• Title/Summary/Keyword: $P_0$-function

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EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRÖDINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN ℝN

  • Kim, Jae-Myoung;Kim, Yun-Ho;Lee, Jongrak
    • Journal of the Korean Mathematical Society
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    • v.56 no.6
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    • pp.1529-1560
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    • 2019
  • We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

Correlation Analysis of Ocular Dominance and Levator Palpebrae Superioris Muscle Function (주시안과 눈꺼풀 올림근 기능의 상관관계 분석)

  • Ha, Ki-Young;Suh, Hyeun-Woo;Kim, Boo-Yeong;Kim, Tae-Yeon;Park, Sung-Gyu
    • Archives of Plastic Surgery
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    • v.37 no.3
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    • pp.265-270
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    • 2010
  • Purpose: Most of the bilateral structures in our body are not perfectly balanced, such that one side is preferred than the other or it has physiological superiority. Eyes also have an imbalance; the eye with sensory and motional superiority compared to the other is called dominant eye. Authors of this study focused on analyzing the correlation between the dominant eye and levator palpebrae superioris muscle. Methods: The subject of this study was 42 patients with no ptosis and with no past history of blepharoplasty. Hand dominance was identified through questionnaire and dominant eye was identified by hole-in-the-card dominance test (Dolman's test) in all patients. The function of levator palpebrae superioris muscle was measured by MLD (marginal limbal distance). During the measuring procedure, frontalis muscle was not inhibited to avoid the eyelid skin hooding. Results: Out of 42 patients, 27 patients (64.3%) were right ocular dominant, 15 patients (35.7%) were left ocular dominant, 36 patients (85.7%) were right hand dominant and 4 patients (9.5%) were left hand dominant. Out of 27 right ocular dominant patients, right MLD was larger than the left in 26 patients (96.3%). It was larger in average of 0.47 mm (p<0.001) in 27 right ocular dominant patients. Also, left MLD was larger than the right in 11 patients (73.3%) out of 15 left ocular dominant patients. It was larger in average of 0.57 mm (p=0.003) in 27 left ocular dominant patients. MLD on the side of the dominant eye was larger in average of 0.50 mm (p<0.001) than the MLD of non-dominant eye side. Right MLD was larger than the left in average of 0.28mm (p=0.010) in right hand dominant patients, and left MLD was larger than the right in average of 1.15 mm (p=0.025) in left hand dominant patients. Conclusion: The function of levator palpebrae muscle differs in right and left, and the difference correlates with the dominant eye. Also, the function of levator palpebrae muscle is stronger in the dominant eye. We were able to present statistical evidence regarding the difference of the function in right and left levator palpebrae muscle. This may be a factor worth consideration in terms of balancing the eyes during the blepharoplasty.

Fusion Research in the Association of Lung Function with Pulse Pressure and Blood Lipid in Adults (성인의 맥압과 혈청지질 및 폐기능의 관계 융합 연구)

  • Jo, Yoon-Kyung;Sung, Hyun-Ho
    • Journal of the Korea Convergence Society
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    • v.9 no.11
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    • pp.203-208
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    • 2018
  • The purpose of this study was to investigate whether there is a relationship between pulmonary function, serum lipid and pulse pressure, which is a risk factor of cardiovascular disease, in subjects with 109 office workers(51 males and 58 females) be at Seoul, Korea. The mean age of the subjects was $43.44{\pm}7.23$ years old (male $43.44{\pm}7.27$, fenale $49.1{\pm}11.5$). The subjects' height, weight, BMI, systolic and diastolic blood pressures were measured and there was statistical difference between men and women.The mean pulse pressure of the subjects was $47.82{\pm}9.02mmHg$, and the mean of FVC was $84.26{\pm}9.91%$. There was no difference between men and women in both. There was a positive correlation between pulse pressure and systolic blood pressure in males (p<0.01) and females (p<0.01), and FVC and HDL in males were positively correlated (p<0.05). Pulse pressure and %FVC were negatively correlated (r =-0.267, P<0.01). Pulse pressure and %FVC were negatively correlated (r =-0.267, P<0.01). Regression analysis showed that PP was the independent affected %FVC. Therefore, pulse pressure and %FVC may be useful as a predictor of cardiovascular disease in middle-aged subjects with normal, suggest a long-term convergence follow-up is warranted to elucidate the incidence of cardiovascular disease.

