• 대한수학회지
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• 제43권6호
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• pp.1199-1217
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• 2006

The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the T-th hyper-Kloosterman sums Kl(h, k+1, r;q) and the hyper Cochrane sums C(h, q; m, k), and give an interesting mean value formula.

• 대한수학회보
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• 제60권3호
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• pp.611-622
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• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

• 대한수학회보
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• 제50권2호
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• pp.451-458
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• 2013

The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind mean value of the generalized Kloosterman sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.

• 대한수학회지
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• 제47권6호
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• pp.1107-1122
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• 2010

In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, $\chi$; q), and give several sharp asymptotic formulae.

• 대한수학회지
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• 제46권4호
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• 대한수학회지
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• 제44권1호
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• pp.11-24
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• 2007

The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

• Korean Journal of Radiology
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• 제23권11호
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• pp.1044-1054
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• 2022

Objective: This study aimed to investigate whether a deep learning reconstruction (DLR) method improves the image quality, stent evaluation, and visibility of the valve apparatus in coronary computed tomography angiography (CCTA) when compared with filtered back projection (FBP) and hybrid iterative reconstruction (IR) methods. Materials and Methods: CCTA images of 51 patients (mean age ± standard deviation [SD], 63.9 ± 9.8 years, 36 male) who underwent examination at a single institution were reconstructed using DLR, FBP, and hybrid IR methods and reviewed. CT attenuation, image noise, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and stent evaluation, including 10%-90% edge rise slope (ERS) and 10%-90% edge rise distance (ERD), were measured. Quantitative data are summarized as the mean ± SD. The subjective visual scores (1 for worst -5 for best) of the images were obtained for the following: overall image quality, image noise, and appearance of stent, vessel, and aortic and tricuspid valve apparatus (annulus, leaflets, papillary muscles, and chordae tendineae). These parameters were compared between the DLR, FBP, and hybrid IR methods. Results: DLR provided higher Hounsfield unit (HU) values in the aorta and similar attenuation in the fat and muscle compared with FBP and hybrid IR. The image noise in HU was significantly lower in DLR (12.6 ± 2.2) than in hybrid IR (24.2 ± 3.0) and FBP (54.2 ± 9.5) (p < 0.001). The SNR and CNR were significantly higher in the DLR group than in the FBP and hybrid IR groups (p < 0.001). In the coronary stent, the mean value of ERS was significantly higher in DLR (1260.4 ± 242.5 HU/mm) than that of FBP (801.9 ± 170.7 HU/mm) and hybrid IR (641.9 ± 112.0 HU/mm). The mean value of ERD was measured as 0.8 ± 0.1 mm for DLR while it was 1.1 ± 0.2 mm for FBP and 1.1 ± 0.2 mm for hybrid IR. The subjective visual scores were higher in the DLR than in the images reconstructed with FBP and hybrid IR. Conclusion: DLR reconstruction provided better images than FBP and hybrid IR reconstruction.

• 대한수학회보
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• 제52권1호
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• 응용통계연구
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• 제31권4호
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• pp.447-461
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• 2018

국내 영화 산업 매출은 매년 증가하고 있다. 극장은 영화의 1차 판매 경로이며, 극장을 이용하는 관객 수는 부가판권에 영향을 준다. 따라서 극장을 이용하는 관객의 수는 영화 산업 매출에 직결되는 중요한 요소이다. 본 논문에서 특정일의 관객 수를 예측하기 위하여 다중선형회귀모형과 Bass 모형을 결합한 Hybrid 모형을 고려한다. 두 모형을 결합함으로써 회귀분석의 예측값을 Bass 모형의 예측값으로 보정하였다. 분석에는 개봉일이 모두 다른 세 영화를 이용하였다. All subset regression 방법을 이용해 모든 가능한 조합을 생성하고 5중 교차검증(5-fold cross validation)을 통해 5번 모형을 추정한다. 이 때 제곱근평균오차가 가장 작은 모형으로 예측값을 구한 뒤 Bass 모형의 예측값과 결합해 최종 예측값을 구하게 된다. 과거데이터가 존재할수록 Bass 모형의 가중치는 증가하면서 예측값에 보정효과를 준다는 것을 확인할 수 있었다.

• Steel and Composite Structures
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• 제52권2호
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• pp.145-163
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• 2024

This paper presents six novel hybrid machine learning (ML) models that combine support vector machines (SVM), Decision Tree (DT), Random Forest (RF), Gradient Boosting (GB), extreme gradient boosting (XGB), and categorical gradient boosting (CGB) with the Harris Hawks Optimization (HHO) algorithm. These models, namely HHO-SVM, HHO-DT, HHO-RF, HHO-GB, HHO-XGB, and HHO-CGB, are designed to predict the ultimate strength of both rectangular and circular reinforced concrete (RC) columns. The prediction models are established using a comprehensive database consisting of 325 experimental data for rectangular columns and 172 experimental data for circular columns. The ML model hyperparameters are optimized through a combination of cross-validation technique and the HHO. The performance of the hybrid ML models is evaluated and compared using various metrics, ultimately identifying the HHO-CGB model as the top-performing model for predicting the ultimate shear strength of both rectangular and circular RC columns. The mean R-value and mean a20-index are relatively high, reaching 0.991 and 0.959, respectively, while the mean absolute error and root mean square error are low (10.302 kN and 27.954 kN, respectively). Another comparison is conducted with four existing formulas to further validate the efficiency of the proposed HHO-CGB model. The Shapely Additive Explanations method is applied to analyze the contribution of each variable to the output within the HHO-CGB model, providing insights into the local and global influence of variables. The analysis reveals that the depth of the column, length of the column, and axial loading exert the most significant influence on the ultimate shear strength of RC columns. A user-friendly graphical interface tool is then developed based on the HHO-CGB to facilitate practical and cost-effective usage.