In this paper, parametric polynomial minimal surfaces of degree six with isothermal parameter are discussed. We firstly propose the sufficient and necessary condition of a harmonic polynomial parametric surface of degree six being a minimal surface. Then we obtain two kinds of new minimal surfaces from the condition. The new minimal surfaces have similar properties as Enneper’s minimal surface,...

which is a symplectic analog of the well-known de Rham–Hodge ∗operator on oriented Riemannian manifolds: one should use the symplectic form instead of the Riemannian metric. Going further, one can define operator δ = ± ∗ d∗, δ = 0. The form α is called symplectically harmonic if dα = 0 = δα. However, unlike de Rham–Hodge case, there exist simplectically harmonic forms which are exact. Because o...

Following the analytic approach to thermodynamics developed by Stückelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction ter...

Recently there has been much interest in the Liouville type theorems for harmonic maps. For a detailed survey and progress in this direction, see the works by Hildebrandt [4], Eells and Lemaire [2]. Here we would like to mention that for all known results, the conditions on the harmonic maps can be divided into two kinds. The first of these conditions concerns the finiteness of the energy of th...

and Applied Analysis 3

Vibrational dynamics of folded proteins is studied using a Gaussian model in which the protein is viewed as a network, residues representing the junctions, and the connectivity being established by a single parameter harmonic potential. Application to seven proteins showed that the local packing density plays a major role in determining the vibrational spectrum at time scales of picoseconds. At...

A new one-dimensional model, the multicomponent Calogero model of B N-type confined in the harmonic potential, is introduced. The Lax pair of this model is determined, and then a set of functionally independent conserved operators are constructed. Moreover, the energy spectrums of the above model are obtained by three different methods.

‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.