• Kyungpook Mathematical Journal
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• 제49권3호
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• pp.483-492
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• 2009

In this paper we give formulae for sums of products of two Horadam type generalized Fibonacci numbers with the same recurrence equation and with possibly different initial conditions. Analogous improved alternating sums are also studied as well as various derived sums when terms are multiplied either by binomial coefficients or by members of the sequence of natural numbers. These formulae are related to the recent work of Belbachir and Bencherif, $\v{C}$erin and $\v{C}$erin and Gianella.

• 대한수학회지
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• 제36권3호
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• pp.489-507
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• 1999

We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure d$\alpha$(x) in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to g(x)d$\alpha$(x) is the same as that of extreme zeros of orthogonal polynomials with respect to d$\alpha$(x) when g(x) is a polynomial with all zeros in a certain interval determined by d$\alpha$(x). several illustrating examples are also given.

• 성인간호학회지
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• 제25권1호
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• pp.53-61
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• 2013

Purpose: The purpose of the study was to identify the levels of anxiety, depression and uncertainty of patients who participated in the clinical trials for anticancer drug, and to identify correlations among these variables. Methods: Cross-sectional survey used the Symptom Check List-90-Revision and the Mishel Uncertainty in Illness Scale from 106 subjects in 2011. The data were analyzed using descriptive statistics, t-test, ANOVA, Pearson correlation coefficients. Results: The mean score of anxiety was 2.06, that of depression 2.35, and that of uncertainty 2.61. Anxiety and depression (r=.70), anxiety and uncertainty (r=.44), depression and uncertainty (r=.60) were significantly correlated each other. The levels of anxiety, depression and uncertainty were different in various characteristics of the subjects, such as education, recurrence, and economic burden. Conclusion: The results of the study indicate that when implementing psychosocial interventions for cancer patients who participate in clinical trial, factors such as education, economic burden, and recurrence should be integrated into the intervention. Further studies applying theoretical model would be helpful to identify directional relationships among the variables that are important in psychosocial well-being of cancer patients undergoing clinical trial.

• Korean Journal of Radiology
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• 제23권11호
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• pp.1078-1088
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• 2022

Objective: To develop and validate a model using radiomics features from apparent diffusion coefficient (ADC) map to diagnose local tumor recurrence in head and neck squamous cell carcinoma (HNSCC). Materials and Methods: This retrospective study included 285 patients (mean age ± standard deviation, 62 ± 12 years; 220 male, 77.2%), including 215 for training (n = 161) and internal validation (n = 54) and 70 others for external validation, with newly developed contrast-enhancing lesions at the primary cancer site on the surveillance MRI following definitive treatment of HNSCC between January 2014 and October 2019. Of the 215 and 70 patients, 127 and 34, respectively, had local tumor recurrence. Radiomics models using radiomics scores were created separately for T2-weighted imaging (T2WI), contrast-enhanced T1-weighted imaging (CE-T1WI), and ADC maps using non-zero coefficients from the least absolute shrinkage and selection operator in the training set. Receiver operating characteristic (ROC) analysis was used to evaluate the diagnostic performance of each radiomics score and known clinical parameter (age, sex, and clinical stage) in the internal and external validation sets. Results: Five radiomics features from T2WI, six from CE-T1WI, and nine from ADC maps were selected and used to develop the respective radiomics models. The area under ROC curve (AUROC) of ADC radiomics score was 0.76 (95% confidence interval [CI], 0.62-0.89) and 0.77 (95% CI, 0.65-0.88) in the internal and external validation sets, respectively. These were significantly higher than the AUROC values of T2WI (0.53 [95% CI, 0.40-0.67], p = 0.006), CE-T1WI (0.53 [95% CI, 0.40-0.67], p = 0.012), and clinical parameters (0.53 [95% CI, 0.39-0.67], p = 0.021) in the external validation set. Conclusion: The radiomics model using ADC maps exhibited higher diagnostic performance than those of the radiomics models using T2WI or CE-T1WI and clinical parameters in the diagnosis of local tumor recurrence in HNSCC following definitive treatment.

