The problem of explicit generation of unitary operators for atomic systems with degenerate energy levels is considered. The Lie algebra structure is used to derive constructive control schemes for the creation of arbitrary superposition states and selective population interchanges for a transition between two three-fold degenerate energy levels.

We show that in the worst case, Q(nd) sidedness queries are required to determine whether a set of n points in Rd is affinely degenerate, i .e . , whether it contains d + 1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing Q(nd) “collapsible” simplices, any one of which can b...

First, mathematical formulae faithfully describing the distributions of amino acids and codons and reproducing the degeneracies in the various known genetic codes, including the standard genetic code, are constructed, by hand. Second, we summarize another mathematical approach relying on the use of q-deformations to describe these same genetic codes, and add a new application not considered bef...

For hydrologic applications, terrain models should have few local minima, and drainage lines should coincide with edges. We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for higher-order Delaunay triangulations. Two heu...

We show that in the worst case, (n d) sidedness queries are required to determine whether a set of n points in IR d is aanely degenerate, i.e., whether it contains d + 1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing (n d) \collapsible" simplices, any one of which can be m...

the purpose of this study was to determine the effect of two levels of four commercial multi-enzymes on the apparent metabolizable energy corrected for nitrogen (amen) and digestibility of crude fat, crude protein, dry matter, and organic matter in broiler chickens through total excreta collection method. one hundred thirty male broiler chicks were assigned to 45 metabolic cages involving 9 tre...

We show that triangulating a set of points with elevations such that the number of local minima of the resulting terrain is minimized is NP-hard for degenerate point sets. The same result applies when there are no degeneracies for higher-order Delaunay triangulations. Two heuristics are presented to minimize the number of local minima for higher-order Delaunay triangulations, and they are compa...