• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.155-166
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• 2023

In 2018, Andrews introduced the partition functions ${\mathfrak{EO}}$(n) and ${\bar{\mathfrak{EO}}}$(n). The first of these denotes the number of partitions of n in which every even part is less than each odd part, and the second counts the number of partitions enumerated by the first in which only the largest even part appears an odd number of times. In 2021, Pore and Fathima introduced a new partition function ${\mathfrak{EO}}_e$(n) which counts the number of partitions of n which are enumerated by ${\bar{\mathfrak{EO}}}$(n) together with the partitions enumerated by ${\bar{\mathfrak{EO}}}$(n) where all parts are odd and the number of parts is even. They also proved some particular congruences for ${\bar{\mathfrak{EO}}}$(n) and ${\mathfrak{EO}}_e$(n). In this paper, we establish infinitely many families of congruences modulo 2, 4, 5 and 8 for ${\bar{\mathfrak{EO}}}$(n) and modulo 4 for ${\mathfrak{EO}}_e$(n). For example, if p ≥ 5 is a prime with Legendre symbol $({\frac{-3}{p}})=-1$, then for all integers n ≥ 0 and α ≥ 0, we have ${\bar{\mathfrak{EO}}}(8{\cdot}p^{2{\alpha}+1}(pn+j)+{\frac{19{\cdot}p^{2{\alpha}+2}-1}{3}}){\equiv}0$ (mod 8); 1 ≤ j ≤ (p - 1).

• Korean Journal of Soil Science and Fertilizer
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• v.8 no.2
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• pp.69-80
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• 1975

Relationships between yield and various nitrogen efficiencies, between efficiencies and between efficiency and nitrogen uptake amount of rice plant were proposed and tested using data from N.P.K simple trials about 30 to 50 locations, for three years. Established relationships are well in accordance with experimental results by showing highly significant correlations between them. The overall indications are that high yielding capacity of fields with fertilizer application, depends primarily on high fertilizer nitrogen uptake by increasing fertilizer use efficiency (Eu), secondly the efficiency (Ef) of absorbed fertilizer nitrogen (Nf) and fertilization efficiency (Fe) and also depends much on nitrogen efficiency for grain yield (E) to great extend and that the efficiency (Es) of soil nitrogen (Ns) contributes to E more than Ef does. All nitrogen efficiencies are negatively correlated with the uptake amount of corresponding nitrogen and counterpart efficiency. Es and Ef could be determined firstly by difference method and secondly E versus Cs (Cs=Ns/Ns+Nf) plotting and thirdly E-Cs plotting with labelled fertilizermethod using the equation E=Es Cs+B where B=Ef Cf but a constant under the given condition and at last Y-Ns plotting with labelled fertilizer using Eq Y=$Es{\cdot}Ns+B$ where B=$Ef{\cdot}Nf$. Es which seems not much variable from field to field is mostly greater (about 80% of tested fields) than Ef which is much variable and depends much on fertilizer form. The relationships tested and well agreed are as follows: 1. Y=$Es{\cdot}Ns+Ef{\cdot}Nf$ (Y is yield) 2. E=$Es{\cdot}Cs+Ef{\cdot}Cf$ where Cf=Nf/Nf+Ns 3. E=b-aN where E=E, Es or Ef and N=N, Ns or Nf respectively, (E=Y/N, N=Nf+Ns), b is theoretical maximum under the given system and a is tangent at N=O of the curve, Y=EN. 4. Fe=Ef Eu and Se=$Es{\cdot}Eu$ where Se is efficiency of soil available nitrogen. 5. E=$(Se{\cdot}Cs+Fe{\cdot}Cf)/Eu$ 6. Y=$Es{\cdot}Eu{\cdot}Sf+Ef{\cdot}Eu{\cdot}Fn$or Y=$Es{\cdot}Eu{\cdot}Ea{\cdot}Sn+Ef{\cdot}Eu{\cdot}Fn $where Sf=$Ea{\cdot}Sn$, Ea is soil available nitrogen equivalent to fertilizer(Sf) divided by total soil nitrogen (Sn).

