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    Extensions of the Heisenberg group by one-parameter groups of dilations which are subgroups of the affine and the symplectic groups
    (2015-02-01) ;
    Schulz, Eckart
    Extensions of the multidimensional Heisenberg group by one-parameter groups of matrix dilations are introduced and classified up to isomorphism. Each group is isomorphic to both, a subgroup of the symplectic group and a subgroup of the affine group, and its metaplectic representation splits into two irreducible subrepresentations, each of which is equivalent to a subrepresentation of the wavelet representation.
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    Mathematical Model for an Autonomous Vehicle to Fulfill the Closed Area
    (2022-01-01) ;
    Chitsakul, Pakkinee
    ;
    This research presents the mathematical model to roam an autonomous vehicle in a closed region with minor coincident areas. This model is Blind Algorithm, no literature that concern on mathematical model. It is essential for agricultural technology, for example, shoveling soil for planting, spraying liquid fertilizer, harvesting agricultural products, to control the movement of the vehicle with the redundant path is as less as possible is benefited to decrease the working hours and also the burning oil and more for cost-saving without any expensive hardware. The almost wholly filled farmland depends on the shape, the size of the area, and the vehicle dimension.