• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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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.

• The Pure and Applied Mathematics
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• v.21 no.3
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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.

• The Journal of Korean Philosophical History
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• no.57
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• pp.57-90
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• 2018

In this discussion, as a way to verify the existence of the system to regulate Zhou dynasty's $z{\bar{o}}ng-mi{\grave{a}}o$(宗廟) numbers, the discussion was focused on '$mi{\grave{a}}o$ (廟)' and '$g{\bar{o}}ng$(宮)' in the records of "$Ch{\bar{u}}n-qi{\bar{u}}$(春秋)". As for the parts where the contents of scripture sentences were not specific, the context of the case was investigated through the writings in "$Zu{\breve{o}}-zhu{\grave{a}}n$(左傳)" and other materials. In the cases of the usage of the letter, '$mi{\grave{a}}o$(廟 : a ruler's house, a nation's royal court)', in the scripture sentences in "$Ch{\bar{u}}n-qi{\bar{u}}$(春秋)", the followings need to be noticed. In $t{\grave{a}}i-mi{\grave{a}}o$(太廟) of State $L{\check{u}}$(魯), nationwide events and a ruler's political ancestral rite, $d{\grave{i}}$(?) ritual, were performed, and fancy tools for ancestral rites used in those rituals were equipped. As for the $z{\bar{o}}ng-mi{\grave{a}}o$(宗廟) of a ruler of those times, a ritual of royal court, $ch{\acute{a}}o$(朝) rite, was performed. The usage case of the letter, '$g{\bar{o}}ng$(宮 : house)', is as the following. In $g{\bar{o}}ng$(宮) where a ruler's personal family lived was a family ancestral rite for them carried out. The record about the ornate decorating for the $hu{\acute{a}}n-g{\bar{o}}ng$ house(桓宮), which can be said to have been the political base of $s{\bar{a}}n-hu{\acute{a}}n-sh{\grave{i}}$(三桓氏), three politically noble families of State $L{\check{u}}$(魯), is outstanding. The $x{\bar{i}}-g{\bar{o}}ng$ house(西宮) during $X{\bar{i}}-g{\bar{o}}ng$(魯 僖公)'s reign and a $x{\bar{i}}n-g{\bar{o}}ng$ house(新宮 : a newly built house) destroyed by fire at the third year of $Ch{\acute{e}}ng-g{\bar{o}}ng$(魯 成公), are assumed to have been a ruler's another house, such as the $ch{\check{u}}-g{\bar{o}}ng$ house(楚宮) in which $Xi{\bar{a}}ng-g{\bar{o}}ng$(魯 襄公) used to enjoy staying, which is different from the viewpoint that it might be a $m{\acute{i}}-g{\bar{o}}ng$ shrine(?宮 : a house constructed as a shrine for the deceased father or the deceased grand father) that had been formed since Han dynasty. It has been discussed that, regarding the records that the '$w{\check{u}}-g{\bar{o}}ng$ house(武宮) was built' and that the '$y{\acute{a}}ng-g{\bar{o}}ng$ house(煬宮) was built', certain buildings were established with the symbols of '$w{\check{u}}$(武 : martial arts and force of arms)' and '$y{\acute{a}}ng$(煬 : to burn and get rid of everything)', and the events that a lord stood as its lord continued. Therefore, its main goal was not the performance of a dutiful ancestral rite by a ruler of those times for deceased rulers, for instance, $W{\check{u}}-g{\bar{o}}ng$(魯 武公) or $Y{\acute{a}}ng-g{\bar{o}}ng$(魯 煬公), but display of certain political symbolism through the ritual. This symbolism is most obvious with the $hu{\acute{a}}n-g{\bar{o}}ng$ house(桓宮) and the $x{\bar{i}}-g{\bar{o}}ng$ house(僖宮). As a consequence, all $mi{\grave{a}}os$(廟) and $g{\bar{o}}ngs$(宮) in scripture sentences had the functions of a shrine in some part, but it has been verified that they were not the buildings set up as a shrine to follow '$z{\bar{o}}ng-mi{\grave{a}}o$(宗廟)'s number regulation system' of '$ti{\bar{a}}nz{\check{i}}-7-mi{\grave{a}}o$(天子七廟 : an emperor owns seven $mi{\grave{a}}os$(廟))' or '$zh{\bar{u}}h{\acute{o}}u-5-mi{\grave{a}}o$(諸侯五廟 : a lord owns five $mi{\grave{a}}os$(廟))'.

• East Asian mathematical journal
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• v.21 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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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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• v.30 no.2
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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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• v.31 no.1
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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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• v.44 no.5
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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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• 2003.11a
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• pp.680-696
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• 2003

• East Asian mathematical journal
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• v.6 no.1
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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 $x{\varepsilon}D(A)$.