• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.369-378
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• 2001

In this paper, we obtain the following results: Let f be a transcendental entire function with log M(r,f)=$O(log r)^\beta (e^{log r}^\alpha)\; (0\leq\alpha<1,\beta>1$). Then every component of N(f) is bounded. This result generalizes the result of Baker.

• East Asian mathematical journal
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• v.16 no.1
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• pp.9-16
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• 2000

The authors aim at providing some identities involving the hypergeometric function via some known or presumably new formulas for the incomplete Beta and their associated functions. Some properties of the Beta and Gamma functions are also considered.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.745-756
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• 2019

In this paper, we establish the log convexity and Turán type inequalities of extended (p, q)-beta functions. Likewise, we present the log-convexity, the monotonicity and Turán type inequalities for extended (p, q)-confluent hypergeometric function by utilizing the inequalities of extended (p, q)-beta functions.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• Korean Journal of Clinical Laboratory Science
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• v.45 no.4
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• pp.131-138
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• 2013

Insulin resistance and pancreatic beta cell dysfunction have been established as being related to the diabetes. Lately, what is emphasizing is that those have been shown as something related to the metabolic syndrome and cardiovascular disease. Homeostasis model assessment (HOMA), simple index is calculated on blood levels of fasting glucose and insulin. And HOMA has been widely validated and applied for insulin resistance and pancreatic beta cell dysfunction. We also assessed the factors relative to insulin resistance and ${\beta}$ cell function determined by HOMA. The data from the 2010 Korean National Health and Nutrition Examination Survey were used. Analysis was done for 3,465 nondiabetic subjects (male 1,357, female 2,108). At baseline, anthropometric measurements were done and fasting glucose, insulin, lipid (Total cholesterol, HDL cholesterol, LDL cholesterol and Triglycerides) profiles were measured. HOMA-insulin resistance (HOMA-IR) and beta cell function (HOMA ${\beta}$-cell) were calculated from fasting glucose and insulin levels. In male, the value of HOMA-IR and HOMA ${\beta}$-cell was the highest among 30's and decreased as the age increased. In female, the value of HOMA-IR increased with age, while HOMA ${\beta}$-cell decreased. High HOMA-IR and low HOMA ${\beta}$-cell were associated with the highest value of fasting glucose and systolic blood pressure. Low HOMA-IR and high HOMA ${\beta}$-cell showed the lowest concentration of fasting glucose and the highest concentration of HDL cholesterol. High HOMA-IR and high HOMA ${\beta}$-cell were connected with BMI, Total cholesterol, LDL cholesterol, and Triglycerides. There was a negative correlation between HOMA ${\beta}$-cell and age. The correlation coefficients of HOMA-IR and HOMA ${\beta}$-cell showed the highest value among weight, BMI and WC.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Journal of the Korean Society of Physical Medicine
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• v.14 no.2
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• pp.97-105
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• 2019

PURPOSE: This study examined the factors related to school-based activity performance in school-aged children with spastic cerebral palsy (CP). METHODS: The Gross Motor Function Systems (GMFCS), Manual Ability Classification System (MACS), Communication Function Classification System (CFCS) as functional classifications, and the physical activity performance of the School Function Assessment (SFA) were measured in 79 children with spastic CP to assess the student's performance of specific school-related functional activities. RESULTS: All the function classification systems were correlated significantly with the physical activity performance of the SFA ($r_s=-.47$ to -.80) (p<.05). The MACS (${\beta}=-.59$), GMFCS (${\beta}=-.23$), CFCS (${\beta}=-.21$), and age (${\beta}=-.15$) in order were predictors of the physical activity performance of the SFA (84.8%)(p<.05). CONCLUSION: These functional classification systems can be used to predict the school-based activity performance in school-aged children with CP. In addition, they can contribute to the selection of areas for intensive interventions to improve the school-based activity performance.

• Journal of Korean Academy of Fundamentals of Nursing
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• v.19 no.4
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• pp.511-518
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• 2012

Purpose: This study was done to identify the relationship of family function, self-efficacy and self-leadership, and to identify factors affecting self-leadership in adolescents. Method: Sampling was done using a convenience sampling method and 779 adolescents were recruited between June 4 and 15, 2012. Data were collected using self-report questionnaires which included general characteristics, family function, self-efficacy and self-leadership. Data were analyzed using descriptive, t-test, one way ANOVA, Scheffe test, Pearson correlation coefficient, and stepwise regression analysis with SPSS/WIN 19.0. Results: The major findings of this study were as follow; 1) There were significant relationships between self-leadership and family function (r=.36, p<.001), and self-efficacy (r=.51, p<.001). 2) Self-leadership was significantly associated with self-efficacy (${\beta}$=.42, p<.001), family function (${\beta}$=.20, p<.001), satisfactory relationships with teachers (${\beta}$=.12, p<.001), experience as a leader (${\beta}$=.10, p=.001), higher school records (${\beta}$=.17, p<.001), and medium school records (${\beta}$=.11, p=.001). These variables explained 40.4% of variance in adolescents' self-leadership. Conclusion: The results of this study indicate that there is a relationship between family function, self-efficacy and self-leadership in adolescents and that in developing intervention programs to promote self-leadership, in adolescents, these variables should be considered.

• Biomolecules & Therapeutics
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• v.20 no.5
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• pp.433-445
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• 2012

During the course of evolution, animals encountered the harmful effects of fungi, which are strong pathogens. Therefore, they have developed powerful mechanisms to protect themselves against these fungal invaders. ${\beta}$-Glucans are glucose polymers of a linear ${\beta}$(1,3)-glucan backbone with ${\beta}$(1,6)-linked side chains. The immunostimulatory and antitumor activities of ${\beta}$-glucans have been reported; however, their mechanisms have only begun to be elucidated. Fungal and particulate ${\beta}$-glucans, despite their large size, can be taken up by the M cells of Peyer's patches, and interact with macrophages or dendritic cells (DCs) and activate systemic immune responses to overcome the fungal infection. The sampled ${\beta}$-glucans function as pathogen-associated molecular patterns (PAMPs) and are recognized by pattern recognition receptors (PRRs) on innate immune cells. Dectin-1 receptor systems have been incorporated as the PRRs of ${\beta}$-glucans in the innate immune cells of higher animal systems, which function on the front line against fungal infection, and have been exploited in cancer treatments to enhance systemic immune function. Dectin-1 on macrophages and DCs performs dual functions: internalization of ${\beta}$-glucan-containing particles and transmittance of its signals into the nucleus. This review will depict in detail how the physicochemical nature of ${\beta}$-glucan contributes to its immunostimulating effect in hosts and the potential uses of ${\beta}$-glucan by elucidating the dectin-1 signal transduction pathway. The elucidation of ${\beta}$-glucan and its signaling pathway will undoubtedly open a new research area on its potential therapeutic applications, including as immunostimulants for antifungal and anti-cancer regimens.