The problems given at IMC-9, Warsaw, july 19-25, 2002
Author: Mădălina Berinde / Vasile Berinde
Abstract: We present the problems given at IMC-9, Warsaw, July 19-25, 2002, followed by solutions and some comments. The note could be useful to those students who intend to train themselves for the mathematics competitions for university students.
Abstract: The implicit function is a basic theorem of mathematical analysis and it has a major importance in many mathematical problems. This theorem has many formulations, see . Every category of functions has its own special version of implicit function theorem and there are particular versions adapted to Banach spaces, algebraic geometry and to functions that are not even smooth.
The aim of this article is to state and to proof a version of analytic implicit function theorem for functions of two variables. Then we will give an application.
Triangles in which an angle is a mean of the others
Author: Mariana Sanziana Pop / Ileana Balazs
Abstract: In this article we determine all the triangles which have an angle equal to the geometric, arithmetic, harmonic or quadratic mean of the others. The angles are measured in degrees. We also study the particular case when the measures of the angles are integer numbers.
Abstract: In this article we will define the notion of circle escribable to a quadrilateral corresponding to a side of the quadrilateral.
Then, in some conditions, the escribable circle's radius will be determined.
In the end, the article contains identities and inequalities checked by the circle's radius escribabel to a quadrilateral.
Abstract: This paper was written for clarifying a counting problem used in the hypergeometric probabilistic scheme. Through a simple Combinatorics principles we shall explain some approaches which have appeared in many books.
Abstract: Based on a difficult problem from the entering examination in the Mathematics Faculty of Bucharest in September 1977, our paper analyses the wanted or involuntary undecipherings of the mathematical enunciations.There are criticized some kinds of faults, often appeared in the problem texts, proposed to be solved an this as a consequence of the multiple-choise examinations, absolutely unusual in Romania, and more, unrecommended for Mathematics.