The aim of this paper is to present a general algorithm for solving the nonlinear operator equations in a Hilbert space, namely the k -order Taylor expansion algorithm, k1 .

After using of some important limits in Advanced Mathematics,we may choose one of the methods in computation,such as method of improvisation and method of replacement with equivalent infinitesimal and method of Taylor expansion,to g.

We use the Taylor expansion to analyze the signature space,which is obtained from calculating the input-output cross-correlation of the DUT(Device Under Testing),to get the delay time of signature-pair.

We can popularize real analysis to complex analysis by the Taylor expansion of analytic function and Laurent expansion in function of the complex variable.

Taylor expansion gives proof to the uniqueness theorem and the maximum modules principle, which is simple and clear at a glance, compared with the traditional proo

This paper is devoted to the study of the Taylor expansions of smooth functions on groups of Heisenberg type G , the Taylor expansions of smooth functions onG× R+ , and then existence and uniqueness for viscosity solutions of a kind of partialdifferential equations on groups of Heisenberg type.

By making use of the integral property of geometrically convex functions and geometrical convexity of the two exponential functions,this paper obtains two new estimation formulas of the remainder term in Taylor expansion of ex(x>0) and e-x(x>0),and two new inequalities.