In this paper, automorphisms of the algebra of q-difference operators, as an associative algebra for arbitrary q and as a Lie algebra for q being not a root of unity, are determined.
We introduce the concept of <i>q</i>-calculus in quantum geometry. This involves the <i>q</i>-differential and <i>q</i>-integral operators. With these, we study the basic rules gove...We introduce the concept of <i>q</i>-calculus in quantum geometry. This involves the <i>q</i>-differential and <i>q</i>-integral operators. With these, we study the basic rules governing <i>q</i>-calculus as compared with the classical Newton-Leibnitz calculus, and obtain some important results. We introduce the reduced <i>q</i>-differential transform method (R<i>q</i>DTM) for solving partial <i>q</i>-differential equations. The solution is computed in the form of a convergent power series with easily computable coefficients. With the help of some test examples, we discover the effectiveness and performance of the proposed method and employing MathCAD 14 software for computation. It turns out that when <i>q</i> = 1, the solution coincides with that for the classical version of the given initial value problem. The results demonstrate that the R<i>q</i>DTM approach is quite efficient and convenient.展开更多
文摘In this paper, automorphisms of the algebra of q-difference operators, as an associative algebra for arbitrary q and as a Lie algebra for q being not a root of unity, are determined.
文摘We introduce the concept of <i>q</i>-calculus in quantum geometry. This involves the <i>q</i>-differential and <i>q</i>-integral operators. With these, we study the basic rules governing <i>q</i>-calculus as compared with the classical Newton-Leibnitz calculus, and obtain some important results. We introduce the reduced <i>q</i>-differential transform method (R<i>q</i>DTM) for solving partial <i>q</i>-differential equations. The solution is computed in the form of a convergent power series with easily computable coefficients. With the help of some test examples, we discover the effectiveness and performance of the proposed method and employing MathCAD 14 software for computation. It turns out that when <i>q</i> = 1, the solution coincides with that for the classical version of the given initial value problem. The results demonstrate that the R<i>q</i>DTM approach is quite efficient and convenient.
