Flag-transitive block designs and unitary groups

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

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Block designs for variety trials

The Journal of Agricultural Science ◽

10.1017/s0021859600055507 ◽

1978 ◽

Vol 90 (2) ◽

pp. 395-400 ◽

Cited By ~ 83

Author(s):

H. D. Patterson ◽

E. R. Williams ◽

E. A. Hunter

Keyword(s):

Block Designs ◽

Incomplete Block ◽

Variety Trials ◽

Rectangular Lattices

SummaryIn this paper we present a series of resolvable incomplete block designs suitable for variety trials with any number of varieties v in the range 20 ≤v ≤ 100. These designs usefully supplement existing square and rectangular lattices. They are not necessarily optimal in the sense of having smallest possible variances but their efficiencies are known to be high.

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Förster Resonance Energy Transfer in Linear DNA Multifluorophore Photonic Wires: Comparing Dual versus Split Rail Building Block Designs

Advanced Optical Materials ◽

10.1002/adom.202100884 ◽

2021 ◽

pp. 2100884

Author(s):

Paul D. Cunningham ◽

Christopher M. Spillmann ◽

Joseph S. Melinger ◽

Mario G. Ancona ◽

Young C. Kim ◽

...

Keyword(s):

Energy Transfer ◽

Building Block ◽

Resonance Energy Transfer ◽

Resonance Energy ◽

Förster Resonance Energy Transfer ◽

Block Designs ◽

Linear Dna ◽

Dual Versus ◽

Photonic Wires ◽

Förster Resonance

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The intersection graph of a finite simple group has diameter at most 5

Archiv der Mathematik ◽

10.1007/s00013-021-01583-3 ◽

2021 ◽

Author(s):

Saul D. Freedman

Keyword(s):

Simple Group ◽

Upper Bound ◽

Finite Simple Group ◽

Unitary Groups ◽

Intersection Graph ◽

Monster Group ◽

Prime Dimension

AbstractLet G be a non-abelian finite simple group. In addition, let $$\Delta _G$$ Δ G be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of $$\Delta _G$$ Δ G has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

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