Risk Factors Associated with Loneliness in the Elderly Living Alone (독거노인의 외로움에 영향을 미치는 위험요인)

  • Lee, Seung Woo;Paik, Ki Chung;Lee, Kyung Kyu;Lee, Seok Bum;Kim, Kyung Min;Kim, Dohyun;Lee, Jung Jae
    • Korean Journal of Psychosomatic Medicine
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    • v.27 no.2
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    • pp.173-180
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    • 2019
  • Objectives : Loneliness is associated with negative mental and physical health. However, little is known about the risk factors of loneliness in the Korean elderly living alone. The aim of this study was to examine sociodemographic and social network related risks for loneliness among the elderly living alone. Methods : This is a cross-sectional study that enrolled 1,091 subjects who are the community-residing elderly living alone. Sociodemographic status, medical condition, cognition, mood disorder and levels of loneliness were collected using a self-administered questionnaire and a specific semi-structured interview conducted by a trained nurse. Descriptive statistics were used to analyze data regarding sociodemographic variable and loneliness. Univariate and Multivariate regression analyses were applied to examine factors associated with loneliness. Results : The mean score of loneliness was 3.8 (SD=1.7). No family contact (standardized β=0.115, p<0.001), no religious attendance (standardized β=0.057, p=0.028), no gathering with friends (standardized β=0.088, p=0.001) and high score of Short for of Geriatric Depression Scale (standardized β=0.502, p<0.001) were significantly associated with high loneliness in the elderly living alone. Conclusions : Family function, social network and depressive mood could be significant risk factors for high loneliness in the elderly living alone. Public health promotion efforts to reduce loneliness should focus on improving family function, social network and decreasing depression.

Relevance between cognitive function and oral health status in the elderly: Focusing on Korean Longitudinal Study of Aging (노인의 인지기능과 구강건강상태의 관련성: 고령화연구패널조사(Korean Longitudinal Study of Aging)를 중심으로)

  • Kim, In-Ja;Moon, Hee-Jung
    • Journal of Korean society of Dental Hygiene
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    • v.22 no.5
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    • pp.333-340
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    • 2022
  • Objectives: This study aimed to confirm the association between cognitive function and oral health status in the elderly. Methods: In this study, 5,794 respondents, aged 55 or older, who had participated in the 7th aging research panel survey were used. Statistical analyses were performed using a complex samples cross-tabulation analysis, complex samples general linear model, and a complex sample multinomial logistic regression analysis. Results: After analyzing the cognitive function of the elderly according to their oral health conditions, it was found that suspicions of dementia (19.6%) and cognitive function decline (25.9%) were more common for those who wore dentures than for those who did not wear dentures (p<0.001). Compared to those who did not wear dentures, those who wore dentures were linked to a 1.665 times higher suspicion of dementia (p<0.001). In comparison, cognitive decline was 0.964 times lower when the number of natural teeth increased by 1, and it was 0.941 times lower when the oral health evaluation index for the elderly increased by 1 point (p<0.001). Conclusions: As a result of this study, it was confirmed that cognitive function and oral health status are related in the elderly. Therefore, systematic measures for oral health management and oral health promotion should be prepared in tandem with awareness of possible cognitive decline in the elderly.

ON ESTIMATION OF UNIFORM CONVERGENCE OF ANALYTIC FUNCTIONS BY (p, q)-BERNSTEIN OPERATORS

  • Mursaleen, M.;Khan, Faisal;Saif, Mohd;Khan, Abdul Hakim
    • Korean Journal of Mathematics
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    • v.27 no.2
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    • pp.505-514
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    • 2019
  • In this paper we study the approximation properties of a continuous function by the sequence of (p, q)-Bernstein operators for q > p > 1. We obtain bounds of (p, q)-Bernstein operators. Further we prove that if a continuous function admits an analytic continuation into the disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, then $B^n_{p,q}(g;z){\rightarrow}g(z)(n{\rightarrow}{\infty})$ uniformly on any compact set in the given disk $\{z:{\mid}z{\mid}{\leq}{\rho}\}$, ${\rho}>0$.

REAL-VARIABLE CHARACTERIZATIONS OF VARIABLE HARDY SPACES ON LIPSCHITZ DOMAINS OF ℝn

  • Liu, Xiong
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.3
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    • pp.745-765
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    • 2021
  • Let Ω be a proper open subset of ℝn and p(·) : Ω → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the author introduces the "geometrical" variable Hardy spaces Hp(·)r (Ω) and Hp(·)z (Ω) on Ω, and then obtains the grand maximal function characterizations of Hp(·)r (Ω) and Hp(·)z (Ω) when Ω is a strongly Lipschitz domain of ℝn. Moreover, the author further introduces the "geometrical" variable local Hardy spaces hp(·)r (Ω), and then establishes the atomic characterization of hp(·)r (Ω) when Ω is a bounded Lipschitz domain of ℝn.

INEQUALITIES FOR THE ANGULAR DERIVATIVES OF CERTAIN CLASSES OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISC

  • Ornek, Bulent Nafi
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.325-334
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    • 2016
  • In this paper, a boundary version of the Schwarz lemma is investigated. We take into consideration a function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$ holomorphic in the unit disc and $\|\frac{f(z)}{{\lambda}f(z)+(1-{\lambda})z}-{\alpha}\|$ < ${\alpha}$ for ${\mid}z{\mid}$ < 1, where $\frac{1}{2}$ < ${\alpha}$ ${\leq}{\frac{1}{1+{\lambda}}}$, $0{\leq}{\lambda}$ < 1. If we know the second and the third coefficient in the expansion of the function $f(z)=z+c_{p+1}z^{p+1}+c_{p+2}z^{p+2}+{\cdots}$, then we can obtain more general results on the angular derivatives of certain holomorphic function on the unit disc at boundary by taking into account $c_{p+1}$, $c_{p+2}$ and zeros of f(z) - z. We obtain a sharp lower bound of ${\mid}f^{\prime}(b){\mid}$ at the point b, where ${\mid}b{\mid}=1$.

