The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of t...

A two-dimensional analytical solution is presented for stresses and displacements in an elastic curved beam forming incomplete ring frictionless unbonded contact with a rigid pin loaded by point force the presence of clearance. The circular modeled as thick ring, constrained at both ends plane stress state. displacement fields within are derived from biharmonic Airy function, according to Miche...

This paper addresses the direct and inverse source problems for stochastic acoustic, biharmonic, electromagnetic, elastic wave equations in a unified framework. The driven is assumed to be centered generalized microlocally isotropic Gaussian random field, whose covariance relation operators are classical pseudodifferential operators. Given source, shown well-posed sense of distributions regular...

Abstract The electromagnetic theory is considered in the framework of generally covariant approach, that applied to analysis electromagnetism noninertial coordinate and frame systems. special-relativistic formulation Maxwell’s electrodynamics arises flat Minkowski spacetime when general transformations are restricted a class preserving line element. particular attention paid rotating reference ...

Surface-enhanced Raman Scattering (SERS) of rhodamine 6G (R6G) adsorbed on biharmonic metallic grating structures was studied. Biharmonic metallic gratings include two different grating components, one acting as a coupler to excite surface plasmon polaritons (SPP), and the other forming a plasmonic band gap for the propagating SPPs. In the vicinity of the band edges, localized surface plasmons ...

This paper deals with the study of the transcendental equations: sin(j + v)/(s + v) = ±sin(i v)/(s v), where v = (s2 y2)'/2. These equations are obtained in the study of some boundary value problems for a modified biharmonic equation using the PapkovichFadle series. Some numerical solutions obtained with an iterative procedure are given. Introduction. It is well known that the governing equatio...

this paper is concerned with the study of the existence of positive solutions for a navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. the existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. our resul...

in this paper, we study b-focal curves of biharmonic b -general helices according to bishop frame in the heisenberg group heis   finally, we characterize the b-focal curves of biharmonic b- general helices in terms of bishop frame in the heisenberg group heis