• 한국농공학회지
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• 제31권4호
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• pp.81-89
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• 1989

This study is to determine seasonal consumptive use of water of a design year during growing period (June-September) for paddy rice in Suwon. To obtain Dry flay Index which is defined as the number of probable dry days occurring at a design year, Slade Partly Un- symmetrical Distribution Function was adopted. Dry Day Index was analysed with 5, 10 and 30 day-term. And each of them was evaluated with recurrence intervals of 1, 3, 5, 10 and 20 year using 49 years daily rainfall data('35-'83). Their singnificance were tested at 1% level by X$^2$ test. On the basis of these values, Probable Evapotranspiration (ET) which is the daily average ET for the sum of both ET on dry days and ET on rainy days were esti- mated using 5 years daily actual ET data(' 82-' 86). Their Crop Coefficients were also de- termined by the modified Penman equation(1977) proposed by Doorenbos & Pruitt.

• 대한수학회지
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• 제55권4호
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• pp.975-986
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• 2018

Some new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomilas were introduced recently by Kilar and Simsek ([5]) and we study the two variable Fubini polynomials as Appell polynomials whose coefficients are the Fubini polynomials. In this paper, we would like to utilize umbral calculus in order to study two variable higher-order Fubini polynomials. We derive some of their properties, explicit expressions and recurrence relations. In addition, we express the two variable higher-order Fubini polynomials in terms of some families of special polynomials and vice versa.

• 대한수학회지
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• 제54권5호
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• pp.1605-1621
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• 2017

The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.205-228
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• 2005

Let I(f) be the integral defined by : $I(f) = \int\limits_{a}^{b} f(x)w(x)dx$ with f a given function, w a nonclassical weight function and [a, b] an interval of IR (of finite or infinite length). We propose to calculate the approximate value of I(f) by using a new scheme for deriving a non-linear system, satisfied by the three-term recurrence coefficients of semi-classical orthogonal polynomials. Finally we studies the Stability and complexity of this scheme.

• 대한수학회논문집
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• 제38권2호
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• pp.341-354
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• 2023

In this article, an alternating Fibonacci sequence is defined from a second-order linear homogeneous recurrence relation with constant coefficients. Then, the determinant, inverse, and eigenvalues of the circulant matrices with entries in the first row having the formation of the sequence are formulated explicitly in a simple way. In this study, the method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations. For the eigenvalues, the known formulation from the case of general circulant matrices is simplified by considering the specialty of the sequence and using cyclic group properties. We also propose algorithms for the formulation to show how efficient the computations are.

• 보건의료산업학회지
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• 제13권3호
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• pp.163-172
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• 2019

Objectives: With the rapidly increasing incidence of cancer worldwide, it has become important for health care professionals to both provide care for cancer patients and to address the challenges faced by family caregivers of cancer patients. This study aims to identify the factors affecting depression among cancer patients' family caregivers. The results of this study suggest the need to propose programs for family caregivers as well as cancer patients. Methods: Participants were 219 caregivers who were informed of the study purpose and agreed to participate. Data were analyzed using t-tests, one-way ANOVA, Scheffe's test, Pearson correlation coefficients, and multiple stepwise regression with the SPSS/WIN 25.0 program. Results: The mean score for depression among cancer patients' family caregivers was $1.57{\pm}.40$ (range: 0-3). Depression was significantly different based on age, relationship with the patient, education, occupation, cancer recurrence, care days per week, financial burden, site of cancer, and health status. Analysis using multiple regression showed that model 1 showed 16% of the factors predicting depression among cancer patients' family caregivers (F=6.16, p<.001) including occupation, recurrence, and health status of the caregiver. Model 3, which included additional burnout, showed 37% of the factors predicting depression (F=12.36, p<.001). Conclusions: These results suggest that it is necessary to develop programs for prevention and management of depression among cancer patients' family caregivers.