Let k be a field of characteristic zero and let f ∈ k[x]. The m-th cyclic resultant of f is rm = Res(f, x − 1). We characterize polynomials having the same set of nonzero cyclic resultants. Generically, for a polynomial f of degree d, there are exactly 2 distinct degree d polynomials with the same set of cyclic resultants as f . However, in the generic monic case, degree d polynomials are uniqu...

In most fields of natural science, the density of individuals is usually determined from counts in defined areas of known dimensions. When tree density is being measured, the delimitation of plots of up to a hectare or acre in area, presents some difficulties and is time-consuming. Because of the reciprocal relationship between. density and nearness of individuals to one another it is necessary...

All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X859433 +X288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

There is a natural linkage between the molecular structures and the bio-medical and pharmacology characteristics. A topological index can be considered as transformation of chemical structure in to real number and has been used as a predictor parameter. There are certain vertex-degree-based topological indices which has been used extensively in the chemical graph theory but recently no further ...

The exact distance p-power of a graph G, denoted G[#p], is on vertex set V(G) in which two vertices are adjacent if they at exactly p G. Given integers k and p, we define f(k, p) to be the maximum possible order clique p-powers graphs with degree + 1. It easily observed that 2) ≤ k2 We prove equality may only hold connected component G isomorphic member class Pk incidence finite projective k-ge...

OBJECTIVE To use a statewide population-based genealogic database to evaluate the relationship between Parkinson disease (PD) and cancer subtypes. DESIGN Using a computerized genealogy for the Utah pioneers and their descendants linked to a statewide cancer registry and statewide death certificates, we estimated relative risks for cancer in individuals with PD listed on their death certificate,...