A Computer Verification of a Conjecture About Erdos-Mordell Curve

In this paper we consider Erdos-Mordell inequality and its extension in the plane of triangle to the Erdos-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdos-Mordell curve.

A note on solutions of the matrix equation AXB=C

This paper deals with necessary and sufficient condition for consistency of the matrix equation $AXB = C$. We will be concerned with the minimal number of free parameters in Penroses formula $X = A^(1)CB^(1) + Y - A^(1)AYBB^(1)$ for obtaining the general solution of the matrix equation and we will establish the relation between the minimal number of free parameters and the ranks of the matrices A and B. The solution is described in the terms of Rohdes general form of the {1}-inverse of the matrices A and B. We will also use Kronecker product to transform the matrix equation $AXB = C$ into the linear system $(B^T otimes A)vecX = vec C$.

Non-reproductive and reproductive solutions of some matrix equations

In this paper we analyzed solutions of some complex matrix equations related to pseudoinverses using the concept of reproductivity. Especially for matrix equation AXB=C it is shown that Penroses general solution is actually the case of the reproductive solution.

The Compositions of the Differential Operations and Gateaux Directional Derivative

In this paper we determine the number of the meaningful compositions of higher order of the differential operations and Gateaux directional derivative.

Some combinatorial aspects of differential operation compositions on space $R^n$

In this paper we present a recurrent relation for counting meaningful compositions of the higher-order differential operations on the space $R^{n}$ (n=3,4,...) and extract the non-trivial compositions of order higher than two.

A note on higher-order differential operations

In this paper we consider successive iterations of the first-order differential operations in space ${bf R}^3.$

A Note About the {Ki(z)} Functions

In the article [Petojevic 2006], A. Petojevi c verified useful properties of the $K_{i}(z)$ functions which generalize Kurepas [Kurepa 1971] left factorial function. In this note, we present simplified proofs of two of these results and we answer the open question stated in [Petojevic 2006]. Finally, we discuss the differential transcendency of the $K_{i}(z)$ functions.