On permutation polynomials over finite fields

A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded

On well-rounded ideal lattices - II

We study well-rounded lattices which come from ideals in quadratic number fields, generalizing some recent results of the first author with K. Petersen. In particular, we give a characterization of ideal well-rounded lattices in the plane and show that a positive proportion of real and imaginary quadratic number fields contains ideals giving rise to well-rounded lattices.Comment: 13 pages; to appear in the International Journal of Number Theor

A solid-phase enzyme-linked assay for vitamin B 12

A new solid-phase enzyme-linked competitive binding assay for vitamin B 12 (cyanocobalamin) is described. The assay is based on the competition between analyte B 12 molecules and a glucose-6-phosphate dehydrogenase-vitamin B 12 conjugate for a limited number of R-protein binding sites immobilized on sepharose particles. After appropriate incubation and washing steps, the enzyme activity bound to the solid-phase is inversely related to the concentration of B 12 in the sample. Under optimized conditions, the method can detect B 12 in the range of 3×10 −10 −1×10 −8 M (using 100 μ l sample) with high selectivity over other biological molecules.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41626/1/604_2005_Article_BF01197285.pd

On permutation polynomials over finite fields

A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded.Peer Reviewe