• 대한수학회논문집
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• 제32권2호
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• pp.233-260
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• 2017

Let R be a factorial domain. In this work we investigate the connections between the arithmetic of Int(R) (i.e., the ring of integer-valued polynomials over R) and its monadic submonoids (i.e., monoids of the form {$g{\in}Int(R){\mid}g{\mid}_{Int(R)}f^k$ for some $k{\in}{\mathbb{N}}_0$} for some nonzero $f{\in}Int(R)$). Since every monadic submonoid of Int(R) is a Krull monoid it is possible to describe the arithmetic of these monoids in terms of their divisor-class group. We give an explicit description of these divisor-class groups in several situations and provide a few techniques that can be used to determine them. As an application we show that there are strong connections between Int(R) and its monadic submonoids. If $R={\mathbb{Z}}$ or more generally if R has sufficiently many "nice" atoms, then we prove that the infinitude of the elasticity and the tame degree of Int(R) can be explained by using the structure of monadic submonoids of Int(R).

• Korean Journal of Mathematics
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• 제19권1호
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• pp.1-16
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• 2011

In this paper, using differential operator, we have introduce new class of p-valent uniformly convex functions in the unit disc U = {z : |z| < 1} and obtain the coefficient bounds, extreme bounds and radius of starlikeness for the functions belonging to this generalized class. Furthermore, partial sums $f_k(z)$ of functions $f(z)$ in the class $S^*({\lambda},{\alpha},{\beta})$ are considered. The various results obtained in this paper are sharp.

• 대한수학회지
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• 제47권2호
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• pp.351-361
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• 2010

For a bounded linear operator T on a separable complex infinite dimensional Hilbert space $\mathcal{H}$, we say that T is a quasi-class (A, k) operator if $T^{*k}|T^2|T^k\;{\geq}\;T^{*k}|T|^2T^k$. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class (A, k) operators.

• 대한수학회보
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• 제39권4호
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• pp.687-704
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• 2002

We show that the class of inner chordarc domains is properly contained in the class of exterior quasiconvex domains. We also show that the class of exterior quasiconvex domains is properly contained in the class of John disks. We give the conditions which make the converses of the above results be true. Next , we show that an exterior quasiconvex domain satisfies certain growth conditions for the exterior Riemann mapping. From the results we show that the domain satisfies the Bernstein inequality and the integrated version of it. Finally, we assume that f is a function which is continuous in the closure of a domain D and analytic in D. We show connections between the smoothness of f and the rate at which it can be approximated by polynomials on an exterior quasiconvex domain and a $Lip_\alpha$-extension domain.

• 대한수학회지
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• 제52권1호
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• pp.1-21
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• 2015

C-domains are defined via class semigroups, and every C-domain is a Mori domain with nonzero conductor whose complete integral closure is a Krull domain with finite class group. In order to extend the concept of C-domains to rings with zero divisors, we study v-Marot rings as generalizations of ordinary Marot rings and investigate their theory of regular divisorial ideals. Based on this we establish a generalization of a result well-known for integral domains. Let R be a v-Marot Mori ring, $\hat{R}$ its complete integral closure, and suppose that the conductor f = (R : $\hat{R}$) is regular. If the residue class ring R/f and the class group C($\hat{R}$) are both finite, then R is a C-ring. Moreover, we study both v-Marot rings and C-rings under various ring extensions.

• Journal of Korean Dental Science
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• 제16권2호
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• pp.156-163
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• 2023

Purpose: The aim of this study was to evaluate the feasibility of deep learning techniques to classify the morphology and severity of peri-implantitis bone defects based on periapical radiographs. Materials and Methods: Based on a pre-trained and fine-tuned ResNet-50 deep learning algorithm, the morphology and severity of peri-implantitis bone defects on periapical radiographs were classified into six groups (class I/II and slight/moderate/severe). Accuracy, precision, recall, and F1 scores were calculated to measure accuracy. Result: A total of 971 dental images were included in this study. Deep-learning-based classification achieved an accuracy of 86.0% with precision, recall, and F1 score values of 84.45%, 81.22%, and 82.80%, respectively. Class II and moderate groups had the highest F1 scores (92.23%), whereas class I and severe groups had the lowest F1 scores (69.33%). Conclusion: The artificial intelligence-based deep learning technique is promising for classifying the morphology and severity of peri-implantitis. However, further studies are required to validate their feasibility in clinical practice.

