• Title/Summary/Keyword: $L^p$ space

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Symmetry Properties of 3-dimensional D'Atri Spaces

  • Belkhelfa, Mohamed;Deszcz, Ryszard;Verstraelen, Leopold
    • Kyungpook Mathematical Journal
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    • v.46 no.3
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    • pp.367-376
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    • 2006
  • We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

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Detection of the fluorescent emission of hydrogen in the Taurus cloud

  • Dae-Hui Lee;In-Su Yuk;Jang-Hyeon Park;Ho Jin;Gwang-Il Seon;Uk-Won Nam;Won-Yong Han;Gyeong-Uk Min;Gwang-Seon Yu
    • Bulletin of the Korean Space Science Society
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    • 2004.04a
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    • pp.99-99
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    • 2004
  • We detected and analyzed molecular hydrogen fluorescence in the Taurus Cloud using the Far-ultraviolet Imaging Spectrograph (FIMS) on the STSAT-1 which was launched at SeP. 27 2003. FIMS is optimized for observing diffuse emission lines in the interstellar medium in the wavelength bands of 900-l150 and 1300-1700 angstrom. The Taurus region is a local molecular cloud which is good for studying molecular hydrogen fluorescence emissions. (omitted)

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The consistency estimation in nonlinear regression models with noncompact parameter space

  • Park, Seung-Hoe;Kim, Hae-Kyung;Jang, Sook-Hee
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.377-383
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    • 1996
  • We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

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Inorganic Nutrient Removal Efficiency of Aquatic Plants from Recirculating Aquaculture System (수생식물을 이용한 담수 순환여과식 양식용수내의 무기영양염 처리 효율)

  • 마진석;오승용;조재윤
    • Journal of Aquaculture
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    • v.16 no.3
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    • pp.171-178
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    • 2003
  • Inorganic nutrients such as nitrogen and phosphate compounds accumulate in recirculating aquaculture systems. These nutrients must be removed from the system before they affect pH and fish health. For this purpose, aquatic plants are a simple and inexpensive method of removal. There are four commonly used aquatic plants: Eichhornia crassipes (water hyacinth), Pistia stratiotes (water lettuce), Hygrophila angustifolia, and Hydrocotyle leucocephala in freshwater recirculating aquaculture systems in Korea, but their efficiencies are not known. Therefore, removal efficiencies of inorganic nutrients from a freshwater recirculating aquaculture water with four commonly used aquatic plants were tested. Removing efficiencies of TAN, N $O_2$$^{[-10]}$ -N, and N $O_3$$^{[-10]}$ -N of the plants in 210 L aquaria for 48-hour period were tested. The removing efficiencies of TAN, N $O_3$$^{[-10]}$ -N, and P $O_4$$^{3-}$-P of the two most effective plants, water hyacinth and water lettuce, were also tested in 690 L (surface area of 1.55 $m^2$) tanks under 2 different initial stocking densities, 4 kg and 6 kg, for 22 days. Proximate analysis major nutrients and N and P contents of the all plants were analyzed for calculating net removal weight of N and P by the plants. Water lettuce was the most effective for removing TAN, N $O_2$$^{[-10]}$ -N, and N $O_3$$^{[-10]}$ -N from the water for 48-hour period tested followed by water hyacinth and Hygrophila angustifolia. Water lettuce reduced TAN, N $O_2$$^{[-10]}$ -N, and N $O_3$$^{[-10]}$ -N concentration from 2.3 mg/L, 0.197 mg/L, and 21.4 mg/L to 0.4 mg/L, 0.024 mg/L and 17.4 mg/L, respectively while water hyacinth reduced them down to 0.6 mg/L, 0.029 mg/L and 17.9 mg/L, respectively. The concentrations of TAN, N $O_2$$^{[-10]}$ -N, and N $O_3$$^{[-10]}$ -N in Hydrocotyle leucocephala group were rather increased up to 3.7 mg/L, 5.7 mg/L and 48.2 mg/L, respectively. This is because the creeping stem of Hydrocotyle leucocephala had to be cut to meet stocking weight resulting in decaying of the stem in the aquaria during experiment. The net growth in weight of water hycinth and water lettuce of 4 kg each in the 1.55 $m^2$ tanks for 22 days were 9.768 kg and 10.803 kg respectively, and those at initial weight of 6 kg each were 8.393 kg and 9.433 kg, respectively. The reason of lower net growth in the later group was restricted growth space. Nitrogen and phosphorus contents in water hyacinth were 2.89% and 0.27%, and those in water lettuce were 3.87% and 0.36%, respectively. Average quantities of removed N and P from 1.55 $m^2$ tanks by water hyacinth for 22 days were 18.9 g and 1.75 g, while those by water lettuce were 36.8 g and 3.5 g, respectively. Therefore water lettuce showed much higher efficiencies for removing both N and P from recirculating aquaculture water than water hyacinth.

HADAMARD-TYPE FRACTIONAL CALCULUS

  • Anatoly A.Kilbas
    • Journal of the Korean Mathematical Society
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    • v.38 no.6
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    • pp.1191-1204
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    • 2001
  • The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

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HOLOMORPHIC MEAN LIPSCHITZ FUNCTIONS ON THE UNIT BALL OF ℂn

  • Kwon, Ern Gun;Cho, Hong Rae;Koo, Hyungwoon
    • Journal of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.189-202
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    • 2013
  • On the unit ball of $\mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${\int}_0^1\;{\omega}_p(t,f)^q\frac{dt}{t^1+{\alpha}q}\;<\;{\infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${\omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $\mathbb{C}^n$.

