17,968 research outputs found
On the unique representability of spikes over prime fields
For an integer , a rank- matroid is called an -spike if it
consists of three-point lines through a common point such that, for all
, the union of every set of of these lines has
rank . Spikes are very special and important in matroid theory. In 2003 Wu
found the exact numbers of -spikes over fields with 2, 3, 4, 5, 7 elements,
and the asymptotic values for larger finite fields. In this paper, we prove
that, for each prime number , a ) representable -spike is only
representable on fields with characteristic provided that .
Moreover, is uniquely representable over .Comment: 8 page
On the Unitarity Triangles of the CKM Matrix
The unitarity triangles of the Cabibbo-Kobayashi-Maskawa (CKM)
matrix are studied in a systematic way. We show that the phases of the nine CKM
rephasing invariants are indeed the outer angles of the six unitarity triangles
and measurable in the -violating decay modes of and mesons.
An economical notation system is introduced for describing properties of the
unitarity triangles. To test unitarity of the CKM matrix we present some
approximate but useful relations among the sides and angles of the unitarity
triangles, which can be confronted with the accessible experiments of quark
mixing and violation.Comment: 9 Latex pages; LMU-07/94 and PVAMU-HEP-94-5 (A few minor changes are
made, accepted for publication in Phys. Lett. B
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