• Title/Summary/Keyword: ${\sigma}$-derivation

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A STUDY OF DIFFERENTIAL IDENTITIES ON 𝜎-PRIME RINGS

  • Adnan Abbasi;Md. Arshad Madni;Muzibur Rahman Mozumder
    • Communications of the Korean Mathematical Society
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    • v.38 no.3
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    • pp.679-693
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    • 2023
  • Let 𝓡 be a 𝜎-prime ring with involution 𝜎. The main objective of this paper is to describe the structure of the 𝜎-prime ring 𝓡 with involution 𝜎 satisfying certain differential identities involving three derivations 𝜓1, 𝜓2 and 𝜓3 such that 𝜓1[t1, 𝜎(t1)] + [𝜓2(t1), 𝜓2(𝜎(t1))] + [𝜓3(t1), 𝜎(t1)] ∈ 𝒥Z for all t1 ∈ 𝓡. Further, some other related results have also been discussed.

SHRIMP U-Pb Zircon Ages of the Jinju Formation and Silla Conglomerate, Gyeongsang Basin (경상분지 진주층 및 신라역암의 SHRIMP U-Pb 저어콘 연령분포 및 그 의미)

  • Lee, Tae-Ho;Park, Kye-Hun;Chun, Jong-Hwa;Yi, Kee-Wook
    • The Journal of the Petrological Society of Korea
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    • v.19 no.1
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    • pp.89-101
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    • 2010
  • To constrain the depositional ages of the Gyeongsang sedimeantary formations, SHRIMP U-Pb ages were determined from detrital zircons in three samples: (1) a pebble-bearing sandstone from the lowermost Jinju Formation of the Sindong Group and (2) two conglomerates from the Silla Conglomerate of the Hayang Group. Their concordia ages are $112.4{\pm}1.3(2{\sigma})$ Ma and $110.4{\pm}2.0(2{\sigma})$ Ma respectively. Such ages represent the maximum deposition ages for the lowermost Jinju Formation and Silla Conglomerate, indicating the deposition of the Jinju Formation started from late Aptian and lasted to early Albian, then deposition of the rather thin Chilgok Formation and Silla Conglomerate was followed during the Albian. The age distribution of the analyzed detrital zircons indicates the presence of protoliths, or zircons derived from them, regarding a wide span of igneous activities from Mesozoic to Archean. Among such ages, there are Mesoproterozoic, Neoproterozoic and Paleozoic igneous activities, which have not been known or seldom reported from Korean peninsula. These ages further suggest the possible presence of rocks with such ages during the deposition periods or their derivation through a long river system developed into the continents at the time of deposition.

A Review of the Progress with Statistical Models of Passive Component Reliability

  • Lydell, Bengt O.Y.
    • Nuclear Engineering and Technology
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    • v.49 no.2
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    • pp.349-359
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    • 2017
  • During the past 25 years, in the context of probabilistic safety assessment, efforts have been directed towards establishment of comprehensive pipe failure event databases as a foundation for exploratory research to better understand how to effectively organize a piping reliability analysis task. The focused pipe failure database development efforts have progressed well with the development of piping reliability analysis frameworks that utilize the full body of service experience data, fracture mechanics analysis insights, expert elicitation results that are rolled into an integrated and risk-informed approach to the estimation of piping reliability parameters with full recognition of the embedded uncertainties. The discussion in this paper builds on a major collection of operating experience data (more than 11,000 pipe failure records) and the associated lessons learned from data analysis and data applications spanning three decades. The piping reliability analysis lessons learned have been obtained from the derivation of pipe leak and rupture frequencies for corrosion resistant piping in a raw water environment, loss-of-coolant-accident frequencies given degradation mitigation, high-energy pipe break analysis, moderate-energy pipe break analysis, and numerous plant-specific applications of a statistical piping reliability model framework. Conclusions are presented regarding the feasibility of determining and incorporating aging effects into probabilistic safety assessment models.

Derivation of work-hardening exponent using continuous indentation technique (연속압입시험법을 이용한 가공경화지수의 유도)

  • Jeon, Eun-Chae;Ahn, Jeong-Hoon;Kwon, Dong-Il
    • Proceedings of the KSME Conference
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    • 2000.11a
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    • pp.256-261
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    • 2000
  • In this study, we derived work-hardening exponent using continuous indentation test technique. Continuous indentation test technique is a powerful method to evaluate mechanical properties, such as hardness, modulus, ${\sigma}-{\varepsilon}$ curves and etc. It has many merits conventional indentation test has. The relationship between true stress and mean contact pressure and between strain and indentation depth were derived. While the indenter pushes the materials, the region around the indenter is deflected elastically. It is called elastic deflection. And pile-up phenomenon related to plastic deformation around the indenter increased the contact depth, and sink-in phenomenon decreases. So we calibrated contact depth change by considering elastic deflection and pile-up/sink-in. Using calibrated contact depth we redefined the relationship between true stress and mean contact pressure and between strain and contact depth. Through these relationship we could derive work-hardening exponent by analyzing load-depth curves. And it showed good agreement with tensile test results.

