The problem we are dealing with is the following: find two sequences an and bn such that the average of the first bn triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the an-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the seque...

we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

Abstract A batch of nickel-cobalt alloy coatings was pulse-electroplated on gun steel (PCrNi3MoVA) surface, in which weight fractions Co element are 39.9 %, 55.5 67.5 and 79.8 respectively. The formations phase crystal structure were investigated by X-ray diffraction analysis. layers’ surface morphology chemical composition analyzed scanning electron microscopy coupled with energy dispersive sp...

We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or non-deterministic, has the same power to the square tile assembly system in computation, which is Turing universal. By providing counter-examples, we show that the triangu...