• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.587-592
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• 1996

In 1950, Nash [5] first proved the existence of equilibrium for games where the player's preferences are representable by continuous quasiconcave utilities and the strategy sets are simplexes. Next Debreu [3] proved the existence of equilibrium for abstract economies. Recently, the existence of Nash equilibrium can be further generalized in more general settings by several athors, e.g. Shafer-Sonnenschein [6], Borglin-Keiding [2], Yannelis-Prabhaker [8]. In the above results, the convexity assumption is very essential and the main proving tools are the continuous selection technique and the existence of maximal elements. Still there have been a number of generalizations and applications of equilibrium existence theorem in generalized games.

• Journal of Korean Neurosurgical Society
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• v.41 no.6
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• pp.411-413
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• 2007

We report on a diabetic 52-year-old man who complained ocular floating sensation, headache and dizziness, in whom a left parieto-occipital dural ateriovenous fistulas [DAVFs], fed by bilateral superficial temporal arteries and occipital artery, drained into the cortical vein of the left parieto-occipital convexity. Because the patient's chief complaint was ocular symptom for diabetic retinopathy, we initially didn't consider an DAVFs until brain magnetic resonance imaging [MRI] was done. Diffusion-weighted brain MRI revealed acute cerebral infarction and microhemorrhage in the lesion. Transarterial embolization with mixture of glue and lipiodol obliterated the DAVFs completely. Although the DAVFs fed by multi-arteries, the fistulous portion has been disappeared after embolization via an only left occipital artery Endovascular embolization of the fistula led to symptomatic improvement, except ocular discomfort.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.589-599
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• 2023

The object of this study is to introduce a new subclass of univalent analytic functions on the open unit disk. This subclass is created by utilizing univalent analytic functions with negative coefficients. We first explore the specific properties that functions in this subclass must possess before examining their coefficient characterization. By applying this approach, we observe several fascinating features, including coefficient approximations, growth and distortion theorems, extreme points and a demonstration of the radius of starlikeness and convexity for functions belonging to this subclass.

• The korean journal of orthodontics
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• v.27 no.2
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• pp.197-208
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• 1997

Class III malocclusion patients can be approached with many different types of treatment methods, and thus, each patient's problems must be accurately evaluated to allow selection of the best possible treatment method. Cephalometric analysis is an essential part of diagnosis and treatment planning of orthodontic patients, and it would certainly be helpful if reliable cephalometric guidelines could be set. The author divided 482 Class III malocclusion patients(253 males and 229 females) into fourgroups according to different types of treatment methods they have received to correct imbalance between upper and lower jaws: 1) orthopedic appliance (face mask & RPE), 2) camouflage treatment with fixed appliance, 3) surgical-orthodontic treatment, 4) cross-bite correction with removable plates/ functional appliance. Cephalometric values at the time of first clinical examination were compare among the four groups. Cephalometric analysis indicates the following results: 1)the amounts of antero-posterior and vertical skeletal discrepancies and dental compensation were greatest in surgery group 2) SNB, Wits, distance from Nasion Perpendicular Plane to point a facial angle, facial convexity, and APDI were greater in orthopedic appliance group than fixed appliance(camouflage) group, but there was no statistical difference 3) removable plates/ functional appliance group showed least amounts of skeletal discrepancies and dental compensation with statistical significance.

• The korean journal of orthodontics
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• v.27 no.2
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• pp.181-196
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• 1997

The purpose of this study was to describe growth changes of soft tissue profile in koreans with normal occlusion and to get differences between male and female. The biennial serial cephalometric radiographs of 26 samples (15 males, 11 females) with normal occlusion from 8.5 years to 18.5 years of age were used in this study. The following results were obtained : 1. Both sexes had lower facial parts more protruded at 18.5 years of age than 8.5 years of age : in total facial convexity angle, male showed a decrease(P<0.01) and female showed no significant difference(P>0.05). 2. In the growth changes of soft tissue thickness, male outgrew female in the areas of nose and upper and lower lips, and female outgrew male in the pogonion area 3. In the growth changes of upper facial height and upper part of lower facial height, male's was higher than female's growth (P<0.05). 4. The ratio of the upper facial height over the lower facial height showed a decrease at 18.5 years of age than 8.5 years of age(P<0.01). The ratio of upper vs lower part of lower facial height and that of upper lip height vs lower lip height showed no significant difference(P>0.05). 5. Male showed a sustained change into older age compared with female in soft tissue profiles.

• The korean journal of orthodontics
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• v.40 no.3
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• pp.134-144
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• 2010

Objective: The aim of this study was to evaluate the volumes and areas of the upper airways in children with Class II malocclusion, using three dimensional cone-beam computed tomography (CBCT) and to compare the volumetric and cross-sectional measurements and cephalometric variables to investigate possible relationships between the upper airway and facial morphology. Methods: CBCT scans were obtained from 37 subjects (17 boys and 20 girls; average age, 11.02 years). The upper airway volumes and areas were measured, and compared with cephalometric variables. Results: The area of the PNS-posterior plane ($S_{PP}$) was significantly smaller in the Class II malocclusion group (p < 0.05). Also, the volumetric and cross-sectional measurements were lower in Class II than in Class I malocclusion groups, although the differences were not significant between the two groups (p > 0.05). The Class II malocclusion group showed significantly smaller values of PFH, mandibular body length, pog to N perp and showed larger values of FMA, ANB, and facial convexity than the Class I malocclusion group. The volume of the upper airway in front of PNS point (WN) showed negative correlation with ANB (p < 0.05). Conclusions: The Class II malocclusion group had a narrower upper airway associated with a decreased posterior facial height and a divergent growth pattern than the Class I malocclusion group.

