Modified wave operators for nonlinear Schrödinger equations in one and two dimensions.

Hayashi, Nakao; Naumkin, Pavel I.; Shimomura, Akihiro; Tonegawa, Satoshi

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Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions.

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Explicit lower bounds for linear forms in two logarithms

Nicolas Gouillon (2006)

Journal de Théorie des Nombres de Bordeaux

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We give an explicit lower bound for linear forms in two logarithms. For this we specialize the so-called Schneider method with multiplicity described in []. We substantially improve the numerical constants involved in existing statements for linear forms in two logarithms, obtained from Baker’s method or Schneider’s method with multiplicity. Our constant is around $5 . 10^{4}$ instead of $10^{8}$ .

Unique continuation property for the Kadomtsev-Petviashvili (KP-II) equation.

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On the papers of Ramachandra and Kátai

A. Sankaranarayanan, K. Srinivas (1992)

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Oscillation of Mertens’ product formula

Harold G. Diamond, Janos Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

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Mertens’ product formula asserts that $\prod_{p \leq x} (1 - \frac{1}{p}) log x \to e^{- γ}$ as $x \to \infty$ . Calculation shows that the right side of the formula exceeds the left side for $2 \leq x \leq 10^{8}$ . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on $π (x) - li x$ , this and a complementary inequality might change their sense for sufficiently large values of $x$ . We show this to be the case.