We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thin-film micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of th...

In design and fabricate drive shafts with high value of fundamental natural frequency that represented high value of critical speed; using composite materials instead of typical metallic materials could provide longer length shafts with lighter weight. In this paper, multi-objective optimization (MOP) of a composite drive shaft is performed considering three conflicting objectives: fundamental ...

The main aim of this paper is to introduce three classes $H^0_{p,q}$, $H^1_{p,q}$ and $TH^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. First, we discuss the starlikeness and convexity of mappings in $H^0_{p,q}$ and $H^1_{p,q}$. Then establish the covering theorem for mappings in $H^1_{p,q}$. Finally, we determine the extreme points of the class $TH^*_{p}$.

Using the three critical points theorem by B. Ricceri [23], we obtain a multiplicity result for a class of nonlocal problems in OrliczSobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.

A polynomial is determined by its roots and its leading coefficient. If you set the roots in motion, the critical points will move too. Using only tools from the undergraduate curriculum, we find an inverse square law that determines the velocities of the critical points in terms of the positions and velocities of the roots. As corollaries we get the Polynomial Root Dragging Theorem and the Pol...

Let $P$ be a complex polynomial of the form $P(z)=zdisplaystyleprod_{k=1}^{n-1}(z-z_{k})$,where $|z_k|ge 1,1le kle n-1$ then $ P^prime(z)ne 0$. If $|z|

1. Generalized Sphere Theorem As a first application of the critical point theory of distance funciton, we shall prove Theorem 1.1 (Grove-Shiohama). Let (M, g) be a complete simply connected Riemann-ian manifold with K > 1 4 and diam(M, g) ≥ π, then M is homeomorphic to S m. So Grove-Shiohama's theorem implies the sphere theorem. Proof. Let p, q ∈ M so that dist(p, q) = diam(M, g). In what foll...

we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [To...