• Journal of the Korean Statistical Society
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• 제28권3호
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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)

• 대한수학회논문집
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• 제37권4호
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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.

• 대한수학회보
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• 제44권4호
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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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• 제37권2호
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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.

• 대한수학회보
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• 제57권4호
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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.

• 감성과학
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• 제16권3호
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• pp.409-416
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• 2013

집중은 관련된 사건을 선택적으로 주의하고, 관련 없는 사건을 무시하는 인간의 중요한 인지 기능중의 하나이다. 인간의 집중 능력을 관리 이용하는 컴퓨터 기반 장치에 있어서 집중과 비집중 상태를 구분하는 것은 필수적으로 요구되는 조건이다. 본 논문에서는, 뇌파신호로부터 분류기의 입력으로 사용되는 특징을 효율적으로 추출하기 위하여 비선형 반복 패턴 분석기법과 스펙트럼 분석 기법을 새로이 결합하였고(13개 특징 추출), 서포트벡터머신, 역전파 알고리즘, 선형분리, 로지스틱 회귀 분류 기반 분류기들을 포함하는 집중-비집중 분류기들의 성능을 분석하였다. 그중에서 81 %의 정확도를 보이는 서포트벡터머신 분류기가 가장 좋은 성능을 보였다. 또한 스펙트럼 분석으로 추출한 특징만을 사용하였을 경우(76 % 정확도)가 비선형 분석 방법으로 추출한 특징만을 사용했을 경우(67 % 정확도)보다 좀 더 우수한 성능을 보였다. 비선형-스펙트럼 분석법을 복합 적용한 서포트벡터머신 분류기가 추후 집중 관련 장비 설계에 있어서 효율적으로 적용될 수 있을 것이다.

• 호남수학학술지
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• 제41권4호
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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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• 제25권2호
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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.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1998년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Spring 1998
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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.

• Bulletin of the Korean Chemical Society
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• 제12권2호
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• pp.170-177
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• 1991

A lattice mean field theory is developed to investigate the conformational properties of monolayer amphiphiles at the air-water interface. By generalizing Dill and Cantor's method and by extending Whittington's recurrence equation, we derive the supermatrix recurrence equation which is applied to calculation of various segment density profiles and order parameter, etc. In deriving the equation, we incorporated the chain stiffness effect and the chain connectivity which are distinguished features of linear chain molecule. Our result shows that, as the surface coverage $\sigma$ increases the chain ordering process with respect to vertical axis of the lattice system becomes dominant.