On the Hyperbolicity Domain of the Polynomial x^n + a1x^(n-1) + 1/4+ an

∗ Partially supported by INTAS grant 97-1644

Polynomial Automorphisms Over Finite Fields

It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

Quadratic Mean Radius of a Polynomial in C(Z)

* Dedicated to the memory of Prof. N. Obreshkoff

Neither security nor development? Czech and Hungarian identities and interests in the provincial reconstruction teams in Afghanistan

This article builds on the securitisation and post-development literature and it scrutinises the Czech and Hungarian legitimising discourses of the two countries’ respective Provincial Reconstruction Teams (PRTs) in the Logar and Baghlan provinces of Afghanistan from 2007 to 2013. In spite of the hybrid civil–military character of the PRTs, their security–development nexus was absent and they were respectively securitised and “developmentalised” only indirectly and to a varying extent. The PRTs were mostly justified by the Czech Republic's NATO membership as an identity issue and they were justified as a Hungarian national interest and as both an obligation and an opportunity. Rather than merely importing NATO's arguments as suggested by the previous literature, the depoliticisation and positive connotation of the intervention in Afghanistan was constructed by the domestic NATO-related identities and interests in the Czech Republic and Hungary.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

The Eccentric Connectivity Polynomial of some Graph Operations

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

On the Factorization of the Poincaré Polynomial: A Survey

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.

Assuming identities online:experimental linguistics applied to the policing of online paedophile activity

This article uses a research project into the online conversations of sex offenders and the children they abuse to further the arguments for the acceptability of experimental work as a research tool for linguists. The research reported here contributes to the growing body of work within linguistics that has found experimental methods to be useful in answering questions about representation and constraints on linguistic expression (Hemforth 2013). The wider project examines online identity assumption in online paedophile activity and the policing of such activity, and involves dealing with the linguistic analysis of highly sensitive sexual grooming transcripts. Within the linguistics portion of the project, we examine theories of idiolect and identity through analysis of the ‘talk’ of perpetrators of online sexual abuse, and of the undercover officers that must assume alternative identities in order to investigate such crimes. The essential linguistic question in this article is methodological and concerns the applicability of experimental work to exploration of online identity and identity disguise. Although we touch on empirical questions, such as the sufficiency of linguistic description that will enable convincing identity disguise, we do not explore the experimental results in detail. In spite of the preference within a range of discourse analytical paradigms for ‘naturally occurring’ data, we argue that not only does the term prove conceptually problematic, but in certain contexts, and particularly in the applied forensic context described, a rejection of experimentally elicited data would limit the possible types and extent of analyses. Thus, it would restrict the contribution that academic linguistics can make in addressing a serious social problem.

Operators with Polynomial Coefficients and Generalized Gelfand-Shilov Classes

2010 Mathematics Subject Classification: Primary 35S05, 35J60; Secondary 35A20, 35B08, 35B40.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.