• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.15-30
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• 2024

In this paper, we focus on partial isometry elements and strongly EP elements on a ring. We construct characterizing equations such that an element which is both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have a solution in a given set. In particular, an element a ∈ R^# ∩ R^† is a partial isometry element if and only if the equation x = x(a^†)^*a^† has at least one solution in {a, a#, a^†, a^*, (a^#)^*, (a^†)^*}. An element a ∈ R^#∩R^† is a strongly EP element if and only if the equation (a^†)^*xa^† = xa^†a has at least one solution in {a, a^#, a^†, a^*, (a^#)^*, (a^†)^*}. These characterizations extend many well-known results.

• Nuclear Engineering and Technology
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• v.55 no.9
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• pp.3352-3358
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• 2023

Nuclear medicine seems to be a decent choice of medicine in the recent decade. The radioactive isotopes ⁵¹Cr, ⁸⁹Sr, ⁹⁹Tc, ¹³¹I, ¹³³Xe, ¹³⁷Cs and ¹⁵³Sm are extremely essential in nuclear medicine. The excitation functions of the ⁵⁴Fe (n, α) ⁵¹Cr, ⁹²Zr (n, α) ⁸⁹Sr, ¹⁰²Rh (n, α) ⁹⁹Tc, 134Cs (n, α) ¹³¹I, ¹³⁶Ba (n, α) ¹³³Xe, ¹⁴⁰La (n, α) ¹³⁷Cs and ¹⁵⁶Gd (n, α) ¹⁵³Sm reactions were calculated in this study using the EMPIRE 3.2.3 and TALYS 1.95 nuclear codes. Additionally, the cross sections at 14-15 MeV were calculated using empirical formulae and the experimental data. The computer codes were compared to the experimental data and Empirical formulas as well as the evaluated data (TENDL 2021, JENDL 3.3, JENDL 5, JEFF 3.3, EAF 2010, CENDL 3.1, CENDL 3.2, ROSFOND 2010, FENDL 3.2 b, and BROND 3.1).

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.99-105
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• 2022

The objective of this research paper is to prove that an additive mapping T from a semiprime ring R to itself will be centralizer having a suitable torsion restriction on R if it satisfy any one of the following algebraic equations (a) 2T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ + xⁿyⁿT(xⁿ) (b) 3T(xⁿyⁿxⁿ) = T(xⁿ)yⁿxⁿ+xⁿT(yⁿ)xⁿ+xⁿyⁿT(xⁿ) for every x, y ∈ R. Further, few extensions of these results are also presented in the framework of *-ring.

• Korean Journal of Mineralogy and Petrology
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• v.36 no.3
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• pp.185-197
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• 2023

