Tatjana Lutovac

The natural algorithmic approach of mixed trigonometric-polynomial problems

AbstractThe aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form ∑i=1nαixpicosqixsinrix>0

Refined Estimates and Generalizations of Inequalities Related to the Arctangent Function and Shafer’s Inequality

\sum_{i=1}^{n}\alpha _{i}x^{p_{i}} \cos ^{q_{i}} x\sin ^{r_{i}} x>0

Sharpening and generalizations of Shafer-Fink and Wilker type inequalities: a new approach

by reducing them to polynomial inequalities. Finally, we show the great applicability of this algorithm and, as an example, we use it to analyze some new rational (Padé) approximations of the function cos2x and to improve a class of inequalities by Yang. The results of our analysis could be implemented by means of an automated proof assistant, so our work is a contribution to the library of automatic support tools for proving various analytic inequalities.

Detecting Loops During Proof Search in Propositional Affine Logic

In this paper we propose a new method for sharpening and refinements of some trigonometric inequalities. We apply these ideas to some inequalities of Wilker–Cusa–Huygens type.

Detection and analysis of some redundancies in linear logic sequent proofs

In this paper we give some sharper refinements and generalizations of inequalities related to Shafers inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.

A New Method for Proving Some Inequalities Related to Several Special Functions

In this paper, we give some sharper refinements and generalizations of inequalities related to Shafer-Fink’s inequality for the inverse sine function stated in Theorems 1, 2, and 3 of Bercu (Math. Probl. Eng. 2017: Article ID 9237932, 2017).

About some exponential inequalities related to the sinc function

In this paper we propose and prove some generalizations and sharpenings of certain inequalities of Wilker;s and Shafer-Finks type. Application of the Wu-Debnath theorem enabled us to prove some double sided inequalities.

An approach to automated reparation of failed proof attempts in propositional linear logic sequent calculus

It is well-known that proof search, in general, does not terminate. In some decidable logics (e.g. intuitionistic propositional logic) it is possible to give a terminating sequent calculus, i.e. one in which a naive backward proof search will always terminate. However, such calculi are not always available, even for decidable logics. In this paper we investigate the incorporation of a loop detection mechanism into an inference system for propositional affine logic (i.e. propositional linear logic with arbitrary weakening). This logic is decidable, but no terminating sequent calculus for it is known. We adapt the history techniques used for intuitionistic and modal logics, but in this case we cannot assume that the context will always be non-decreasing. We show how to overcome this problem, and hence to provide a loop detection mechanism for propositional affine logic.