Well-Posedness and Asymptotic Stability of a Non-Linear Porous System with a Delay Term
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Authors: H. MAKHELOUFI, N. MEZOUAR AND M. BAHLIL
DOI: 10.46793/KgJMat2105.751E
Abstract:
We prove that there is no circulant Hadamard matrix H with first row [h1,…,hn] of order n > 4, under some linear conditions on the hi’s. All these conditions hold in the known case n = 4, so that our results can be thought as characterizations of properties that only hold when n = 4. Our first conditions imply that some eigenvalue λ of H is a sum of
terms h
jωj,
where ω is a primitive n-th root of 1. The same conclusion holds also
if some complex arithmetic means associated to λ are algebraic
integers (second conditions). Moreover, our third conditions, related to
the recent notion of robust Hadamard matrices, implies also the
nonexistence of these circulant Hadamard matrices. If some of the
conditions fail, it appears (to us) very difficult to be able to prove the
result.
Keywords:
Circulant matrices, Hadamard matrices, eigenvalues, unit circle, cyclotomic fields.
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