Integrable equations in (1 + 1) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in (2 + 1) dimensions have also the analogous hierarchies to those in (1 + 1) dimensions. Explicitly is discussed the Bogoyavlenskii-Schiff(BS) equation. For the BS hierarchy, there appears an ambiguity in...

Fermat's Last Theorem—which we shall abbreviate to FLT—is the (as yet unproved) assertion that the Diophantine equation x" + y" — z" has no solutions in positive integers if 11 ^ 3. It would suffice to deal with the case in which n is prime, and this is where the most significant work has been done. None the less it is not yet known even whether FLT is true for infinitely many prime exponents. ...

The line-structured light vision sensor has been used widely in industrial vision measuring fields due to its simple structure, small volume, light weight, low cost, convenient calibration, and high accuracy of measurement. To locate the reference sphere precisely with line-structured light vision sensor, a mathematical model based on the measuring principle of line-structured light vision sens...

in this paper, two api x70 steel pipes (with spiral seam weld) of 56 inch outside diameter and 0.780 inch wall thickness were girth welded first. next, hole drilling tests were conducted for strain measurement on the surfaces of the pipes. the values of residual stresses on the internal and external surfaces of the pipe were determined, from strain data using astm 837 standard. the experimental...

The electric power system is continuously growing in its size, complexity and required reliability. There an increased risk due to transient overvoltages which can deteriorate the insulation for different components. a need monitoring of voltages better monitor effects them on It be achieved using non-contact voltage measurement technique. study elucidates theory practical application measureme...