相关论文: Triakis Solids and Harmonic Functions
We introduce notions of bi-unitary, bi*-unitary and bi**-unitary harmonic numbers, along with their preliminary study.
In this article, Bohr type inequalities for some complex valued harmonic functions defined on the unit disk are given. All the results are sharp.
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial…
We consider several aspects of high-order harmonic generation in solids: the effects of elastic and inelastic scattering; varying pulse characteristics; and inclusion of material-specific parameters through a realistic band structure. We…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
It was recently established that a function which is harmonic on an infinite cylinder and vanishes on the boundary necessarily extends to an entire harmonic function. This paper considers harmonic functions on an annular cylinder which…
Let E be a Frobenius category, let_E_ denote its stable category. The shift functor on_E_ induces a first shift functor on the category of acyclic complexes with entries in_E_ by pointwise application. Shifting a complex by 3 positions…
High-order harmonic generation (HHG) from atoms is a coherent light source that opens up attosecond physics, but it is the application of HHG to solids that brings much of excitement for the last decade. Here we report a completely new kind…
We prove some isoperimetric type inequalities for real harmonic functions in the unit disk belonging to the Hardy space $h^p$, $p>1$ and for complex harmonic functions in $h^4$. The results extend some recent results on the area. Further we…
In general, the product of harmonic forms is not harmonic. We study the top exterior power of harmonic two-forms on compact Kaehler manifolds. Often, it is not harmonic. This phenomenon is related to the geometry of the manifold and to the…
This is an example on the cohomology of threefolds.
In this paper, we first find an estimate for the range of polyharmonic mappings in the class $HC_{p}^{0}$. Then, we obtain two characterizations in terms of the convolution for polyharmonic mappings to be starlike of order $\alpha$, and…
We use functions of a bicomplex variable to unify the existing constructions of harmonic morphisms from a 3-dimensional Euclidean or pseudo-Euclidean space to a Riemannian or Lorentzian surface. This is done by using the notion of…
We present new sharp assertions concerning multipliers in various spaces of harmonic functions in the unit ball of $R^n$
In this note we give a p-adic proof of Hodge symmetry for smooth, projective threefolds over complex numbers.
The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles…
We study quartic double solids admitting icosahedral symmetry.
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
We construct new explicit proper biharmonic functions on the $3$-dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $H^2\times\rn$ and $S^2\times\rn$.
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.