The article surveys a number of potential theory results in the discrete setting of trees and in an application to complex analysis. On trees for which the associated random walk is recurrent, we discuss Riesz decomposition, flux, a type of potential called H-potential, and present a new result dealing with the boundary behaviour of H-potentials on a specific recurrent homogeneous tree. On gene...

This present study investigated the temporal effects of type 1 diabetes mellitus (T1DM) on adolescent skeletal muscle growth, morphology and contractile properties using a 90% partial pancreatecomy (Px) model of the disease. Four week-old male Sprague-Dawley rats were randomly assigned to Px (n = 25) or Sham (n = 24) surgery groups and euthanized at 4 or 8 weeks following an in situ assessment ...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

We investigate the boundary value problem for biharmonic operators on Heisenberg group. The inherent features of Hn make it an appropriate environment studying symmetry rules and interaction analysis geometry with manifolds. goal this paper is to prove that a weak solution operator group exists. Our key tools are version Mountain Pass Theorem classical variational theory. This will be interest ...

This is a supplement to our previous research note [3]. In [3], we gave a characterization of biharmonic curves in Minkowski 3-space. More precisely, we pointed out that every biharmonic curves with nonnull principal normal in Minkowski 3-space is a helix, whose curvature κ and torsion τ satisfy κ2 = τ2. In the classification of biharmonic curves in Minkowski 3-space due to Chen and Ishikawa [1...

Regular convergence, together with other types of have been studied since the 1970s for discrete approximations linear operators. In this paper, we consider eigenvalue approximation a compact operator $T$ that can be written as an problem holomorphic Fredholm function $F(\eta) = T-\frac{1}{\eta} I$. Focusing on finite element methods (conforming, discontinuous Galerkin, non-conforming, etc.), s...

Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like: θ θ 2 sin sin b a + . The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes unde...

Human T cell leukemia virus type I (HTLV-I) is a persistent virus that causes adult T cell leukemia and tropical spastic paraparesis/HTLV-I-associated myelopathy. Studies on rabbits have shown that viral proteins encoded by the open reading frames pX-I and pX-II are required for the establishment of the persistent infection. To examine the in vivo production of these proteins in humans, we have...

In this work, we compare different mesh moving techniques for monolithically-coupled fluid-structure interactions in arbitrary Lagrangian–Eulerian coordinates. The mesh movement is realized by solving an additional partial differential equation of harmonic, linear-elastic, or biharmonic type. We examine an implementation of time discretization that is designed with finite differences. Spatial d...

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter family of non-minimal conformal biharmonic immersions of cylinder into R and ...