• Bulletin of the Korean Mathematical Society
• /
• v.40 no.4
• /
• pp.553-564
• /
• 2003

We give sufficient coefficient conditions for starlikeness of a class of complex-valued multivalent meromorphic harmonic and orientation preserving functions in outside of the unit disc. These coefficient conditions are also shown to be necessary if the coefficients of the analytic part of the harmonic functions are positive and the coefficients of the co-analytic part of the harmonic functions are negative. We then determine the extreme points, distortion bounds, convolution and convex combination conditions for these functions.

• Tribology and Lubricants
• /
• v.4 no.2
• /
• pp.60-67
• /
• 1988

Conventional theory of gear mechanism can't be applied to analyze the harmonic drive due to specific movement of the teeth. This paper deals with an analysis of kinematics and geometry of the tooth engagement of a harmonic drive comprising circular spline, flexspline and wave generator. A theoretical new tooth profile of the flexspline in meshing internal rigid gear with involute profile is obtained. Characteristics of harmonic drive reducer are shown according to parameters such as deviation coefficient, deviation distance, addendum modification coefficient. As an example, the design of harmonic drive with 1:80 reduction ratio is presented.

• Korean Journal of Mathematics
• /
• v.15 no.2
• /
• pp.171-176
• /
• 2007

The purpose of this paper is to study harmonic univalent mappings defined in ${\Delta}=\{z:{\mid}z{\mid}>1\}$ that map ${\infty}$ to ${\infty}$. Some coefficient estimates are obtained in a normalized class of mappings.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.349-353
• /
• 2007

In this paper, we obtain some coefficient bounds of harmonic univalent mappings by using properties of the analytic univalent function on ${\Delta}$={z : |z| > 1}.

• Korean Journal of Mathematics
• /
• v.10 no.1
• /
• pp.1-3
• /
• 2002

In this paper, we obtain some coefficient bounds of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.749-756
• /
• 2009

In this paper, we obtain some coefficient bounds of harmonic univalent mappings on $\Delta=\{z\;:\;{\mid}z{\mid}\;>\;1\}$ which are starlike, convex, or convex in one direction.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.2
• /
• pp.163-167
• /
• 2004

In this paper, we obtain some coefficient estimates of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}$ = {z : |z| > 1}.

• Kyungpook Mathematical Journal
• /
• v.61 no.2
• /
• pp.269-278
• /
• 2021

In this paper, we investigate harmonic univalent functions convex in the direction 𝜃, for 𝜃 ∈ [0, 𝜋). We find bounds for |f_z(z)|, ${\mid}f_{\bar{z}}(z){\mid}$ and |f(z)|, as well as coefficient bounds on the series expansion of functions convex in a given direction.

• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.803-813
• /
• 2006

We define and investigate a subclass of complex valued harmonic convex functions that are univalent and sense preserving in the open unit disk. We obtain coefficient conditions, extreme points, distortion bounds, convolution conditions for the above family of harmonic functions.

• Journal of the Korean Mathematical Society
• /
• v.51 no.3
• /
• pp.567-592
• /
• 2014

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notions of harmonic Alexander operator and harmonic Libera operator are introduced and their properties are investigated.