A new method of quantitative evaluation of teaching processes is elaborated. On the base of scores data, the method permits to evaluate efficiency of teaching within one group of students and comparative teaching efficiency in two or more groups. As basic characteristics of teaching efficiency...

We extend the method of Ghasemi and Marshall (SIAM J. Optim. 22(2):460–473, <CitationRef CitationID="CR1">2012</CitationRef>), to obtain a lower bound f <Subscript>gp,M </Subscript> for a multivariate polynomial <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$f(\mathbf{x}) \in\mathbb{R}[\mathbf {x}]$</EquationSource> </InlineEquation> of degree ≤2d in n variables <Emphasis Type="Bold">x=(x <Subscript>1</Subscript>,…,x <Subscript> n </Subscript>) on the closed ball <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\{ \mathbf{x} \in\mathbb{R}^{n} :...</equationsource></inlineequation></subscript></subscript></emphasis></equationsource></inlineequation></subscript></citationref>