• 대한수학회지
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• 제59권5호
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• pp.911-926
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• 2022

Let u be a function on a locally finite graph G = (V, E) and Ω be a bounded subset of V. Let 𝜀 > 0, p > 2 and 0 ≤ λ < λ₁(Ω) be constants, where λ₁(Ω) is the first eigenvalue of the discrete Laplacian, and h : V → ℝ be a function satisfying h ≥ 0 and $h{\not\equiv}0$. We consider a perturbed Yamabe equation, say $$\{\begin{array}{lll}-{\Delta}u-{\lambda}u={\mid}u{\mid}^{p-2}u+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω and ∂Ω denote the interior and the boundary of Ω, respectively. Using variational methods, we prove that there exists some positive constant 𝜀₀ > 0 such that for all 𝜀 ∈ (0, 𝜀₀), the above equation has two distinct solutions. Moreover, we consider a more general nonlinear equation $$\{\begin{array}{lll}-{\Delta}u=f(u)+{\varepsilon}h,&&\text{ in }{\Omega},\\u=0,&&\text{ on }{\partial}{\Omega},\end{array}$$ and prove similar result for certain nonlinear term f(u).

• 대한수학회보
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• 제60권4호
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• pp.863-872
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• 2023

Let n ⩾ 2 be an integer, we denote the smallest integer b such that gcd {(ⁿ_k) : b < k < n - b} > 1 as b(n). For any prime p, we denote the highest exponent α such that p^α | n as v_p(n). In this paper, we partially answer a question asked by Hong in 2016. For a composite number n and a prime number p with p | n, let n = a_mp^m + r, 0 ⩽ r < p^m, 0 < a_m < p. Then we have $$v_p\(\text{gcd}\{\(n\\k\)\;:\;b(n)1\}\)=\{\array{1,&&a_m=1\text{ and }r=b(n),\\0,&&\text{otherwise.}}$$

• 영어영문학
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• 제57권5호
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• pp.871-887
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• 2011

In Lacanian terms, the real, which is a non-representative Ding an sich, is indirectly approachable only in and through language. This 'speaking of the real' is made possible through a restoration of the missing link between one signifier, S1 and another signifier, S₂, as is manifested in the Lacanian formula of metaphor. In Freudian terms of textual metaphor, the missing link is restored by substituting a new edition for an old edition of one's historical text of life. This is what this essay means by the metaphorical/dualistic structure of the analytic/literary text. And this is a way of talking about an intertextuality between literature and psychoanalysis in the sense of the 'text as psyche' and the 'psyche as text.' Applying the 'signifying substitution' to the Oedipus complex, the Oedipal child can find a meaning(s), "my erotic indulgement with my Mom is wrong" by metaphorically substituting S₂: the Name of the Father for S1: the Desire of the Mother. This meaning leads to the constitution of the human subject and the formation of the incest taboo, one of the most significant distinctive features of the human being as distinguished from the animals. We can see a similar metaphorical structure of S1-S2 taking place in the literary texts such as Macbeth and "Dover Beach": in the course of the stage of life being substituted for the primal scene in the former, and the plain of Tucydides for a bed scene in the latter, respectively.

• Journal of information and communication convergence engineering
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• 제20권4호
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• pp.309-316
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• 2022

This investigation is aimed at automatic text summarization on large-scale Vietnamese datasets. Vietnamese articles were collected from newspaper websites and plain text was extracted to build the dataset, that included 1,101,101 documents. Next, a new single-document extractive text summarization model was proposed to evaluate this dataset. In this summary model, the k-means algorithm is used to cluster the sentences of the input document using different text representations, such as BoW (bag-of-words), TF-IDF (term frequency - inverse document frequency), Word2Vec (Word-to-vector), Glove, and FastText. The summary algorithm then uses the trained k-means model to rank the candidate sentences and create a summary with the highest-ranked sentences. The empirical results of the F1-score achieved 51.91% ROUGE-1, 18.77% ROUGE-2 and 29.72% ROUGE-L, compared to 52.33% ROUGE-1, 16.17% ROUGE-2, and 33.09% ROUGE-L performed using a competitive abstractive model. The advantage of the proposed model is that it can perform well with O(n,k,p) = O(n^(k+2/p)) + O(nlog₂n) + O(np) + O(nk²) + O(k) time complexity.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.689-702
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• 2019

Let 𝓐 and 𝓑 be real (or complex) algebras. We investigate the stability of a sequence F = {f₀, f₁, ⋯, f_n, ⋯ } of mappings from 𝓐 into 𝓑 satisfying the higher functional equation: $$f_n(x+y+zw)=f_n(x)+f_n(y)+\;{\normalsize\sum\limits_{\tiny{i+j=n \atop i{\leq}j}}}\;[f_i(z)f_j(w)+c_{ij}f_i(w)f_j(z)]$$ for each n = 0, 1, ⋯ and all x, y, z, w ∈ 𝓐, where $$c_{ij}=\left\{1{\text{ if }}i{\neq}j,\\0{\text{ if }}i=j.\right.$$.

