Unit-vector fields n on a convex polyhedron P subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to minimisers and local minimisers of the Dirichlet energy, and may be regarded as S-valued harmonic maps on P . We consider unit-vector fields which are continuous away fro...

The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into a series of simple problems that are easy to be solved. This note gives an elementary introduction to the basic solution procedure of the homotopy perturbation method. Particular attention is paid to constructing a suitable homotopy equation. Thi...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modification of homotopy analysis method (HAM), in order to obtain dual solutions analytically with hi...

This thesis contains three papers. Paper A and Paper B deal with homotopy theory and Paper C deals with Topological Data Analysis. All three papers are written from a categorical point of view. In Paper A we construct categories of short hammocks and show that their weak homotopy type is that of mapping spaces. While doing this we tackle the problem of applying the nerve to large categories wit...

In this letter, the approximate solution of nonlinear heat diffusion and heat transfer and also the energy balance for a differential fin element are developed via Homotopy Analysis Method HAM. This method is a strong and easy–to–use analytic tool for investigating nonlinear problems, which does not need small parameters. Homotopy analysis method contains the auxiliary parameter h , which provi...

A homotopy action of a group G on a space X is a homomorphism from G to the group HAUT(X) of homotopy classes of homotopy equivalences of X. George Cooke developed an 'obstruction theory to determine if a homotopy action is equivalent up to homotopy to a topological action. The question studied in this paper is: Given a diagram of spaces with homotopy actions of G and maps between them that are...

in recent years, numerous approaches have been applied for finding the solutions of functional equations. one of them is the optimal homotopy asymptotic method. in current paper, this method has been applied for obtaining the approximate solution of fisher equation. the reliability of the method will be shown by solving some examples of various kinds and comparing the obtained outcomes with the ...

In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotop...