In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from frame. Also, in present study consider weak biharmonic and harmonic 1-type curves by using mean curvature vector field curve. We also whose is kernel Laplacian. give theorems them Euclidean 3-space. Moreover, classifications these type curves.

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

In this study, we investigate the intial value problem (IVP) for a time-fractional fourth-order equation with nonlinear source terms. More specifically, consider biharmonic exponential nonlinearity and Cahn–Hilliard equation. By using Fourier transform concept, generalized formula mild solution as well smoothing effects of resolvent operators are proved. For IVP associated first one, by Orlicz ...

Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closedform expression, some providing other desirable properties at the expen...

Laguerreminimal (L-minimal) surfaces are theminimizers of the energy ∫ (H2 −K)/KdA. They are a Laguerre geometric counterpart of Willmore surfaces, the minimizers of ∫ (H2 − K)dA, which are known to be an entity of Möbius sphere geometry. The present paper provides a new and simple approach to L-minimal surfaces by showing that they appear as graphs of biharmonic functions in the isotropic mode...

We report on a comparative study of grating based plasmonic band gap cavities. Numerically, we calculate the quality factors of the cavities based on three types of grating surfaces; uniform, biharmonic and Moiré surfaces. We show that for biharmonic band gap cavities, the radiation loss can be suppressed by removing the additional grating component in the cavity region. Due to the gradual chan...

Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...

B.Y. Chen introduced biharmonic submanifolds in Euclidean spaces and raised the conjecture ”Any biharmonic submanifold is minimal”. In this article, we show some affirmative partial answers of generalized Chen’s conjecture. Especially, we show that the triharmonic hypersurfaces with constant mean curvature are minimal. M.S.C. 2010: 58E20, 53C43.