Myocardial Blood Flow Quantified by Low-Dose Dynamic CT Myocardial Perfusion Imaging Is Associated with Peak Troponin Level and Impaired Left Ventricle Function in Patients with ST-Elevated Myocardial Infarction

  • Jingwei Pan;Mingyuan Yuan;Mengmeng Yu;Yajie Gao;Chengxing Shen;Yining Wang;Bin Lu;Jiayin Zhang
    • Korean Journal of Radiology
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    • v.20 no.5
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    • pp.709-718
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    • 2019
  • Objective: To investigate the association of myocardial blood flow (MBF) quantified by dynamic computed tomography (CT) myocardial perfusion imaging (MPI) with troponin level and left ventricle (LV) function in patients with ST-segment elevated myocardial infarction (STEMI). Materials and Methods: Thirty-five STEMI patients who successfully had undergone reperfusion treatment within 1 week of their infarction were consecutively enrolled. All patients were referred for dynamic CT-MPI. Serial high-sensitivity troponin T (hs-TnT) levels and left ventricular ejection fraction (LVEF) measured by echocardiography were recorded. Twenty-six patients with 427 segments were included for analysis. Various quantitative parameters derived from dynamic CT-MPI were analyzed to determine if there was a correlation between hs-TnT levels and LVEF on admission and again at the 6-month mark. Results: The mean radiation dose for dynamic CT-MPI was 3.2 ± 1.1 mSv. Infarcted territories had significantly lower MBF (30.5 ± 7.4 mL/min/100 mL versus 73.4 ± 8.1 mL/min/100 mL, p < 0.001) and myocardial blood volume (MBV) (2.8 ± 0.9 mL/100 mL versus 4.2 ± 1.1 mL/100 mL, p = 0.044) compared with those of reference territories. MBF showed the best correlation with the level of peak hs-TnT (r = -0.682, p < 0.001), and MBV showed a moderate correlation with the level of peak hs-TnT (r = -0.437, p = 0.026); however, the other parameters did not show any significant correlation with hs-TnT levels. As for the association with LV function, only MBF was significantly correlated with LVEF at the time of admission (r = 0.469, p = 0.016) and at 6 months (r = 0.585, p = 0.001). Conclusion: MBF quantified by dynamic CT-MPI is significantly inversely correlated with the level of peak hs-TnT. In addition, patients with lower MBF tended to have impaired LV function at the time of their admission and at 6 months.

Correlation Between the Activities of Daily Living Assessment and Gross Motor Function Measures in Children with Spastic Cerebral Palsy

  • You, Hee-Joo;Park, Sun-Wook;Lee, Han-Suk
    • The Journal of Korean Physical Therapy
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    • v.27 no.6
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    • pp.425-429
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    • 2015
  • Purpose: This study was to identify the whether there is any correlation between Gross Motor Function Measures (GMFM) and Functional independence Measurement for children (WeeFIM) in order to identify a relevance of daily life motor with gross motor function of children with cerebral palsy. Methods: Subjects were instructed to evaluated by an occupational therapist using WeeFIM (reliability 0.83-0.99) and by a physical therapist using GMFM (reliability 0.93). 10 male children and 13 female children among 23 children being diagnosed as cerebral palsy were targeted for this study. A correlation between GMFM and WeeFIM was analyzed with Kendall correlation. Results: Participants showed significant correlation between GMFM and WeeFIM in all categories, except in the GMFM's walking running jumping category, standing category of GMFM and self care, sphincter control, communication category of WeeFIM. Lying rolling and sitting and crawling kneeling area of GMFM showed a significant correlation with self care(r=0.35, 0.39, 0.4), sphincter control (r=0.45, 0.43, 0.61), mobility transfer (r=0.44, 0.36, 0.64), locomotion (r=0.41, 0.35, 0.74), communication (r=0.4, 0.44, 0.51), and social cognition (r=0.43, 0.51, 0.64) area of WeeFIM (p<0.05). Standing of GMFM and mobility transfer (r=0.74), locomotion (r=0.47) and social cognition (r=0.4) area of WeeFIM showed a significant correlation (p<0.05). Conclusion: These findings indicated significant correlation between activity of daily living (ADL) and gross motor function of children with cerebral palsy. However, because there are a few results that are not significant, both assessment tools should be used for evaluations so that treatment can be achieved with an accurate assessment and establish a therapeutic plan.