in this paper, biharmonic slant helices are studied according to bishop frame in the heisenberg group heis3. we give necessary and sufficient conditions for slant helices to be biharmonic. the biharmonic slant helices arecharacterized in terms of bishop frame in the heisenberg group heis3. we give some characterizations for tangent bishop spherical images of b-slant helix. additionally, we illu...

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

A vast majority of hard coal deposits in Poland have a multi-seam structure, hence the presence mining remnants left from previous operations. The impact those (exploitation edges or residual pillars) can further intensify geomechanical phenomena occurring rock mass, leading to changes original state stress. This applies all layers within strata, including thick and coherent ones (referred as t...

The solution to the biharmonic equation in a simply connected region in the plane is computed in terms of the Goursat functions. The boundary conditions are conformally transplanted to the disk with a numerical conformal map. A linear system is obtained for the Taylor coeecients of the Goursat functions. The coeecient matrix of the linear system can be put in the form I + K where K is the discr...

We examine the convergence characteristics of a preconditioned Krylov subspace solver applied to the linear systems arising from low-order mixed finite element approximation of the biharmonic problem. The key feature of our approach is that the preconditioning can be realized using any “black-box” multigrid solver designed for the discrete Dirichlet Laplacian operator. This leads to preconditio...

We consider the problem of acceleration of the Alternative Directions Implicit (ADI) scheme for Dirichlet problem for biharmonic equation. The second Douglas scheme is used as the main vehicle and two full time steps are organised in a single iteration unit in which the explicit operators are arranged differently for the second step. Using an a priori estimate for the spectral radius of the ope...

The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconformingMorley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic...

In this article, we show the existence of at least three solutions to a Navier boundary problem involving the p(x)-biharmonic operator. The technical approach is mainly base on a three critical points theorem by Ricceri.