• Journal of the Korean Statistical Society
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• v.28 no.3
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• pp.279-296
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• 1999

In this paper we establish some recurrence relations for both single and product moments of order statistics from a doubly truncated linear- exponential distribution with increasing hazard rate. These recurrence relations would enable one to compute all the higher order moments of order statistics for all sample sizes from those of the lower order in a simple recursive way. In addition, percentage points of order statistics are also discussed. These generalize the corresponding results for the linear- exponential distribution with increasing hazard rate derived by Balakrishnan and Malik(1986)

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.977-988
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• 2022

The Padovan sequence is the third-order linear recurrence (𝓟_n)_n≥0 defined by 𝓟_n = 𝓟_n-2 + 𝓟_n-3 for all n ≥ 3 with initial conditions 𝓟₀ = 0 and 𝓟₁ = 𝓟₂ = 1. In this paper, we investigate a generalization of the Padovan sequence called the k-generalized Padovan sequence which is generated by a linear recurrence sequence of order k ≥ 3. We present recurrence relations, the generalized Binet formula and different arithmetic properties for the above family of sequences.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.841-849
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• 2007

In this paper we discuss the Hyers-Ulam-Rassias stability of a system of first order linear recurrences with variable coefficients in Banach spaces. The concept of the Hyers-Ulam-Rassias stability originated from Th. M. Rassias# stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. As an application, the Hyers-Ulam-Rassias stability of a p-order linear recurrence with variable coefficients is proved.

• Radiation Oncology Journal
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• v.37 no.2
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• pp.117-126
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• 2019

Purpose: The purpose of this study was to characterize and evaluate the clinical significance of volume changes of soft tissue sarcomas during radiation therapy (RT), prior to definitive surgical resection. Materials and Methods: Patients with extremity or pelvis soft tissue sarcomas treated at our institution from 2013 to 2016 with RT prior to resection were identified retrospectively. Tumor volumes were measured using cone-beam computed tomography obtained daily during RT. Linear regression evaluated the linearity of volume changes. Kruskal-Wallis tests, Mann-Whitney U tests, and linear regression evaluated predictors of volume change. Logistic and Cox regression evaluated volume change as a predictor of resection margin status, histologic treatment response, and tumor recurrence. Results: Thirty-three patients were evaluated. Twenty-nine tumors were high grade. Prior to RT, median tumor volume was 189 mL (range, 7.2 to 4,885 mL). Sixteen tumors demonstrated significant linear volume changes during RT. Of these, 5 tumors increased and 11 decreased in volume. Myxoid liposarcoma (n = 5, 15%) predicted decreasing tumor volume (p = 0.0002). Sequential chemoradiation (n = 4, 12%) predicted increasing tumor volume (p = 0.008) and corresponded to longer times from diagnosis to RT (p = 0.01). Resection margins were positive in three cases. Five patients experienced local recurrence, and 7 experienced distant recurrence, at median 8.9 and 6.9 months post-resection, respectively. Volume changes did not predict resection margin status, local recurrence, or distant recurrence. Conclusion: Volume changes of pelvis and extremity soft tissue sarcomas followed linear trends during RT. Volume changes reflected histologic subtype and treatment characteristics but did not predict margin status or recurrence after resection.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1033-1048
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• 2020

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.

• Science of Emotion and Sensibility
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• v.16 no.3
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• pp.409-416
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• 2013

Attention is one of important cognitive functions in human affecting on the selectional concentration of relevant events and ignorance of irrelevant events. The discrimination of attentional and inattentional status is the first step to manage human's attentional capability using computer assisted device. In this paper, we newly combine the non-linear recurrence pattern analysis and spectrum analysis to effectively extract features(total number of 13) from the electroencephalographic signal used in the input to classifiers. The performance of diverse types of attention-inattention classifiers, including supporting vector machine, back-propagation algorithm, linear discrimination, gradient decent, and logistic regression classifiers were evaluated. Among them, the support vector machine classifier shows the best performance with the classification accuracy of 81 %. The use of spectral band feature set alone(accuracy of 76 %) shows better performance than that of non-linear recurrence pattern feature set alone(accuracy of 67 %). The support vector machine classifier with hybrid combination of non-linear and spectral analysis can be used in later designing attention-related devices.

• Annals of Hepato-Biliary-Pancreatic Surgery
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• v.27 no.2
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• pp.158-165
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• 2023

Backgrounds/Aims: Within two years of surgery, 70% of resected intrahepatic cholangiocarcinoma (iCCA) recur. Better biomarkers are needed to identify those at risk of "early recurrence" (ER). In this study, we defined ER and investigated whether preoperative neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), and systemic-inflammatory index were prognostic of both overall relapse and ER after curative hepatectomy for iCCA. Methods: A retrospective cohort of patients who underwent curative-intent hepatectomy for iCCA between 2005 and 2017 were created. The cut-off timepoint for the ER of iCCA was estimated using a piecewise linear regression model. Univariable analyses of recurrence were conducted for the overall, early, and late recurrence periods. For the early and late recurrence periods, multivariable Cox regression with time-varying regression coefficient analysis was used. Results: A total of 113 patients were included in this study. ER was defined as recurrence within 12 months of a curative resection. Among the included patients, 38.1% experienced ER. In the univariable model, a higher preoperative NLR (> 4.3) was significantly associated with an increased risk of recurrence overall and in the first 12 months after curative surgery. In the multivariable model, a higher NLR was associated with a higher recurrence rate overall and in the ER period (≤ 12 months), but not in the late recurrence period. Conclusions: Preoperative NLR was prognostic of both overall recurrence and ER after curative iCCA resection. NLR is easily obtained before and after surgery and should be integrated into ER prediction tools to guide preoperative treatments and intensify postoperative follow-up.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.863-870
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• 2019

In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.20-27
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• 1998

In the current seismic design codes design earthquake is usually defined as the earthquake with the 90 percent probability of not being exceeded in the life time of a structure which is assumed as 50 years equivalent to the earthquake with 475 year recurrence period. However the life time of tall building structures may be much longer than 50 yers. The current seismic design code requires the modal analysis or dynamic time history analysis for the buildings with the height exceeding a certain height limit. The objective of this study is to collect the earthquake ground motion(EQGM) which can be used for dynamic time history analysis for tall buildings. For this purpose linear elastic design response spectrum (LEDRS) in the code is scaled to account for the recurrence period of the design earthquake. The earthquake ground motions which has been recorded are calibrated to fit the scaled LEDRS. The set of calibrated EQGM can be treated as design EQGM for the design of tall building with longer lifetime than ordinary building.