• Bulletin of the Korean Mathematical Society
• /
• v.44 no.3
• /
• pp.475-482
• /
• 2007

In this paper, we study composition operators $C_{\varph}f=f^{\circ}{\varph}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1337-1346
• /
• 2017

We define Bloch-type spaces of ${\mathcal{C}}^1({\mathbb{H}})$ on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator ${\mathcal{C}}_{\phi}$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.

• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1169-1181
• /
• 2006

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.327-329
• /
• 1994

The Dirichlet problem (DP) on the upper half plane {z = x ＋ iy : y > 0} is to find a real-valued harmonic function u(x, y) satisfying u(x, 0) = g(x) almost everywhere for some reasonably nice function g defined on the real line, which is called the data on the boundary for (DP).(omitted)

• Communications of the Korean Mathematical Society
• /
• v.9 no.2
• /
• pp.337-353
• /
• 1994

Let H be a Schrodinger operator in $L^2$(R) H =(equation omitted) ＋ V(x), with supp V ⊂ [-R, R]. A number $z_{0}$ / in the lower half-plane is called a resonance for H if for all $\phi$ with compact support 〈$\phi$, $(H - z)^{-l}$ $\phi$〉 has an analytic continuation from the upper half-plane to a part of the lower half-plane with a pole at z = $z_{0}$ . Thus a resonance is a sort of generalization of an eigenvalue. For Im k > 0, ($H - k^2$)$^{-1}$ is an integral operator with kernel, given by Green's function(omitted)

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.771-776
• /
• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

• 한국정보디스플레이학회:학술대회논문집
• /
• 2006.08a
• /
• pp.822-825
• /
• 2006

We propose a transflective In-Plane Switching mode in which patterned retarder is placed only on the reflective area of the upper substrate side. By selecting optic axes of Half Wavelength Plate and Liquid Crystal as 24 and 90 degree with respect to polarizer, condition of low reflectance for visible wavelength range at black state is found.

• The Journal of Korean Academy of Prosthodontics
• /
• v.43 no.1
• /
• pp.41-51
• /
• 2005

Statement of problem. Anatomic landmarks have been used in the orientation of occlusal plane and the determination of vertical dimension for edentulous patients. Such as labial vestibules of anterior region and hamular notches, retromolar pads of posterior region are very useful anatomic landmarks for fabrication of occlusion rim because they are to be identified on master casts. Therefore, if average distances between landmarks of maxillae and mandible in dentate subjects are measured and applied, not only occlusal plane but also vertical dimension can be established initially. Purpose. The purpose of this study is to measure vertical distances between anatomic landmarks and to present a guide to the orientation of occlusal plane and the determination of vertical dimension of edentulous patients. Material and method. Upper and lower border-molded casts were made in 93 Korean dentulous subjects, mean age 25 years. Incisal edges of central incisors, bottoms of labial vestibules, hamular notches and the half level of retromolar pads were marked on casts. Measurements of vertical distances from incisal edge of central incisor to the bottom of labial vestibule, between upper and lower bottoms of labial vestibules, from hamular notch to retromolar pad and from hamular notch to the occlusal plane established by the incisal edge of maxillary central incisor and mesiopalatal cusps of both maxillary first molars were made on each cast. Results and conclusion. 1. The mean distance from the incisal edge of central incisor to the bottom of labial vestibule was 20.8mm(SD 1.7) on upper casts and 17.3mm(SD 1.4) on lower casts. 2. The mean distance between both bottoms of labial vestibules of upper and lower casts was 35.0mm(SD 2.7). 3 The mean distance from hamular notch to the half level of retromolar pad was 5.0mm(SD 1.3). 4. The mean distance from hamular notch to occlusal plane was 7.9mm(SD 1.5). 5. Distances from incisal edge of central incisor to labial vestibule on lower casts(P<0.01) and from hamular notch to retromolar pad(P<0.0001) were greater in male than in female.

• The Journal of Korean Academy of Prosthodontics
• /
• v.41 no.5
• /
• pp.640-655
• /
• 2003

Statement of problem : The beauty has a little different meaning according to a time, culture, and nation. Purpose : This study was undertaken to determine the Korean perception of the altered upper anterior dental esthetics including the lack of symmetry, the midline deviation, the gingival exposure, the inclination of incisal plane, the type of incisal plane, and the type of gingival line. Material and Method : 670 subjects were participated in this survey. A questionnaire accompanied by 12 sets of computer-manipulated images using 3D MAX 4.2 software was used to record the ranking of the geometric preference related to the anterior esthetic discrepancies in three or four degrees of alteration. The statistical significance of the differences between the groups was determined by a one-way ANOVA and a t-test. Results : The results obtained were as follows: 1) The Korean perception of the anterior dental esthetics according to the subjects' occupation, sex, and age was most affected by occupation. 2) The masked image emphasizing the dentition and lips appeared stranger than the non-masked image at the same alteration. 3) The lack of symmetry, which was expressed as a unilateral discoloration of the tooth, showed incongruity in any teeth of the anterior dentition. The incongruity was more severe as the degree occurred closer to the midline. 4) The deviation of midline was showed more severe strangeness as the degree of deviation increased. However, more than half of the subjects did not perceive a deviation of 5mm. 5) During smiling, the exposure of the upper gingiva showed more severe incongruity as the degree of gingival exposure increased. 77% of the subjects perceived strangeness at the gingival exposure of 4.5mm. 6) The inclination of the incisal plane appeared stranger as the degree of inclination increased. 62% of subjects perceived strangeness at the $7.5^{\circ}$ inclination of the incisal plane. 7) The type of incisal plane showed increasing strangeness in the order of convex/downward, straight/horizontal, and concave/upward. 80% of subjects perceived strangeness at concave/upward. 8) The type of gingival line was showed increasing incongruity in the order of the same, a little above, and a little under the zenith of the lateral incisor to the line joining the zenith of the central incisor and the canine. However, less than half the subjects did not perceive strangeness at any alteration of the gingival line. Conclusion : The Korean perception of the upper anterior dental esthetics was different to the westerner's perception in the some respects.

• Communications of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.829-833
• /
• 2021

We investigate the Möbius transformation action of PSL(2, ℝ) on the set of mutually distinct ordered triple points of ℝ ∪ {∞}.