The Gubong Au-Ag deposit consists of eight lens-shaped quartz veins. These veins have filled fractures along fault zones within Precambrian metasedimentary rock. This has been one of the largest deposits in Korea, and is geologically a mix of orogenic-type and intrusion-related types. Korea Mining Promotion Corporation drilled into a quartz vein (referred to as the No. 6 vein) with a width of 0.9 m and a grade of 27.9 g/t Au at a depth of -728 ML by drilling (No. 90-12) in the southern site of the deposit, To further investigate the potential redevelopment of the No. 6 vein, another drilling (No. 04-1) was carried out in 2004. In 2004, samples (wallrock, wallrock alteration and quartz vein) were collected from the No. 04-1 drilling core site to study the occurrence and chemical composition of Ti-bearing minerals (ilmenite, rutile). Rutile from mineralized zone at a depth of -275 ML occur minerals including K-feldspar, biotite, quartz, calcite, chlorite, pyrite in wallrock alteration zone. Ilmenite and rutile from ore vein (No. 6 vein) at a depth of -779 ML occur minerals including white mica, chlorite, apatite, zircon, quartz, calcite, pyrrhotite, pyrite in wallrock alteration zone and quartz vein. Based on mineral assemblage, rutile was formed by hydrothermal alteration (chloritization) of Ti-rich biotite in the wallrock. Chemical composition of ilmenite has maximum values of 0.09 wt.% (HfO₂), 0.39 wt.% (V₂O₃) and 0.54 wt.% (BaO). Comparing the chemical composition of rutile at a depth -275 ML and -779 ML, Rutile at a depth of -779 ML is higher contents (WO₃, FeO and BaO) than rutile at a depth of -275 ML. The substitutions of rutile at a depth of -275 ML and -779 ML are as followed : rutile at a depth of -275 ML Ba²⁺ + Al³⁺ + Hf⁴⁺ + (Nb⁵⁺, Ta⁵⁺) ↔ 3Ti⁴⁺ + Fe²⁺, 2V⁴⁺ + (W⁵⁺, Ta⁵⁺, Nb⁵⁺) ↔ 2Ti⁴⁺ + Al³⁺ + (Fe²⁺, Ba²⁺), Al³⁺ + V⁴⁺+ (Nb⁵⁺, Ta⁵⁺) ↔ 2Ti⁴⁺ + 2Fe²⁺, rutile at a depth of -779 ML 2 (Fe²⁺, Ba²⁺) + Al³⁺ + (W⁵⁺, Nb⁵⁺, Ta⁵⁺) ↔ 2Ti⁴⁺ + (V⁴⁺, Hf⁴⁺), Fe²⁺ + Al³⁺ + Hf ⁴⁺ + (W⁵⁺, Nb⁵⁺, Ta⁵⁺) ↔ 2Ti⁴⁺ + V⁴⁺ + Ba²⁺, respectively. Based on these data and chemical composition of rutiles from orogenic-type deposits, rutiles from Gubong deposit was formed in a relatively oxidizing environment than the rutile from orogenictype deposits (Unsan deposit, Kori Kollo deposit, Big Bell deposit, Meguma gold-bearing quartz vein).

• Nuclear Engineering and Technology
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• v.55 no.1
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• pp.304-309
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• 2023

In the last decade, nuclear medicine appears to be a good choice of medicine. ⁵⁸Co, ⁹⁹Mo, ⁹⁹Tc, ⁹⁹Re, ¹³³Xe and ¹⁸⁶Re are very important radionuclides for nuclear medicine. In this study, the excitation functions of ⁵⁸Ni (n, p) ⁵⁸Co, ⁹⁹Tc (n, p) ⁹⁹Mo, ⁹⁹Ru (n, p) ⁹⁹Tc, ¹³¹Xe (n, p) ¹³¹I, ¹³³Cs (n, p) ¹³³Xe and ¹⁸⁶Os (n, p) ¹⁸⁶Re nuclear reactions were calculated at neutron energies between 1 and 20 MeV using TALYS 1.95 and EMPIRE 3.2 nuclear codes. Furthermore, the cross sections were calculated with the empirical formula derived in our past study at 14-15 MeV. The obtained results were compared with the measured values in EXFOR library, and with the evaluated data of (JENDL-4.0/HE, JEFF-3.3, TENDL-2019, ENDF/B-VIII.0, IRDFF-II, JENDL/ImPACT-18). The results are in good agreement with those of the evaluated data libraries and experimental results and indicates that these radioisotopes can be produced by smaller cyclotrons.

• The Korean Journal of Physiology and Pharmacology
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• v.24 no.6
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• pp.555-561
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• 2020

TWIK-related two-pore domain K⁺ channel-2 (TREK-2) has voltage-independent activity and shows additional activation by acidic intracellular pH (pH_i) via neutralizing the E³³² in the cytoplasmic C terminal (Ct). We reported opposite regulations of TREK-2 by phosphatidylinositol 4,5-bisphosphate (PIP₂) via the alkaline K³³⁰ and triple Arg residues (R^355-357); inhibition and activation, respectively. The G³³⁴ between them appeared critical because its mutation (G³³⁴A) endowed hTREK-2 with tonic activity, similar to the mutation of the inhibitory K³³⁰ (K³³⁰A). To further elucidate the role of putative bent conformation at G³³⁴, we compared the dual mutation forms, K³³⁰A/G³³⁴A and G³³⁴A/R^355-7A, showing higher and lower basal activity, respectively. The results suggested that the tonic activity of G³³⁴A owes to a dominant influence from R^355-7. Since there are additional triple Arg residues (R^377-9) distal to R^355-7, we also examined the triple mutant (G³³⁴A/R^355-7A/R^377-9A) that showed tonic inhibition same with G³³⁴A/R^355-7A. Despite the state of tonic inhibition, the activation by acidic pH_i was preserved in both G³³⁴A/R^355-7A and G³³⁴A/R^355-7A/R^377-9A, similar to the R^355-7A. Also, the inhibitory effect of ATP could be commonly demonstrated under the activation by acidic pH_i in R^355-7A, G³³⁴A/R^355-7A, and G³³⁴A/R^355-7A/R^377-9A. These results suggest that the putative bent conformation at G³³⁴ is important to set the tug-of-war between K³³⁰ and R^355-7 in the PIP₂-dependent regulation of TREK-2.

