Argument estimates of certain multivalent functions involving a linear operator

The purpose of this paper is to derive some argument properties of certain multivalent functions in the open unit disk involving a linear operator. We also investigate their integral preserving property in a sector

Vortex lines in the three-dimensional XY model with random phase shifts

The stability of the ordered phase of the three-dimensional XY-model with random phase shifts is studied by considering the roughening of a single stretched vortex line due to the disorder. It is shown that the vortex line may be described by a directed polymer Hamiltonian with an effective random potential that is long range correlated. A Flory argument estimates the roughness exponent to $\zeta=3/4$ and the energy fluctuation exponent to $\omega=1/2$, thus fulfilling the scaling relation $\omega=2\zeta-1$. The Schwartz-Edwards method as well as a numerical integration of the corresponding Burger's equation confirm this result. Since $\zeta<1$ the ordered phase of the original XY-model is stable.Comment: 8 pages RevTeX, 3 eps-figures include

Argument estimates of certain classes of P-Valent meromorphic functions involving certain operator

In this paper, by making use of subordination , we investigate some inclusion relations and argument properties of certain classes of p-valent meromorphic functions involving&nbsp;certain operator

An example of limit of Lempert Functions

The Lempert function for several poles $a_0, ..., a_N$ in a domain $\Omega$ of $\mathbb C^n$ is defined at the point $z \in \Omega$ as the infimum of $\sum^N_{j=0} \log|\zeta_j|$ over all the choices of points $\zeta_j$ in the unit disk so that one can find a holomorphic mapping from the disk to the domain $\Omega$ sending 0 to $z$. This is always larger than the pluricomplex Green function for the same set of poles, and in general different. Here we look at the asymptotic behavior of the Lempert function for three poles in the bidisk (the origin and one on each axis) as they all tend to the origin. The limit of the Lempert functions (if it exists) exhibits the following behavior: along all complex lines going through the origin, it decreases like $(3/2) \log |z|$, except along three exceptional directions, where it decreases like $2 \log |z|$. The (possible) limit of the corresponding Green functions is not known, and this gives an upper bound for it.Comment: 16 pages; references added to related work of the autho

Hydrodynamic friction of fakir-like super-hydrophobic surfaces

A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surface slip length for a planar shear flow on such a fakir surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical results are in excellent quantitative agreement with previous numerical computations

Rejecting capital-skill complementarity at all costs

Any serious empirical study of factor substitutability has to allow the data to display complementarity as well as substitutability. The standard approach reflecting this idea is a translog specification – this is also the approach used by numerous studies analyzing the relative capital-skill complementarity hypothesis formulated by GRILICHES (1969). According to this hypothesis, the degree of substitutability between skilled labor and capital is lower than that for unskilled labor and capital. Yet, the results of empirical studies investigating this hypothesis are controversial. This paper offers a straightforward explanation: Using a translog approach reduces the issue of factor substitutability or complementarity to a question of cost shares. Our review of translog studies mentioned in HAMERMESH?s (1993) summary on the demand for heterogeneous labor demonstrates that this argument is empirically relevant – all these studies can be reconciled with each other on the basis of the cost-share argument. --Substitutability,Translog Cost Function

The Casimir operator of a metric connection with skew-symmetric torsion

For any triple $(M^n, g, \nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $\Omega$ acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly K\"ahler, cocalibrated $\mathrm{G}_2$-structures) admit unique connections with skew-symmetric torsion. We study the corresponding Casimir operator and compare its kernel with the space of $\nabla$-parallel spinors.Comment: Latex2e, 15 page

L∞(L∞)L^\infty(L^\infty)-boundedness of DG(pp)-solutions for nonlinear conservation laws with boundary conditions

We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estimate is given for the case of several space dimensions and for conservation laws with initial and boundary conditions