We show that homotopy equivalent digital images have isomorphic fundamental groups, even when the homotopy equivalence does not preserve the basepoint. This assertion appeared in [3], but there was an error in the proof; here, we correct the error. We present and explore in detail a pair of digital images with cu-adjacencies that are homotopic but not pointed homotopic. For two digital loops f,...

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...

It is proved that the generalized T-homotopy equivalences preserve the underlying homotopy type of a flow.

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

We describe the use of homotopy (also called parameter embedding and continuation) methods for finding dc operating points and steady-state solutions of BJT and MOS transistor circuits. Past implementation of homotopy algorithms in proprietary industrial circuit simulators proved that they were viable options to resolving convergence difficulties for finding circuits’ dc operating points. In th...

The continuous scaling for fabrication technologies of electronic circuits demands the design of new and improved simulation techniques for integrated circuits. Therefore, this work shows a new double bounded polynomial homotopy based on a polynomial formulation with four solution lines separated by a fixed distance. The new homotopy scheme presents a bounding between the two internal solution ...

We prove that the homotopy theory of parametrized spaces embeds fully and faithfully in the homotopy theory of simplicial presheaves, and that its essential image consists of the locally homotopically constant objects. This gives a homotopy-theoretic version of the classical identification of covering spaces with locally constant sheaves. We also prove a new version of the classical result that...