• Title/Summary/Keyword: lim sup

Search Result 1,213, Processing Time 0.028 seconds

INDUCTIVE LIMIT IN THE CATEGORY OF C* -TERNARY RINGS

  • Arpit, Kansal;Ajay, Kumar;Vandana, Rajpal
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.1
    • /
    • pp.137-148
    • /
    • 2023
  • We show the existence of inductive limit in the category of C*-ternary rings. It is proved that the inductive limit of C*-ternary rings commutes with the functor 𝓐 in the sense that if (Mn, ϕn) is an inductive system of C*-ternary rings, then $\lim_{\rightarrow}$ 𝓐(Mn) = 𝓐$(\lim_{\rightarrow}\;M_{n})$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of C*-ternary rings have been investigated. Finally we obtain $\lim_{\rightarrow}\;M_{n}^{**}$ = $(\lim_{\rightarrow}\;M_{n})^{**}$.

Characterization of Repeated Deactivation and Subsequent Re-activation of Photocatalyst Used in Two Alternatively-operating UV/photocatalytic Reactors of Waste-air Treating System (교대로 운전되는 두 개의 UV/광촉매반응기로 구성된 폐가스 처리시스템에서의 광촉매의 비활성화 및 재생 특성)

  • Lee, Eun Ju;Chung, Chan Hong;Lim, Kwang-Hee
    • Korean Chemical Engineering Research
    • /
    • v.59 no.4
    • /
    • pp.584-595
    • /
    • 2021
  • In this study, the correlation between operating stages of waste air-treating system composed of two alternatively-operating UV/photocatalytic reactors, and the deactivation of photocatalyst used in each operating stage, was investigated by instrumental analysis thereon. The repeated deactivation and subsequent re-generation of photocatalyst used in the waste air treating system of previous investigation performed by Lee and Lim (Korean Chem. Eng. Research, 59(4), 574-583(2021)), were characterized on virgin photocatalyst-carrying porous SiO2 media (A4), used photocatalyst-carrying porous SiO2 media (A1, A2 and A3) collected from the corresponding photocatalytic reactor upon 1st, 2nd, and 3rd run, respectively, regenerated photocatalyst-carrying porous SiO2 media upon 1 time-run (AD1) and 3 times regenerated photocatalyst-carrying porous SiO2 media upon 3 time-runs (AD3) by instrumental analysis including BET analysis, SEM, XPS, SEM-EDS and FT-IR. As a result, the proper regeneration-temperature for deactivated photocatalyst to be regenerated several times (more than 3 times), was suggested below 200 ℃. Such temperature of deactivated photocatalyst-regeneration was almost consistent to the one, according to BET analysis, at which tiny nano-pores blocked by adsorbed ethanol-oxidative and degraded intermediates (AEODI), were regenerated to be reopened through almost complete mineralization of AEODI. In particular, the results of XPS analysis indicated an incurrence of insignificant deactivation of photocatalysis upon 1st run of UV/photocatalytic reactor (A or C) of the previous investigation. In addition, the results of XPS analysis were consistent with the experimental results of the previous investigation in that 1) deactivation of photocatalyst incurred during 2nd run of the UV/photocatalytic reactor (A or C) resulted in decreased removal efficiency, by ca. 5% and 5%, of ethanol and hydrogen sulfide, respectively, compared with its 1st run; 2) there was insignificant difference between the removal efficiencies of its 2nd run and 3rd run. Furthermore, the removal efficiencies of ethanol and hydrogen sulfide for hypothetical 4th run of photocatalytic reactor in the previous investigation, using AD3, were expected to decrease, compared with its 3rd run, by much more than those for 2nd run in the previous investigation did, compared with its 1st run.

Radioactivity concentrations of natural radionuclides in fine dust of Jeju, Korea

  • Chung-Hun Han;Sohyeon Lim;Hee-Jung Im
    • Analytical Science and Technology
    • /
    • v.36 no.4
    • /
    • pp.191-197
    • /
    • 2023
  • Radioactivity concentrations for natural radionuclides were determined from fine dust samples collected in Jeju, Korea according to atmospheric events (Asian dust, haze, fog-mist, and non-event), and radium equivalent activity was calculated. The mean atmospheric radioactivity concentrations for 238U, 232Th, and 40K in 127 fine dust samples were 0.49, 0.24, and 7.23 µBq m-3, respectively, and the radium equivalent activity was 33.25 Bq kg-1. The mean concentrations of 238U and 232Th in the fine dust during the Asian dust period were 1.31 and 1.60 µBq m-3, respectively, above the global average, while the values for the other three atmospheric events were lower. The ratio of 232Th/238U radioactivity during the Asian dust period was 1.22, higher than the ratio for the other three atmospheric events.

Bombesin-based Radiopharmaceuticals for Imaging and Therapy of Cancers Expressing Gastrin-releasing Peptide Receptor

  • Hwi-Soo Lim;Choong Mo Kang
    • Journal of Radiopharmaceuticals and Molecular Probes
    • /
    • v.8 no.2
    • /
    • pp.129-137
    • /
    • 2022
  • Bombesin has a high binding affinity to gastrin-releasing peptide receptor (GRPR) and can be used as a targeting ligand in GRPR-related cancers. Because GRPR is overexpressed in prostate cancer, bombesin analogues have been investigated extensively for diagnosis and treatment of prostate cancer. In nuclear medicine, bombesin derivatives labeled with radiometals such as 55/57Co, 64Cu, 68Ga, 99mTc, and 177Lu or radiohalogen such as 131I and 211At were developed as markers for early detection of tumors and theragnostic tool for cancer treatment. This review focuses on the introduction of bombesin-based radiopharmaceuticals that are studied in pre-clinical or clinical research.

GREEN'S ADDITIVE COMPLEMENT PROBLEM FOR k-TH POWERS

  • Ding, Yuchen;Wang, Li-Yuan
    • Journal of the Korean Mathematical Society
    • /
    • v.59 no.2
    • /
    • pp.299-309
    • /
    • 2022
  • Let k ⩾ 2 be an integer, Sk = {1k, 2k, 3k, …} and B = {b1, b2, b3, …} be an additive complement of Sk, which means all sufficiently large integers can be written as the sum of an element of Sk and an element of B. In this paper we prove that $${{\lim}\;{\sup}}\limits_{n{\rightarrow}{\infty}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^{\frac{k}{k-1}}{\Gamma}(1+{\frac{1}{k}})^{\frac{k}{k-1}}n^{\frac{k}{k-1}}-b_n}{n}}\;{\geqslant}\;{\frac{k}{2(k-1)}}\;{\frac{{\Gamma}(2-{\frac{1}{k}})^2}{{\Gamma}(2-{\frac{2}{k}})}},$$ where 𝚪(·) is Euler's Gamma function.