• 대한수학회보
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• 제59권3호
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• pp.757-780
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• 2022

In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights ω, ρ, φ and ψ to hold the following weak type modular inequality $${\mathcal{U}}^{-1}\({\int_{{\mid}{\mathcal{I}}f{\mid}>{\gamma}}}\;{\mathcal{U}}({\gamma}{\omega}){\rho}\){\leq}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}(C{\mid}f{\mid}{\phi}){\psi}\),$$ where ${\mathcal{I}}$ is the modified integral Hardy operators. We also obtain a necesary and sufficient condition for the following extra-weak type integral inequality $${\omega}\(\{{\left|{\mathcal{I}}f\right|}>{\gamma}\}\){\leq}{\mathcal{U}}{\circ}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}\(\frac{C{\mid}f{\mid}{\phi}}{{\gamma}}\){\psi}\).$$ Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.147-163
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• 2014

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions $$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

• 한국철학논집
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• 제57호
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• pp.57-90
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• 2018

본 논의에서는 주대(周代) 묘수제(廟數制)의 존재 여부를 확인하기 위한 방편으로 "춘추"의 기록 속에 나타나는 '묘'와 '궁'에 대한 집중적인 고찰을 시도하였다. 경문 내용이 구체적이지 않은 부분들은 "좌전"의 글과 기타자료들을 통해 사건의 맥락을 확인하였다. "춘추" 경문에서의 '묘(廟)'자의 쓰임 사례에서 주목할 만한 사항으로는 다음과 같다. 노나라의 태묘에서는 범국가적인 행사[事]와 제왕의 정치적인 제사 의례인 체(?) 의례를 이행하였고, 또 그와 같은 의례에 쓰이는 화려한 예기(禮器)를 구비하였다. 당대 군주의 종묘에서는 조정 의례인 조(朝)의례를 이행하였다. '궁(宮)'자의 쓰임 사례는 다음과 같다. 군주 개인의 가족이 기거했던 궁에서 그를 위한 가족 제사를 이행하였다. 노나라 삼환씨(三桓氏)의 정치적 거점이라 할 수 있는 환궁(桓宮)을 화려하게 장식한 기록이 눈에 띈다. 희공(僖公) 재위 시에 있었던 서궁(西宮)과 성공(成公) 3년에 화재로 소실된 신궁(新宮) 등은, 그것이 예궁(?宮)일 것이라는 한대 이후에 형성된 관점과는 달리, 양공(襄公)이 좋아했던 초궁(楚宮)과도 같은 군주의 또 다른 집이었을 것으로 추정한다. '무궁을 세우고'[立武宮] '양궁을 세웠다'[立煬宮]고 하는 기록은, 어떠한 건축물에 '무(武)'와 '양(煬)'이라고 하는 상징성을 부여해 설립하여 제후가 그곳의 위(位)에 서는 행사가 이어진 것임을 논하였다. 따라서 이것은 무공(武公)이나 양공(煬公) 등의 선군을 위한 당대 군주의 효성스러운 제사 이행이 주된 목적이 아니라, 그 의례를 통해 얻는 특정의 정치적 상징성을 드러내고자 한 것이었다. 이러한 상징성은 환궁(桓宮)과 희궁(僖宮)에서 가장 극명하게 나타난다. 결과적으로, 경문에서의 모든 묘와 궁들은 일정 부분 사당(祠堂)의 기능이 있긴 하지만, '천자7묘'나 '제후5묘'라는 묘수제의 규정에 맞추기 위해 사당으로서 조성한 건축물이 결코 아니었음을 확인하였다.

• East Asian mathematical journal
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• 제21권1호
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• pp.21-26
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• 2005

The purpose of this paper is to show that every generalized Jordan derivation of prime ring with characteristic not two is a generalized derivation on a nonzero Lie ideal U of R such that $u^2{\in}U\;for\;{\forall}u{\in}U$ which is a generalization of the well-known result of I. N. Herstein.

• 대한수학회보
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• 제27권2호
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• pp.113-120
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• 1990

In this paper we introduce S(X, $x_{0}$) which is a generalization of Ellis group G(X, $x_{0}$), and S-sets in S(X, $x_{0}$). In particular we cind the sufficient condition for the group A(I) of all automorphisms of I and K=Iu to be isomorphic, where I is a minimal right ideal and u is an idempotent of I.f I.

