The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

it is proved that by using bounds of eigenvalues of an interval matrix, someconditions for checking positive de niteness and stability of interval matricescan be presented. these conditions have been proved previously with variousmethods and now we provide some new proofs for them with a unity method.furthermore we introduce a new necessary and sucient condition for checkingstability of interv...

We promote the much maligned computational method. The computational method is a paradigm for proving mathematical results where the burden of doing the “grunt work” is given to our able research assistant, the computer. We assert that proofs using the computational method, also known as computer aided proofs, are here to stay. In fact, the use of a computer can make the analysis of complicated...