The Greek mathematician Diophantus of Alexandria noted that the set { 1 16 , 33 16 , 17 4 , 105 16 } has the following property: the product of its any two distinct elements increased by 1 is a square of a rational number (see [3]). Fermat first found a set of four positive integers with the above property, and it was {1, 3, 8, 120}. In 1969, Davenport and Baker [2] showed that if positive inte...

The problem of colouring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs. We show that the choosability χ (G2) of the square of a subcubic graph G of maximum average degree d is at most four if d < 24/11 and G does not contain a 5-cycle, χ (G2) is at most five if d < 7/3 an...

The problem of colouring the square of a graph naturally arises in connection with the distance labelings, which have been studied intensively. We consider this problem for sparse subcubic graphs and show that the choosability χ`(G 2) of the square of a subcubic graph G of maximum average degree d is at most four if d < 24/11 and G does not contain a 5-cycle, χ`(G 2) is at most five if d < 7/3 ...

We state precise results on the complexity of a classical bisectionexclusion method to locate zeros of univariate analytic functions contained in a square. The output of this algorithm is a list of squares containing all the zeros. It is also a robust method to locate clusters of zeros. We show that the global complexity depends on the following quantities: the size of the square, the desired p...

Composite materials are used in aeronautical, automobile, healthcare and marine industries due to their high stiffness, higher strength-to-weight ratio long fatigue life. Thin plate plays vital role manufacturing of engineering structures. Components made from composite often subjected damage while working. Buckling can cause loss stability component which subsequently leads failure the entire ...

Absorption spectra of polycrystalline L-, D-, and DL-tartaric acid have been measured by terahertz time domain spectroscopy (THz-TDS). Different absorption bands are observed for DL-tartaric acid and its enantiomers (L- and D-tartaric acid). This result shows that the THz-TDS can be used for distinguishing between DL-tartaric acid and enantiomers (L- and D-tartaric acid). Moreover, partial leas...