• Korean Journal of Mineralogy and Petrology
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• v.33 no.3
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• pp.195-214
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• 2020

The Samgwang Au-Ag deposit has been one of the largest deposits in Korea. The deposit consists of eight lens-shaped quartz veins which filled fractures along fault zones in Precambrian metasedimentary rock, which feature suggest that it is an orogenic-type deposit. The Ti-bearing minerals occur in wallrock (titanite, ilmenite and rutile) and laminated quartz vein (rutile). They occur minerals including biotite, muscovite, chlorite, white mica, monazite, zircon, apatite in wallrock and white mica, chlorite, arsenopyrite in laminated quartz vein. Chemical composition of titanite has maximum vaules of 3.94 wt.% (Al₂O₃), 0.49 wt.% (FeO), 0.52 wt.% (Nb₂O₅), 0.46 wt.% (Y₂O₃) and 0.43 wt.% (V₂O₅). Titanite with 0.06~0.14 (Fe/Al ratio) and 0.06~0.15 (X_Al (=Al/Al+Fe³⁺+Ti)) corresponds with metamorphic origin and low-Al variety. Chemical composition of ilmenite has maximum values of 0.07 wt.% (ZrO₂), 0.12 wt.% (HfO₂), 0.26 wt.% (Nb₂O₅), 0.04 wt.% (Sb₂O₅), 0.13 wt.% (Ta₂O₅), 2.62 wt.% (As₂O₅), 0.29 wt.% (V₂O₅), 0.12 wt.% (Al₂O₃) and 1.59 wt.% (ZnO). Chemical composition of rutile in wallrock and laminated quartz vein has maximum values of 0.35 wt.%, 0.65 wt.% (HfO₂), 2.52 wt.%, 0.19 wt.% (WO₃), 1.28 wt.%, 1.71 wt.% (Nb₂O₃), 0.03 wt.%, 0.07 wt.% (Sb₂O₃), 0.28 wt.%, 0.21 wt.% (As₂O₅), 0.68 wt.%, 0.70 wt.% (V₂O₃), 0.48 wt.%, 0.59 wt.% (Cr₂O₃), 0.70 wt.%, 1.90 wt.% (Al₂O₃) and 4.76 wt.%, 3.17 wt.% (FeO), respectively. Rutile in laminated quartz vein is higher contents (HfO₂, Nb₂O₃, As₂O₅, Cr₂O₃, Al₂O₃ and FeO) and lower content (WO₃) than rutile in wallrock. The substitutions of rutile in wallrock and laminated quatz vein are as followed : rutile in wallrock [(Fe³⁺, Al³⁺, Cr³⁺) + Hf⁴⁺ + (W⁵⁺, As⁵⁺, Nb⁵⁺) ⟵⟶ 2Ti⁴⁺ + V⁴⁺, 2Fe²⁺ + (Al³⁺, Cr³⁺) + Hf⁴⁺ + (W⁵⁺, As⁵⁺, Nb⁵⁺) ⟵⟶ 2Ti⁴⁺ + 2V⁴⁺], rutile in laminated quartz vein [(Fe³⁺, Al³⁺) + As⁵⁺ ⟵⟶ Ti⁴⁺ + V⁴⁺, (Fe³⁺, Al³⁺) + As⁵⁺ ⟵⟶ Ti⁴⁺ + Hf⁴⁺, 4(Fe³⁺, Al³⁺) ⟵⟶ Ti⁴⁺ + (W⁵⁺, Nb⁵⁺) + Cr³⁺], respectively. Based on these data, titanite, ilmenite and rutile in wallrock were formed by resolution and reconcentration of cations (W⁵⁺, Nb⁵⁺, As⁵⁺, Hf⁴⁺, V⁴⁺, Cr³⁺, Al³⁺, Fe³⁺, Fe²⁺) in minerals of wallrock during regional metamorphism. And then rutile in laminated quartz vein was formed by reconcentration of cations (Nb⁵⁺, As⁵⁺, Hf⁴⁺, Cr³⁺, Al³⁺, Fe³⁺, Fe²⁺) in alteration minerals (white mica, chlorite) and Ti-bearing minerals reaction between hydrothermal fluid originated during ductile shear and Ti-bearing minerals (titanite, ilmenite and rutile) in wallrock.

