In this paper, we have introduced the category of 2-quasi crossed modules for Lie algebras and constructed a pair adjoint functors between that 2-crossed algebras.

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW -complex to the classifying space of a crossed module and also, ...

the aim of this paper is to study the $(alpha‎, ‎gamma)$-prolongation of central extensions‎. ‎we obtain the obstruction theory for $(alpha‎, ‎gamma)$-prolongations and classify $(alpha‎, ‎gamma)$-prolongations thanks to low-dimensional cohomology groups of groups‎.

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In order to study the electronic properties of single-walled carbon nanotube junctions we have fabricated several devices consisting of two crossed nanotubes with electrical leads attached to each end of each nanotube. We correlate the properties of the junctions with the properties of the individual nanotubes: metal–metal, metal–semiconductor, and semiconductor– semiconductor junctions are all...

The cervical spine is the most common site of traumatic vertebral column injuries. Respiratory insufficiency constitutes a significant proportion of the morbidity burden and is the most common cause of mortality in these patients. In seeking to enhance our capacity to treat specifically the respiratory dysfunction following spinal cord injury, investigators have studied the "crossed phrenic phe...

The term "diaschisis," as originally used by Von-Monakow (1), implies an immediate decrease in neuronal activity in a region due to an interruption of its afferent axonal supply. Experimental studies, in animals , of unilateral ischemia in which neuronal function in the contralateral hemisphere was demonstrated to be impaired, provided evidence for such a mechanism (2). The corpus callosum appe...

In this work we deal with actions of vector groupoid which is a new concept in the literature‎. ‎After we give the definition of the action of a vector groupoid on a vector space‎, ‎we obtain some results related to actions of vector groupoids‎. ‎We also apply some characterizations of the category and groupoid theory to vector groupoids‎. ‎As the second part of the work‎, ‎we define the notion...