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On realizability of sign patterns by real polynomials

Vladimir Kostov (2018)

Czechoslovak Mathematical Journal

The classical Descartes’ rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers ( p , n ) , chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree 8 polynomials.

On refinements of certain inequalities for means

Sándor, József Sándor, József (1995)

Archivum Mathematicum

In this paper we obtain certain refinements (and new proofs) for inequalities involving means, results attributed to Carlson; Leach and Sholander; Alzer; Sndor; and Vamanamurthy and Vuorinen.

On relations among the generalized second-order directional derivatives

Karel Pastor (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.

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