• 정보처리학회논문지B
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• 제12B권6호
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• pp.703-714
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• 2005

문서 범주화 분야에 대한 연구들은 전체 문서 단위에 한정되어 왔으나, 오늘날 대부분의 전문들이 주요 주제를을 표현하기 위해서 조직화 된 특정 구조로 기술되고 있어, 텍스트 범주화에 대한 새로운 인식이 필요하게 되었다. 이러한 구조는 부주제(Sub-topic)의 텍스트 블록이나 문단(Passage) 단위의 나열로서 표현되는데, 이러한 구조 문서에 대한 부주제 구조를 반영하기 위해서 문단 단위(Passage-based) 문서 범주화 모델을 제안한다. 제안한 모델에서는 문서를 문단들로 분리하여 각각의 문단에 범주(Category)를 할당하고, 각 문단의 범주를 전체 문서의 범주로 병합하는 방법을 사용한다. 전형적인 문서 범주화와 비교할 때, 두 가지 부가적인 절차가 필요한데, 문단 분리와 문단 병합이 그것이다. 로이터(Reuter)의 4가지 하위 집합과 수십에서 수백 KB에 이르는 전문 테스트 컬렉션(KISTl-Theses)을 이용하여 실험하였는데, 다양한 문단 타입들의 효과와 범주 병합 과정에서의 문단 위치의 중요성에 초점을 맞추었다 실험한 결과 산술적(Window) 문단이 모든 테스트 컬렉션에 대해서 가장 좋은 성능을 보였다. 또한 문단은 문서 안의 위치에 따라 주요 주제에 기여하는 바가 다른 것으로 나타났다.

• 대한수학회지
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• 제38권3호
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제16권8호
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• pp.873-877
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• 2010

CAPTCHA은 스팸이나 로봇에 의한 사이트 자동가입을 막는 계정 생성방지 도구로써, 특정 언어 또는 그림을 해독할 수 있는 인간의 우수한 가독성을 이용한 것으로 일반적으로 컴퓨터 프로그램이 해독하기 어려운 기호, 글자 등을 입력하도록 하여 스팸 또는 자동화 도구 등을 무력화 시키는 보안 기술이다. 하지만 기존에 사용되었던 CAPTCHA 방식은 웹봇 또는 이미지프로세싱, 머신 러닝을 통하여 쉽게 통과할 수 있는 것으로 알려졌다. 본 논문에서는 기존에 사용되었던 Text 기반의 CAPTCHA 시스템과는 달리 이미지 기반의 새로운 CAPTCHA 시스템을 제안한다. 본 논문에서 제공되는 시스템은 일반적으로 현상된 사진의 부분적인 이미지를 추출하여 추출된 이미지의 회전을 통하여 CAPTCHA 시스템을 제공하는 것이다. 사용자 인증은 다음과 같이 검증한다. 먼저 총 8장의 사진에서 각각 서브 이미지를 추출하여, 추출된 서브 이미지를 무작위로 회전시킨다. 무작위로 회전된 서브 이미지를 사용자가 올바르게 교정하면 사용자가 인증된다.

• 대한수학회논문집
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• 제38권3호
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• 대한수학회지
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• 제58권5호
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• pp.1181-1209
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• 2021

In the present paper, we are concerned with the existence of ground state sign-changing solutions for the following Schrödinger-Poisson-Kirchhoff system $$\;\{\begin{array}{lll}-(1+b{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+k(x){\phi}u={\lambda}f(x)u+{\mid}u{\mid}^4u,&&\text{in }{\mathbb{R}}^3,\\-{\Delta}{\phi}=k(x)u^2,&&\text{in }{\mathbb{R}}^3,\end{array}$$ where b > 0, V (x), k(x) and f(x) are positive continuous smooth functions; 0 < λ < λ₁ and λ₁ is the first eigenvalue of the problem -∆u + V(x)u = λf(x)u in H. With the help of the constraint variational method, we obtain that the Schrödinger-Poisson-Kirchhoff type system possesses at least one ground state sign-changing solution for all b > 0 and 0 < λ < λ₁. Moreover, we prove that its energy is strictly larger than twice that of the ground state solutions of Nehari type.