We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian decomposition method (ADM). As an illustrative example we choose a recent application of the HPM to a dynamic system of anisotropic elasticity.

Joint uncertainty decoding has recently achieved promising results by using front-end uncertainty in the back-end in a mathematically consistent framework. One drawback of the method is that it relies on stereo-data or numerical algorithms, such as DPMC, which have high computational complexity and are difficult to deploy in real applications. We propose a Vector Taylor Series (VTS) approach to...

There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...

There are several important observations to make about this definition. (i) The definition says that, for each fixed n, ∑n m=0 amx m becomes a better and better approximation to f(x) as x gets smaller. As x → 0, ∑m=0 amx approaches f(x) faster than x tends to zero. (ii) The definition says nothing about what happens as n → ∞. There is no guarantee that for each fixed x, ∑n m=0 amx m tends to f(...

1 Overview We begin by recalling the Rolle’s Theorem.1 Using this result, we shall derive the Lagrange Form of the Taylor’s Remainder Theorem. Subsequently, we shall derive several mathematical inequalities as a corollary of this result. For example, 1. We shall use the Taylor’s Remainder Theorem to upper and lower bound exponential functions using polynomials. 2. We shall use the Taylor’ Remai...

The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected domains, when universal Taylor series exist, ...

In this paper, we apply the differential transform (DT) method for finding approximate solution of the system of linear and nonlinear Volterra integro-differential equations with variable coefficients, especially of higher order. We also obtain an error bound for the approximate solution. Since, in this method the coefficients of Taylor series expansion of solution is obtained by a recurrence r...