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An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan (2010)

Programs and Algorithms of Numerical Mathematics

The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using c - s transformation and Q R -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.

An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Given a representation π of a local unitary group G and another local unitary group H , either the Theta correspondence provides a representation θ H ( π ) of H or we set θ H ( π ) = 0 . If G is fixed and H varies in a Witt tower, a natural question is: for which H is θ H ( π ) ≠ 0 ? For given dimension m there are exactly two isometry classes of unitary spaces that we denote H m ± . For ε ∈ { 0 , 1 } let us denote m ε ± ( π ) the minimal m of the same parity of ε such that θ H m ± ( π ) ≠ 0 , then we prove that m ε + ( π ) + m ε - ( π ) ≥ 2 n + 2 where n is the dimension of π .

Currently displaying 1461 – 1480 of 1964