallotetrapyrrole units carry respiratory gases or provide sensing and catalytic functions. Conceiving synthetic model systems strongly helps to determine the pertinent chemical foundations for such processes, with recent work highlighting the importance of the prost...

mong the various bifurcation phenomena that may be observed in dynamical systems, gluing bifurcation is an important class of homoclinic bifurcation. The Z2 (or the so called reflection) symmetry plays a crucial role in occurrence of such bifurcation. At the bifurcation point two homoclinic orbits, which are mirror image of each other, appear as glued together at the saddle and thus forming in ...

The presence of a saddle-focus separatrix — a homoclinic curve in Poincaré’s terminology — plays a fundamental role in the onset and existence of chaos in dynamical systems. To observe chaotic behavior of trajectories, for instance, it is sufficient to have two conditions: the existence of a separatrix loop and Shil’nikov’s saddle-focus condition [1]. Consider a three-dimensional dynamical syst...

One new species Belisanadenticulata sp. n. (♂) is reported from northern Vietnam based on material collected by fogging the forest canopy. This species resembles Belisanascharffi Huber, 2005, but can be distinguished by relatively long distance between proximal parts of proximo-lateral apophysis and distal apophysis on male chelicerae, by presence of a nearly saddle-shaped prolateral sclerite o...

This report presents a dynamic procedure for the formation of category trees from a collection of skeletal shape trees. It overcomes several shortcomings of the formation procedure proposed by Baseski [4]. Unlike the method in [4], the structure of a category tree is not fixed at the beginning and can be updated in a dynamic way as a new example is considered. By this way, the true nature of ca...

BACKGROUND New insight into the 3D dynamic behavior of the mitral valve has prompted a reevaluation of annuloplasty ring designs. Force balance analysis indicates correlation between annulus forces and stresses in leaflets and chords. Improving this stress distribution can intuitively enhance the durability of mitral valve repair. We tested the hypothesis that saddle-shaped annuloplasty rings h...

Abstract In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations initial points, referred to as saddle-type , studied. Combining dynamical systems machinery (e.g., compactifications, timescale desingularizations vector fields) with tools from computer-assisted proofs rigorous integrators, the parameterization method for invari...