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Estimation of Ultimate Lateral Resistances of Piles Using CPT Cone Resistance in Sand (사질토지반에서 콘관입저항치 $q_c$에 의한 단말뚝의 극한수평단위지지력 평가)

  • Kim, Min-Kee;Kyung, Doo-Hyun;Hong, Jung-Moo;Lee, Jun-Hwan
    • Journal of the Korean Geotechnical Society
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    • v.24 no.11
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    • pp.71-77
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    • 2008
  • In this study, CPT-based methodology for estimating the ultimate lateral resistance, $p_u$, is proposed and verified for lateral loaded piles in sandy soil. Preexistent methods estimating the ultimate lateral resistance, $p_u$, and the ultimate lateral capacity, $H_u$, of pile have been based on the vertical effective stress, relative density, and the coefficient of lateral earth pressure. Similarly, cone resistance $q_c$ in pure sandy soil is expressed by those essential factors. As correlation between $p_u$ and $q_c$ are normalized with average effective stress ${\sigma}_m$, estimation methodology for the lateral loaded pile of $p_u$ in sandy soil is proposed. The method is verified by calibration chamber test results in pure sand. The standard derivation of estimated $p_u$ is 0.279, and COV (Coefficient Of Variation) of estimated $p_u$ is 0.272. These results showed that the estimated pus by the method are analogous with the measured $p_us$ in calibration chamber test.

Temporal Variations of Ore Mineralogy and Sulfur Isotope Data from the Boguk Cobalt Mine, Korea: Implication for Genesis and Geochemistry of Co-bearing Hydrothermal System (보국 코발트 광상의 산출 광물종 및 황동위원소 조성의 시간적 변화: 함코발트 열수계의 성인과 지화학적 특성 고찰)

  • Yun, Seong-Taek;Youm, Seung-Jun
    • Economic and Environmental Geology
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    • v.30 no.4
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    • pp.289-301
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    • 1997
  • The Boguk cobalt mine is located within the Cretaceous Gyeongsang Sedimentary Basin. Major ore minerals including cobalt-bearing minerals (loellingite, cobaltite, and glaucodot) and Co-bearing arsenopyrite occur together with base-metal sulfides (pyrrhotite, chalcopyrite, pyrite, sphalerite, etc.) and minor amounts of oxides (magnetite and hematite) within fracture-filling $quartz{\pm}actinolite{\pm}carbonate$ veins. These veins are developed within an epicrustal micrographic granite stock which intrudes the Konchonri Formation (mainly of shale). Radiometric date of the granite (85.98 Ma) indicates a Late Cretaceous age for granite emplacement and associated cobalt mineralization. The vein mineralogy is relatively complex and changes with time: cobalt-bearing minerals with actinolite, carbonates, and quartz gangues (stages I and II) ${\rightarrow}$ base-metal sulfides, gold, and Fe oxides with quartz gangues (stage III) ${\rightarrow}$ barren carbonates (stages IV and V). The common occurrence of high-temperature minerals (cobalt-bearing minerals, molybdenite and actinolite) with low-temperature minerals (base-metal sulfides, gold and carbonates) in veins indicates a xenothermal condition of the hydrothermal mineralization. High enrichment of Co in the granite (avg. 50.90 ppm) indicates the magmatic hydrothermal derivation of cobalt from this cooling granite stock, whereas higher amounts of Cu and Zn in the Konchonri Formation shale suggest their derivations largely from shale. The decrease in temperature of hydrothermal fluids with a concomitant increase in fugacity of oxygen with time (for cobalt deposition in stages I and II, $T=560^{\circ}C-390^{\circ}C$ and log $fO_2=$ >-32.7 to -30.7 atm at $350^{\circ}C$; for base-metal sulfide deposition in stage III, $T=380^{\circ}-345^{\circ}C$ and log $fO_2={\geq}-30.7$ atm at $350^{\circ}C$) indicates a transition of the hydrothermal system from a magmatic-water domination toward a less-evolved meteoric-water domination. Sulfur isotope data of stage II sulfide minerals evidence that early, Co-bearing hydrothermal fluids derived originally from an igneous source with a ${\delta}^{34}S_{{\Sigma}S}$ value near 3 to 5‰. The remarkable increase in ${\delta}^{34}S_{H2S}$ values of hydrothermal fluids with time from cobalt deposition in stage II (3-5‰) to base-metal sulfide deposition in stage III (up to about 20‰) also indicates the change of the hydrothermal system toward the meteoric water domination, which resulted in the leaching-out and concentration of isotopically heavier sulfur (sedimentary sulfates), base metals (Cu, Zn, etc.) and gold from surrounding sedimentary rocks during the huge, meteoric water circulation. We suggest that without the formation of the later, meteoric water circulation extensively through surrounding sedimentary rocks the Boguk cobalt deposits would be simple veins only with actinolite + quartz + cobalt-bearing minerals. Furthermore, the formation of the meteoric water circulation after the culmination of a magmatic hydrothermal system resulted in the common occurrence of high-temperature minerals with later, lower-temperature minerals, resulting in a xenothermal feature of the mineralization.

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