A distributed modeling approach has been developed to describe the dynamic behavior of ring resonators. The model includes the effect of large amplitudes around primary resonance frequencies, material and electrostatic nonlinearities. Through a combination of geometric and material nonlinearities, closed-form expression for third-order nonlinearity in mechanical stiffness of bulk-mode ring reso...

∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞-harmonic maps from and into a sphere, quadratic ∞-harmonic maps between Euclidean spaces. We describe all linear and quadratic ∞-harmonic maps between Nil and Euclidean spaces, b...

∞-Harmonic maps are a generalization of ∞-harmonic functions. They can be viewed as the limiting cases of p-harmonic maps as p goes to infinity. In this paper, we give complete classifications of linear and quadratic ∞harmonic maps from and into a sphere, quadratic ∞-harmonic maps between Euclidean spaces. We describe all linear and quadratic ∞-harmonic maps between Nil and Euclidean spaces, be...

Recently, novel application areas in digital geometry processing, such as simulation, dynamics, and medical surgery simulations, have necessitated the representation of not only the surface data but also the interior volume data of a given 3D object. In this paper, we present an efficient framework for the shape approximations of spherical solid objects based on trivariate B-splines. To do this...

We prove that planar homeomorphisms can be approximated by diffeomorphisms in the Sobolev space W 1,2 and in the Royden algebra. As an application, we show that every discrete and open planar mapping with a holomorphic Hopf differential is harmonic.

In the present paper we have studied new subclasses of p-valent harmonic functions in the unit disc and obtain the basic properties such as coefficient bound, distortion properties, extreme points and also we apply integral operator for the same.

This article presents Lp estimates for the gradient of p-harmonic maps. Since the system satisfies a natural growth condition, it is difficult to use standard elliptic estimates. We use spherical coordinates to convert the system into another system with angle functions. The new system can be estimate by the standard elliptic technique. 1. Results Let G ⊂ R (n ∈ {2, 3}) be a bounded and simply ...

Let p be a real number greater than one and let G be a connected graph of bounded degree. In this paper we introduce the p-harmonic boundary of G. We use this boundary to characterize the graphs G for which the constant functions are the only p-harmonic functions on G. It is shown that any continuous function on the p-harmonic boundary of G can be extended to a function that is p-harmonic on G....