We find sharp upper and lower bounds for the degree of an algebraic number in terms of the Q-dimension of the space spanned by its conjugates. For all but seven nonnegative integers n the largest degree of an algebraic number whose conjugates span a vector space of dimension n is equal to 2 n n!. The proof, which covers also the seven exceptional cases, uses a result of Feit on the maximal orde...

A connected algebraic group in characteristic 0 is uniquely determined by its Lie algebra. In this paper an algorithm is given for constructing an algebraic group in characteristic 0, given its Lie algebra. Using this an algorithm is presented for finding a maximal reductive subgroup and the unipotent radical of an algebraic group.

We consider problems in sequence enumeration suggested by Stockhausen’s problem, and derive a generating series for the number of sequences of length k on n available symbols such that adjacent symbols are distinct, the terminal symbol occurs exactly r times, and all other symbols occur at most r − 1 times. The analysis makes extensive use of techniques from the theory of symmetric functions. E...

We find sharp upper and lower bounds for the degree of an algebraic number in terms of the Q-dimension of the space spanned by its conjugates. For all but seven nonnegative integers n the largest degree of an algebraic number whose conjugates span a vector space of dimension n is equal to 2 n n!. The proof, which covers also the seven exceptional cases, uses a result of Feit on the maximal orde...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

in a r etrospective s t udy on the c ancer o f the gal l bladder, done in iran, it s e ems tha t it compr ises 0 . 36% o f a ll the malignant tumors . 1 .7 5% of the patients were fema les and the maximum incidenc e wa s in t he s i x th decade of l i f e. it was interesting t o note that the age ratio bet ween t he males and f ema le s reverses with t he advance o f a ge, s o at the 7th and 8t...

In this paper, we present a class of 2k-variable balanced Boolean functions and a class of 2k-variable 1-resilient Boolean functions for an integer k ≥ 2, which both have the maximal algebraic degree and very high nonlinearity. Based on a newly proposed conjecture by Tu and Deng, it is shown that the proposed balanced Boolean functions have optimal algebraic immunity and the 1-resilient Boolean...

We define the Mordell exceptional locus Z(V ) for affine varieties V ⊂ Ga with respect to the action of a product of Drinfeld modules on the coordinates of Ga. We show that Z(V ) is a closed subset of V . We also show that there are finitely many maximal algebraic φmodules whose translates lie in V . Our results are motivated by DenisMordell-Lang conjecture for Drinfeld modules.