• 한국융합학회논문지
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• 제13권3호
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• pp.1-9
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• 2022

UML(Unified Modeling Language) 클래스 다이어그램은 시스템의 정적인 측면을 표현하며 분석 및 설계부터 문서화, 테스팅까지 사용된다. 클래스 다이어그램을 이용한 모델링이 소프트웨어 개발에 있어 필수적이지만, 경험이 많지 않은 모델러에게 쉽지 않은 작업이다. 도메인 카테고리별로 분류된 클래스 다이어그램 데이터 세트가 제공된다면, 모델링 작업의 생산성을 높일 수 있을 것이다. 본 논문은 클래스 다이어그램 이미지 데이터를 구축하기 위한 자동 분류 기술을 제공한다. 추가 정보 없이 단지 UML 클래스 다이어그램 이미지를 식별하고 도메인 카테고리에 따라 자동 분류한다. 먼저, 웹상에서 수집된 이미지들이 UML 클래스 다이어그램 이미지인지 여부를 판단한다. 그리고, 식별된 클래스 다이어그램 이미지에서 클래스 이름을 추출하여 도메인 카테고리에 따라 분류한다. 제안된 분류 모델은 정밀도, 재현율, F1점수, 정확도에서 각각 100.00%, 95.59%, 97.74%, 97.77%를 달성했으며, 카테고리별 분류에 대한 정확도는 81.1%와 95.2% 사이에 분포한다. 해당 실험에 사용된 클래스 다이어그램 이미지 개수가 충분히 크지 않지만, 도출된 실험 결과는 제안된 자동 분류 방식이 고려할 만한 가치가 있음을 나타낸다.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.545-556
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• 2010

A good amount of work has been done on degree of approximation of functions belonging to Lip${\alpha}$, Lip($\xi$(t),r) and W($L_r,\xi(t)$) and classes using Ces$\`{a}$ro, N$\"{o}$rlund and generalised N$\"{o}$rlund single summability methods by a number of researchers ([1], [10], [8], [6], [7], [2], [3], [4], [9]). But till now, nothing seems to have been done so far to obtain the degree of approximation of functions using (N,$p_n$)(C, 1) product summability method. Therefore the purpose of present paper is to establish two quite new theorems on degree of approximation of function $f\;\in\;Lip({\alpha},r)$ class and $f\;\in\;W(L_r,\;\xi(t))$ class by (N, $p_n$)(C, 1) product summability means of its Fourier series.

• Imaging Science in Dentistry
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• 제46권2호
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• pp.77-85
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• 2016

Purpose: To analyze the relative position of the mandibular foramina (MnFs) in patients diagnosed with skeletal class III malocclusion. Materials and Methods: Computed tomography (CT) images were collected from 85 patients. The vertical lengths of each anatomic point from the five horizontal planes passing through the MnF were measured at the coronoid process, sigmoid notch, condyle, and the gonion. The distance from the anterior ramus point to the posterior ramus point on the five horizontal planes was designated the anteroposterior horizontal distance of the ramus for each plane. The perpendicular distance from each anterior ramus point to each vertical plane through the MnF was designated the horizontal distance from the anterior ramus to the MnF. The horizontal and vertical positions were examined by regression analysis. Results: Regression analysis showed the heights of the coronoid process, sigmoid notch, and condyle for the five horizontal planes were significantly related to the height of the MnF, with the highest significance associated with the MnF-mandibular plane (coefficients of determination ($R^2$): 0.424, 0.597, and 0.604, respectively). The horizontal anteroposterior length of the ramus and the distance from the anterior ramus point to the MnF were significant by regression analysis. Conclusion: The relative position of the MnF was significantly related to the vertical heights of the sigmoid notch, coronoid process, and condyle as well as to the horizontal anteroposterior length of the ascending ramus. These findings should be clinically useful for patients with skeletal class III mandibular prognathism.

• 호남수학학술지
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• 제39권3호
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• pp.331-347
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• 2017

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive coefficients defined by a certain integral operator and a necessary and sufficient condition for a function f to be in this class. We obtain coefficient inequality, meromorphically radii of close-to-convexity, starlikeness and convexity, convex linear combinations, Hadamard product and integral transformation for the functions f in this class.