• Korean Journal of Mathematics
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• 제23권4호
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• 대한수학회지
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• 제37권3호
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• pp.391-410
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• 2000

In the complex case, we construct a q-analogue of the Riemann zeta function q(s) and a q-analogue of the Dirichlet L-function L(s,X), which interpolate the 1-analogue Bernoulli numbers. Using the properties of p-adic integrals and measures, we show that Kummer type congruences for the q-analogue Bernoulli numbers are the generalizations of the usual Kummer congruences for the ordinary Bernoulli numbers. We also construct a q0analogue of the p-adic L-function Lp(s, X;q) which interpolates the q-analogue Bernoulli numbers at non positive integers.

• 공업화학
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• 제7권2호
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• pp.379-386
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• 1996

광 이량화 특성을 나타내는 1-methyl-4-[2-(4-diethylacetylphenyl)ethenyl] pridinium methosulfate(SbQ-A염)를 dimethyl sulfate, terephthalaldehyde mono-(diethyl acetal) 및 4-picoline을 이용하여 합성하였다. 합성된 SbQ-A염을 PVA와 반응시켜 동일(MW=77,000-79,000g/mol) 분자량을 가진 PVA내 SbQ의 함량이 다른 PVA-SbQ-H 시료 및 SbQ의 함량은 약 1.3mol%로 같으나 PVA의 분자량이 다른 PVA-SbQ-L들을 합성하였다. Gray scale(GS)법을 이용하여 측정된 PVA-SbQ 수용성 감광성 고분자의 상대감도는 PVA내 SbQ의 함량이 증가함에 따라 증가하였으며, PVA의 분자량이 낮아질수록 감소하였다. PVA-SbQ-H의 경우 SbQ 함량이 2.63mol%인 시료는 PVA에 ammonium dichromate가 혼합된 기존시료보다 90배 증가된 감도를 나타내었다. PVA-SbQ를 사용하여 형광체 슬러리를 제조하고 사진식각공정을 거쳐 형광체의 미세패턴을 형성하였다. 형광체 슬러리 제조시 양이온 계면활성제인 cetyltrimethyl ammonium chloride를 첨가제로 사용하면 형광면의 해상도가 증가됨을 알았다.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.331-345
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• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• 한국전자거래학회지
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• 제16권2호
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• pp.143-158
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• 2011

본 연구는 Q&A(question and answer:질문-답변) 커뮤니티 사이트에서 집단지성의 특성을 추출하고, 이를 이용한 전문지식이나 정보 검색을 위한 전문영역 검색(vertical search) 을 위한 프레임워크를 제안한다, 많은 Q&A 사이트로부터 얻은 정보는 하나의 집단지성의 형태로 볼 수 있으며, 전문영역 검색은 특정 전문 분야 검색에 초점을 맞춘 검색 방법이다. 제안된 프레임워크는 사용자가 검색하고자 하는 질의어와 연관되어 있는 질문(question)과 답변(answer) 정보를 이용하여 관련어를 확장한 후, 이를 기반으로 전문지식을 요구하는 특정 도메인분야에 적용하게 된다. 이를 통해 일반 검색 엔진을 통해 검색된 검색 결과보다 유용한 정보와 전문적인 상세정보까지 제공해 줄 수 있다.

• 호남수학학술지
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• 제39권4호
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• pp.527-559
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• 2017

The main motivation of this article is to generalized the concept of fuzzy ideals, (${\alpha},{\beta}$)-fuzzy ideals, (${\in},{\in}{\vee}q_k$)-fuzzy ideals of semigroups. By using the concept of $q^{\delta}_K$-quasi-coincident of a fuzzy point with a fuzzy set, we introduce the notions of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal of a semigroup. Special sets, so called $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set, condition for the $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set-set to be left (resp. right) ideals are considered. We finally characterize different classes of semigroups (regular, left weakly regular, right weakly regular) in term of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy ideal of semigroup S.

• 한국정보과학회논문지:소프트웨어및응용
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• 제31권11호
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• pp.1431-1438
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• 2004

강화학습(reinforcement learning)은 온라인으로 환경(environment)과 상호작용 하는 과정을 통하여 목표를 이루기 위한 전략을 학습한다. 강화학습의 기본적인 알고리즘인 Q-learning의 학습 속도를 가속하기 위해서, 거대한 상태공간 문제(curse of dimensionality)를 해결할 수 있고 강화학습의 특성에 적합한 함수 근사 방법이 필요하다. 본 논문에서는 이러한 문제점들을 개선하기 위해서, 온라인 퍼지 클러스터링(online fuzzy clustering)을 기반으로 한 Fuzzy Q-Map을 제안한다. Fuzzy Q-Map은 온라인 학습이 가능하고 환경의 불확실성을 표현할 수 있는 강화학습에 적합한 함수근사방법이다. Fuzzy Q-Map을 마운틴 카 문제에 적용하여 보았고, 학습 초기에 학습 속도가 가속됨을 보였다.

• 대한수학회지
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• 제60권3호
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• pp.565-586
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• 2023

We study the Dirichlet problem for the degenerate nonlocal parabolic equation u_t - a(||∇u||²_L²(Ω))∆u = C_b ||u||^β_L²(Ω) |u|^q(x,t)-2 u log |u| + f in Q_T, where Q_T := Ω × (0, T), T > 0, Ω ⊂ ℝ^N, N ≥ 2, is a bounded domain with a sufficiently smooth boundary, q(x, t) is a measurable function in Q_T with values in an interval [q^-, q⁺] ⊂ (1, ∞) and the diffusion coefficient a(·) is a continuous function defined on ℝ₊. It is assumed that a(s) → 0 or a(s) → ∞ as s → 0⁺, therefore the equation degenerates or becomes singular as ||∇u(t)||2 → 0. For both cases, we show that under appropriate conditions on a, β, q, f the problem has a global in time strong solution which possesses the following global regularity property: ∆u ∈ L²(Q_T) and a(||∇u||²_L²(Ω))∆u ∈ L²(Q_T ).

• East Asian mathematical journal
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• 제36권1호
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Journal of Power Electronics
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• 제16권5호
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• pp.1716-1724
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• 2016

This paper proposes both an active-switched quasi-Z-source inverter (AS-qZSI) and an extended active-switched qZSI (EAS-qZSI), which are based on the classic qZSI. The proposed AS-qZSI adds only one active switch and one diode to the classic qZSI for increasing the voltage boost capability. Compared with other topologies based on the switched-inductor/capacitor qZSI, the proposed AS-qZSI requires fewer passive components in the impedance network under the same boost capability. Additionally, the proposed EAS-qZSI is designed by adding one inductor and three diodes to the AS-qZSI, which offers enhanced boost capability and lower voltage stress across the switches. The performances of the two proposed topologies are verified by simulation and experimental results obtained from a prototype with a 32-bit DSP built in a laboratory.