## Files

On this page I have posted some of my research projects and articles.

The following article is inspired from a problem given in a “Traian Lalescu” contest. Surprisingly, from what I’ve heard, the problem didn’t have a solution then. When studying the proof of Sierpinski’s theorem which states that any function can be written as the sum of two Darboux functions, I came up with the proof for the old problem. The details are in the article.
Functii ciudate
The problem I speak about is solved separately here. The article above has many more details. I proposed the problem for AMM, but they said it’s too hard to publish it alone.
Darboux Problem

This is a problem inspired from the van der Waerden Theorem. The proof given here uses the one dimensional van der Waerden Theorem, but the problem itself is a particular care of the two dimensional van der Waerden Theorem.
Coloring of the Plane (Romanian)

Below is a cute proof of Thales’s Theorem.
Thales (Romanian)

Below are two proofs of important properties of infinite cardinal numbers. (both in Romanian)
Numere cardinale x+x=x
Numere cardinale x.x=x

The following problem was proposed and published in AMM by myself and Cezar Lupu.
Matrix Inequality

This is a problem set, with problems composed or modified by myself. (Romanian)
Problems

This is probably a new proof of Euler’s Polyhedron Formula.
Euler Proof

Beniamin Bogosel-Lucrare de licenta

Master final paper (English) – these

1. October 22, 2010 at 6:45 pm

Am vazut niste solutii interesante pt problema de cardinale si in cartea Megan et al., Bazele analizei prin exercitii si probleme, Helicon 96. Uita-te la pagina 81, parca problema P1.14.6 daca tin bine minte.

• October 22, 2010 at 6:55 pm

Multumesc pentru referinţe. Am găsit şi eu problema în cartea aceea şi după câte ţin minte ideea era cam aceeaşi, folosind axioma lui Zorn. Am postat soluţia aici pentru că am căutat foarte mult pe net după o soluţie la problema aceasta în anul I de facultate, şi nu am găsit nimic până nu am primit indicaţii de la profesorii mei. Acum, cine caută probleme cu numere cardinale pe google poate găsi printre primele rezultate fişierele acestea.

2. March 20, 2013 at 2:07 pm

Hi beni how i can programming finite difference method for non_homogeneous medium using matlab where i work on mesh consist of 32 columns &110 rows
thanks

3. March 24, 2013 at 8:37 pm

I’m not sure what you mean by non homogeneous medium… To do a finite difference method on a grid 32 x 110 you need to define the matrix differently if you represent your unknown as a vector. If you represent your unknown as a matrix you could work on the lines and columns of that matrix to create the finite difference laplacian.