We give a practical criterion characterizing the monogenicity of the integral closure of a Dedekind ring R, based on results on the resultant Res(P,Pi) of the minimal polynomial P of a primitive integral element and of its irreducible factors Pi modulo prime ideals of R. We obtain a generalization and an improvement of the Dedekind criterion (Cohen, 1996) and we give some applications in the ca...

We characterize all cyclotomic polynomials of even degree with coefficients restricted to the set {+1,−1}. In this context a cyclotomic polynomial is any monic polynomial with integer coefficients and all roots of modulus 1. Inter alia we characterize all cyclotomic polynomials with odd coefficients. The characterization is as follows. A polynomial P (x) with coefficients ±1 of even degree N − ...

in this paper, at first we introduce a new index with the name co-pi index and obtain someproperties related this new index. then we compute this new index for tuc4c8(r) nanotubes.

Abstract Using the 1.32 $$\hbox {pb}^{-1}$$ pb - 1 statistics collected at $$J/\psi $$ J / ψ peak with KEDR detector VEPP-4M $$e^{+}e^{-\, }$$ e +</...

In this paper, we prove the continuity of maximum-entropy basis functions using variational analysis techniques. The use of information-theoretic variational principles to derive basis functions is a recent development. In this setting, data approximation is viewed as an inductive inference problem, with the basis functions being synonymous with a discrete probability distribution, and the poly...

The objective of this paper is to study the performance of a sixth order polynomial approach to model hysteresis behaviour of a magnetorheological (MR) damper under harmonic excitations. The polynomial model is developed based on curve fitting from the experimental results and consists of a pair subsystem namely positive and negative acceleration which correspond to the upper and lower curves. ...

A technique is described for the nontentative computer determination of the Galois groups of irreducible polynomials with integer coefficients. The technique for a given polynomial involves finding high-precision approximations to the roots of the polynomial, and fixing an ordering for these roots. The roots are then used to create resolvent polynomials of relatively small degree, the linear fa...

A new interpretation of the basic vector of the free Fock space (FFS) and the FFS is proposed. The approximations to various equations with additional parameters, for n-point information (n-pi), are also considered in the case of non-polynomial nonlinearities.

This article is concerned with the stability analysis of a 2 × conservation law PI and PDP boundary feedback control. In controller case, authors establish sufficient necessary condition for parameters by Walton–Marshall criterion. Moreover, in characteristic equation an exponential polynomial which includes two...

In this exercise n is a large integer. a) Suppose that there is an integer F = ∏k i=1 p ei i with known primes pi and ei > 0 such that F |(n − 1) and F > √ N . Let R = (n − 1)/F and assume that for each i there is an integer ai such that the following conditions hold: a RF i ≡ 1 mod n and (a R(F/pi) i − 1, n) = 1. Show that Z/(n ·Z)× contains a primitive F−th root of unity and conclude that n i...