• The Korean Journal of Food & Health Convergence
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• v.6 no.1
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• pp.9-15
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• 2020

Salinity with sodic condition disturbs germination, retards emergence, and slow down seedling development of Lemon Grass (Cymbopogon citratus).Lemongrass is a perennial grass plant widely distributed worldwide and most especially in tropical and subtropical countries. This research experiment was designed to evaluate the influences of (4 dSm^-1+ 13.5 (mmol L^-1)^-1/2, 5 dSm^-1+ 25 (mmol L^-1)^1/2, 5 dSm^-1+ 30 (mmol L^-1)^1/2, 10 dSm^-1+ 25 (mmol L^-1)^1/2 and 10 dSm^-1+ 30 (mmol L^-1)^1/2) on biomass produce of lemon grass against salt tolerance. The uppermost biomass yield (45.53 gpot^-1) was produced by 4 dSm^-1+ 13.5 (mmol L^-1)^1/2 treatment. The increase in the intensity of salts reduced the growth of lemon grass. Lower biomass yield (79.33 gpot^-1) was gained at 10 dSm^-1+ 30 (mmol L^-1)^1/2. 5 dSm^-1+ 25 (mmol L^-1)^1/2 treatment performed enhanced outcome i.e. the least reduction % over control (5.87). Salinity- sodicity showed serious effect on the growth reduction from 5.87% to33.60%. This reduction gap was affected by the negative effect of salinity and sodicity on Linseed growth. Salinity- sodicity showed severe impact on the growth reduction from 5.87% to33.60%. Based on the findings, lemon Grass (Cymbopogon citratus).was capable to grow up the maximum at 4 dSm^-1+ 13.5 (mmol L^-1)^1/2 treatment.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.213-225
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• 2023

For every n ≥ 2, let ℝⁿ_‖·‖ be Rn with a norm ‖·‖ such that its unit ball has finitely many extreme points more than 2n. We devote to the description of the sets of extreme and exposed points of the closed unit balls of 𝓛(²ℝⁿ_‖·‖) and 𝓛_𝒮(²ℝⁿ_‖·‖), where 𝓛(²ℝⁿ_‖·‖) is the space of bilinear forms on ℝⁿ_‖·‖, and 𝓛_𝒮(²ℝⁿ_‖·‖) is the subspace of 𝓛(²ℝⁿ_‖·‖) consisting of symmetric bilinear forms. Let 𝓕 = 𝓛(²ℝⁿ_‖·‖) or 𝓛_𝒮(²ℝⁿ_‖·‖). First we classify the extreme and exposed points of the closed unit ball of 𝓕. We also show that every extreme point of the closed unit ball of 𝓕 is exposed. It is shown that ext B_{𝓛𝒮(²ℝⁿ‖·‖)} = ext B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖) and exp B_{𝓛𝒮(²ℝⁿ‖·‖)} = exp B_{𝓛(²ℝⁿ‖·‖)} ∩ 𝓛_𝒮(²ℝⁿ_‖·‖), which expand some results of [18, 23, 28, 29, 35, 38, 40, 41, 43].

• East Asian mathematical journal
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• v.40 no.3
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• pp.329-339
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• 2024

In the work we generate arithmetic matrix P^(c,b,a) of (cx² + bx+a)ⁿ from a Pascal matrix P^(1,1). We extend an identity P^(1,1))O^(1,1) = P^(1,1,1) with an obtuse matrix O^(1,1) to k degree polynomials. For the purpose we study P^(1,1)kO^(1,1) and find generating polynomials of O^(1,1)k.