• East Asian mathematical journal
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• 제30권2호
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• pp.173-195
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• 2014

This study, utilizing several features about plane figures covered in the current secondary curriculum of mathematics and reviewing two solutions to cube duplication problem presented by Menaechmus, proving the solution by Nicomedes and visualizing solutions based on Apollonius' 'Conics' by medieval Islam geometricians such as Ab$\bar{u}$ Bakr al-Haraw$\bar{i}$, AbAb$\bar{u}$ J$\acute{a}$far al-Kh$\bar{a}$zin, Nas$\bar{i}$r al-D$\bar{i}$n al-T$\bar{u}s\bar{i}$, Y$\bar{u}$suf al-Mu'taman ibn H$\bar{u}$d, introduce to teachers and students in the field where the question of cube duplication problem comes from and which solving method has developed it and suggests new methods for visualization using dynamic geometry program as well so that the contents reviewed can be used in the filed. The solving methods to cube duplication problem in this paper are very creative and increase the practicality, efficiency and value of Mathematics, and provide students and teachers with the opportunities to reconfirm the importance and beauty of basic knowledge in the secondary geometry in the process of visualization of drawing figures using dynamic geometry program.

• ALGAE
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• 제31권1호
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• pp.49-59
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• 2016

Ulva pertusa, a common bloom-forming green alga, was used as a model system to examine the effects of elevated carbon dioxide (CO₂) and temperature on growth and photosynthetic performance. To do this, U. pertusa was grown under four temperature and CO₂ conditions; ambient CO₂ (400 μatm) and temperature (16℃) (i.e., present), elevated temperature only (19℃) (ET; i.e., warming), elevated CO₂ only (1,000 μatm) (EC; i.e., acidification), and elevated temperature and CO₂ (ET and EC; i.e., greenhouse), and its steady state photosynthetic performance evaluated. Maximum gross photosynthetic rates (GP_max) were highest under EC conditions and lowest under ET conditions. Further, ET conditions resulted in decreased rate of dark respiration (R_d), but growth of U. pertusa was higher under ET conditions than under ambient temperature conditions. In order to evaluate external carbonic anhydrase (eCA) activity, photosynthesis was measured at 70 μmol photons m⁻² s⁻¹ in the presence or absence of the eCA inhibitor acetazolamide (AZ), which inhibited photosynthetic rates in all treatments, indicating eCA activity. However, while AZ reduced U. pertusa photosynthesis in all treatments, this reduction was lower under ambient CO₂ conditions (both present and warming) compared to EC conditions (both acidification and greenhouse). Moreover, Chlorophyll a and glucose contents in U. pertusa tissues declined under ET conditions (both warming and greenhouse) in conjunction with reduced GP_max and R_d. Overall, our results indicate that the interaction of EC and ET would offset each other’s impacts on photosynthesis and biochemical composition as related to carbon balance of U. pertusa.

• Steel and Composite Structures
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• 제44권5호
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• pp.619-632
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• 2022

There are numerous structural details (Longitudinal beam, web plate, U-ribs and I-ribs) in the top and bottom plates of steel box girders, which have significant influences on the longitudinal stress (normal stress) distribution. Clarifying the influence of these structural details on the normal stress distribution is important. In this paper, the ultra-wide steel box girder with large cantilevers of the Jinhai Bridge in China, which is the widest cable-stayed bridge in the world, has been analyzed. A 1:4.5 scale laboratory model of the steel box girder has been manufactured, and the influence of structural details on the normal stress distribution in the top and bottom plates for four different load cases has been analyzed in detail. Furthermore, a three-dimensional finite element model has been established to further investigate the influence regularity of structural details on the normal stress. The experimental and finite element analysis (FEA) results have shown that different structural details of the top and bottom plates have varying effects on the normal stress distribution. Notably, the U-ribs and I-ribs of the top and bottom plates introduce periodicity to the normal stress distribution. The period of the influence of U-ribs on the normal stress distribution is the sum of the single U-rib width and the U-rib spacing, and that of the influence of I-ribs on the normal stress distribution is equal to the spacing of the I-ribs. Furthermore, the same structural details but located at different positions, will have a different effect on the normal stress distribution.

• 한국IT서비스학회:학술대회논문집
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• 한국IT서비스학회 2003년도 추계학술대회
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• pp.680-696
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• 2003

• East Asian mathematical journal
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• 제6권1호
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• pp.111-121
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• 1990

Let E be a locally convex Hausdorff space and let $\Gamma$ be a calibration for E. In this note we proved that if E is sequentially complete and a multi-vaiued operaturA in E is $\Gamma$-accretive such that $D(A){\subset}Re$ (I+$\lambda$A) for all sufficiently small positive $\lambda$, then A generates a nonlinear $\Gamma$-contraction semiproup {T(t) ; t>0}. We also proved that if E is complete, $Gamma$ is a dually uniformly convex calibration, and an operator A is m-$\Gamma$-accretive, then the initial value problem $$\{{\frac{d}{dt}u(t)+Au(t)\;\ni\;0,\;t >0,\atop u(0)=x}\.$$ has a solution $u:[0,\infty){\rightarrow}E$ given by $u(t)=T(t)x={lim}\limit_{n\rightarrow\infty}(I+\frac{t}{n}A)^{-n}x$ each $x{\varepsilon}D(A)$.