• Bulletin of the Korean Mathematical Society
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• v.21 no.1
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• pp.1-5
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• 1984

The notion of linear 2-normed spaces was introduced by S. Gahler ([8,9,10,11]), and these space have been extensively studied by C. Diminnie, R. Ehret, S. Gahler, K. Iseki, A. White, Jr, and others. For nonzero vectors x,y in X, let V(x,y) denote the subspace of X generated by x and y. A linear 2-normed space (X,v) is said to be strictly convex ([3]) if v(x+y,z)=v(x,z)+v(y+z) and z not.mem.V(x,y) imply that y=ax for some a>0. Some characterizations of strict convexity for linear 2-normed spaces are given in [1,3,4,5,12]. Also, a linear 2-normed space (X,v) is said to be strictly 2-convex ([6]) if v(x,y)=v(x,z)=v(y,z)=1/3v(x+z, y+z)=1 implies that z=x+y. These space have been studied in [2,4,6,13]. It is easy to see that every strictly convex linear 2-normed space is always strictly 2-convex but the converse is not necessarily true. Throughout this paper, let (X,v) denote a linear 2-normed space.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.513-533
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• 2004

We present the pricing and hedging method for options with general payoffs in the presence of transaction costs. The convexity of the payoff function-gamma of the options- is an important issue under transaction costs. When the payoff function is convex, Leland-style pricing and hedging method still works. However, if the payoff function is of general form, additional assumptions on the size of transaction costs or of the hedging interval are needed. We do not assume that the payoff is convex as in Leland 〔11〕 and the value of the Leland number is less (bigger) than 1 as in Hoggard et al. 〔10〕, Avellaneda and Paras 〔1〕. We focus on generally recognized asymmetry between the option sellers and buyers. We decompose an option with general payoff into difference of two options each of which has a convex payoff. This method is consistent with a scheme of separating out the seller's and buyer's position of an option. In this paper, we first present a simple linear valuation method of general payoff options, and also propose in the last section more efficient hedging scheme which costs less to hedge options.

• The korean journal of orthodontics
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• v.14 no.1
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• pp.103-113
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• 1984

This work was undertaken to evaluate the integumental response in lower face to hard tissue changes, and to grope the prediction equation for expected integumental profile changes. Cephalometric headplates of 25 persons consisted of 8 Angle's class 1 maxillary protrusive and 17 Angle's class II division 1 patients whose mean age was 15.2 years were traced, diagramatized, and statistically analyzed. The results were as follows; 1. Upper incisor and lips were retracted and convexity of integumental profile decreased concurrently with decrease of hard tissue procumbency, however soft tissue point A', B', and Pog' did not undergo significant changes after orthodontic treatment. 2. Remarkable increment of upper lip thickness and upper lip height was shown and this was related to upper incisor retraction. The ratio between the amount of upper incisor retraction and the increment o f upper lip thickness was approximately 1.16:1. 3. Moderate correlation of upper lip retraction to upper incisor retraction, and of lower lip retraction to lower incisor movement were arranged, and yet comparatively wide variability from subject to subject was shown. 4. It was possible to predict statistically for horizontal alteration of lip position and change of upper lip angulation ground in orthodontic treatment.

• The korean journal of orthodontics
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• v.14 no.1
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• pp.161-172
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• 1984

This study was undertaken to evaluate the cephalometric changes of the soft tissue and skeletal profile subsequent 10 the rapid palatal expansion in 25 Angle's Class III cases, ranging in age from six to fifteen years, with cross-bite of the anterior teeth, underdevelopment of maxilla and facial disharmony Following results were obtained: 1. ANS moved downward, Point A presented forward & downward movement increasing SNA and Point B presented backward & downward movement decreasing SNB. 2. Mandible was rotated to backward & forward and maxilla moved forward & downward with the bite opening and improvement of anterior teeth cross-bite. 3. Soft tissue on mandible was rotated to backward & forward following hard tissue changes causing the decrease of facial convexity angle and backward & downward rotation of Point B', Pog'. 4. Response of the upper lip was more significant in downward than forward direction, and correlated with the upper central incisor and mandible rotation. 5. Response of the lower lip was more significant in downward than backward direction, and correlated with the mandible rotation. 6. There was a rather high degree of correlation between skeletal profile and soft-tissue profile, 1 : LS, $\bar{1}$:Pog', Pog:LS, Pog:LI, Pog:Pog' in horizontal measurements and $\bar{1}$:Pog', Pog:LI, Pog:Pog' in vertical measurements.