Let $\mathbb{F}_q[x]$ be the ring of polynomials over a finite field $\mathbb{F}_q$ and $\mathbb{F}_q(x)$ its quotient field. $\mathbb{P}$ set primes in $\mathbb{F}_q[x]$, let $\mathcal{I}$ all $f$ for which $f(\mathbb{P})\subseteq\mathbb{F}_q[x]$. The existence basis is established using notion characteristic ideal; this shows that free $\mathbb{F}_q[x]$-module. Through localization, explicit ...

A retrospective evaluation of attitudinal, behavioural and knowledge change among diverse stakeholder groups was conducted in Limpopo Province of South Africa to assess the effectiveness of a series of values clarification (VC) interventions. Telephone and face-to-face interview (193) results revealed that over two-thirds (70.2%) reported behavioural changes and 93.2% reported increased compass...

This work has been motivated by recent papers that quantify the density of values generic quadratic forms and other polynomials at integer points, in particular ones use Rogers’ second moment estimates. In this paper, we establish such results a very general framework. Given any subhomogeneous function (a notion to be defined) $$f: \mathbb {R}^n \rightarrow {R}$$ , derive necessary sufficient c...

BACKGROUND Although the Netherlands currently has its own procedure for evaluating chemical compounds and setting occupational exposure limits (OELs), most of these limits were originally adopted in the 1970s from threshold limit values (TLVs) set by the American Conference of Governmental Industrial Hygienists (ACGIH). However, beginning in the late 1980s, criticism about non-scientific consid...

Conventional data envelopment analysis (DEA) models normally assume all inputs and outputs are real valued and continuous. However in problems some inputs and outputs can only take integer values, also, both desirable and undesirable outputs can be generated . In this paper the effect of undesirable outputs in integer DEA model is discussed. The proposed model distinguishes weak disposability o...

this paper uses the weighted l$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. when all variables are integer it finds the whole set of efficient solutions. in each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...