Displaying similar documents to “Quenching time of some nonlinear wave equations”

A note on the Hermite–Rankin constant

Kazuomi Sawatani, Takao Watanabe, Kenji Okuda (2010)

Journal de Théorie des Nombres de Bordeaux

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We generalize Poor and Yuen’s inequality to the Hermite–Rankin constant γ n , k and the Bergé–Martinet constant γ n , k ′ . Moreover, we determine explicit values of some low- dimensional Hermite–Rankin and Bergé–Martinet constants by applying Rankin’s inequality and some inequalities proven by Bergé and Martinet to explicit values of γ 5 ′ , γ 7 ′ , γ 4 , 2 and γ n ( n ≦ 8 ).

Weber’s class number problem in the cyclotomic ℤ 2 -extension of ℚ , II

Takashi Fukuda, Keiichi Komatsu (2010)

Journal de Théorie des Nombres de Bordeaux

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Let h n denote the class number of n -th layer of the cyclotomic ℤ 2 -extension of ℚ . Weber proved that h n ( n ≥ 1 ) is odd and Horie proved that h n ( n ≥ 1 ) is not divisible by a prime number ℓ satisfying ℓ ≡ 3 , 5 ( mod 8 ) . In a previous paper, the authors showed that h n ( n ≥ 1 ) is not divisible by a prime number ℓ less than 10 7 . In this paper, by investigating properties of a special unit more precisely, we show that h n ( n ≥ 1 ) is not divisible by a prime number ℓ less than 1 . 2 · 10 8 . Our argument also leads to the conclusion that h n ( n ≥ 1 ) is not divisible by...

A note on linear perturbations of oscillatory second order differential equations

Renato Manfrin (2010)

Archivum Mathematicum

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Under suitable hypotheses on γ ( t ) , λ ( t ) , q ( t ) we prove some stability results which relate the asymptotic behavior of the solutions of u ' ' + γ ( t ) u ' + ( q ( t ) + λ ( t ) ) u = 0 to the asymptotic behavior of the solutions of u ' ' + q ( t ) u = 0 .

On a theorem of Mestre and Schoof

John E. Cremona, Andrew V. Sutherland (2010)

Journal de Théorie des Nombres de Bordeaux

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A well known theorem of Mestre and Schoof implies that the order of an elliptic curve E over a prime field 𝔽 q can be uniquely determined by computing the orders of a few points on E and its quadratic twist, provided that q > 229 . We extend this result to all finite fields with q > 49 , and all prime fields with q > 29 .