A CHARACTERIZATION OF WEIGHTED BERGMAN-PRIVALOV SPACES ON THE UNIT BALL OF Cn

  • Matsugu, Yasuo;Miyazawa, Jun;Ueki, Sei-Ichiro
    • Journal of the Korean Mathematical Society
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    • v.39 no.5
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    • pp.783-800
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    • 2002
  • Let B denote the unit ball in $C^n$, and ν the normalized Lebesgue measure on B. For $\alpha$ > -1, define $dv_\alpha$(z) = $c_\alpha$$(1-\midz\mid^2)^{\alpha}$dν(z), z $\in$ B. Here $c_\alpha$ is a positive constant such that $v_\alpha$(B) = 1. Let H(B) denote the space of all holomorphic functions in B. For $p\geq1$, define the Bergman-Privalov space $(AN)^{p}(v_\alpha)$ by $(AN)^{p}(v_\alpha)$ = ${f\inH(B)$ : $\int_B{log(1+\midf\mid)}^pdv_\alpha\;<\;\infty}$ In this paper we prove that a function $f\inH(B)$ is in $(AN)^{p}$$(v_\alpha)$ if and only if $(1+\midf\mid)^{-2}{log(1+\midf\mid)}^{p-2}\mid\nablaf\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case 1<p<$\infty$, or $(1+\midf\mid)^{-2}\midf\mid^{-1}\mid{\nabla}f\mid^2\;\epsilon\;L^1(v_\alpha)$ in the case p = 1, where $nabla$f is the gradient of f with respect to the Bergman metric on B. This is an analogous result to the characterization of the Hardy spaces by M. Stoll [18] and that of the Bergman spaces by C. Ouyang-W. Yang-R. Zhao [13].

Pleural Space Elastance and Its Relation to Success Rates of Pleurodesis in Malignant Pleural Effusion

  • Masoud, Hossam Hosny;El-Zorkany, Mahmoud Mohamed;Ahmed, Azza Anwar;Assal, Hebatallah Hany
    • Tuberculosis and Respiratory Diseases
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    • v.84 no.1
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    • pp.67-73
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    • 2021
  • Background: Pleurodesis fails in 10%-40% of patients with recurrent malignant pleural effusions malignant pleural effusion and dyspnea. This study aimed to assess the values of pleural elastance (PEL) after the aspiration of 500 mL of pleural fluid and their relation to the pleurodesis outcome, and to compare the pleurodesis outcome with the chemical characteristics of pleural fluid. Methods: A prospective study was conducted in Kasr El-Aini Hospital, Cairo University, during the period from March 2019 to January 2020. The study population consisted of 40 patients with malignant pleural effusion. The measurement of PEL after the aspiration of 500 mL of fluid was done with "PEL 0.5" (cm H2O/L), and the characteristics of the pleural fluid were chemically and cytologically analyzed. Pleurodesis was done and the patients were evaluated one month later. The PEL values were compared with pleurodesis outcomes. Results: After 4-week of follow-up, the success rate of pleurodesis was 65%. The PEL 0.5 was significantly higher in failed pleurodesis than it was in successful pleurodesis. A cutoff point of PEL 0.5 >14.5 cm H2O/L was associated with pleurodesis failure with a sensitivity and specificity of 93% and 100%, respectively. The patients with failed pleurodesis had significantly lower pH levels in fluid than those in the successful group (p<0.001). Conclusion: PEL measurement was a significant predictor in differentiating between failed and successful pleurodesis. The increase in acidity of the malignant pleural fluid can be used as a predictor for pleurodesis failure in patients with malignant pleural effusion.

NORMAL WEIGHTED BERGMAN TYPE OPERATORS ON MIXED NORM SPACES OVER THE BALL IN ℂn

  • Avetisyan, Karen L.;Petrosyan, Albert I.
    • Journal of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.313-326
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    • 2018
  • The paper studies some new ${\mathbb{C}}^n$-generalizations of Bergman type operators introduced by Shields and Williams depending on a normal pair of weight functions. We find the values of parameter ${\beta}$ for which these operators are bounded on mixed norm spaces L(p, q, ${\beta}$) over the unit ball in ${\mathbb{C}}^n$. Moreover, these operators are bounded projections as well, and the images of L(p, q, ${\beta}$) under the projections are found.

Citric Acid Production and Scale-up in Dual Hollow Fiber Bioreactor (이중실관 생물 반응기에서의 구연산 생산과 Scale-up)

  • 장호남;지동진;심상준
    • Membrane Journal
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    • v.2 no.2
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    • pp.122-128
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    • 1992
  • A study on the citric acid production was performed in various size dual hollow fiber bioreactors with immobilized Aspergillus niger (KCTC 1232). The final dry cell mass density reached 300g/l based on the space volume available for cell growth. Under air and oxygen aeration the volumethe productivity reached 0.63 and 1.02g/l.h, which cormsponded to 10 and 16 fold over those of batch fermentation, respectively. The initial pH of the medium was a critical factor and the lower value resulted in higher citric acid yield. The increase in the feeding rate of medium or the number of reactor unit resulted in the improvement of the productivity due to higher consumption rate of substrate.

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