• Journal of the Korean Vacuum Society
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• v.10 no.1
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• pp.67-71
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• 2001

Optical investigation on Zn-doped InGaN grown by MOCVD was performed by using the photoluminescence. Two different spectra related to Zn-acceptor-like centers occurred at room temperature, with broad emissions peaking at 2.81, and 2.60 eV, Specially, emissions interacted with phonon were observed at 2.81 eV where phonon energy was 92.5 meV From temperature dependent blue-band emissions of InGaN, we observe that the intensity in high energy region was quickly decreased more than that in low energy region with increased temperature, and the peak position at 2.81 eV was blue shift of about 18 meV, The blue-band emmissions would be originated from the transition related to the localized Zn complex centers.

• Magazine of the Korean Society of Agricultural Engineers
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• v.44 no.6
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• pp.106-114
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• 2002

In this study, the results of a series of consolidation test for undisturbed Ariake clay in Japan were analyzed by three methods, e-log p (e: void ratio, p: consolidation pressure), log e-log p and n-log p (n: porosity). Moreover, the characteristics of each analysis method were studied. For undisturbed Ariake clay, the log o-Log p and the n-log p relationships can be found as two groups of straight lines of different gradients, but both the elastic consolidation and plastic consolidation regions of e-log p relationship are expressed as a curve. In this paper, the porosity of consolidation yield n$\_$y/, consolidation yield stress p$\_$y/, and the gradient of the plastic consolidation region C$\_$p/ were represented by the log e-log p method, and n$\_$c/, P$\_$cn/ and C$\_$cn/ were represented by the n-log p method. The meaning and the relationships of each value were studied, and the interrelationships among compression indices i.e. C$\_$cn/, C$\_$p/ and C$\_$c/ are obtained from each analysis method as a function of initial porosity n$\_$0/.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2001-2011
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• 2017

In 1997, H. Li [12] proposed a conjecture: if $M^n(n{\geqslant}3)$ is a complete spacelike hypersurface in de Sitter space $S^{n+1}_1(1)$ with constant normalized scalar curvature R satisfying $\frac{n-2}{n}{\leqslant}R{\leqslant}1$, then is $M^n$ totally umbilical? Recently, F. E. C. Camargo et al. ([5]) partially proved the conjecture. In this paper, from a different viewpoint, we study closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ and also prove that $M^n$ is totally umbilical if the square of length of second fundamental form of the closed convex spacelike hypersurface $M^n$ is constant, i.e., Theorem 1. On the other hand, we obtain that if the sectional curvature of the closed convex spacelike hypersurface $M^n$ in locally symmetric Lorentz space $L^{n+1}_1$ satisfies $K(M^n)$ > 0, then $M^n$ is totally umbilical, i.e., Theorem 2.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.39-46
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• 2023

Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :_R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q₁ ∩ ⋯ ∩ Q_n with r(Q_i :_R M) = 𝖕_i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕_k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists m_j ∈ M such that 𝖕_j = (N :_R m_j). (iii) For each i, j = 1, . . . , n either 𝖕_i ⊆ 𝖕_j or 𝖕_j ⊆ 𝖕_i. Let Γ_E(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q₁∩ ⋯ ∩Q_n-1, Q₁∩ ⋯ ∩Q_n-2, . . . , Q₁} is an independent subset of V (Γ_E(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q₁ ∩ ⋯ ∩ Q_n = 0 is its minimal primary decomposition. Furthermore, it is proved that Γ_E(M)[(0 :_R M)], the induced subgraph of Γ_E(M) by (0 :_R M), is complete.

• The Korean Journal of Ecology
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• v.12 no.2
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• pp.109-122
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• 1989

The vegetation and landscape of Hokkaido were phytosociologically referred. The region of F a g e t e a c r e n a t a e on Hokkaido is divided into two types of deciduous broad-leaved forest: the oak (Quercus mongolica var. grosseserrata) forests mixed with conifers (mainly Abies sachalinensis) and the beech (Fagus crenata) forests of northernmost distribution in far-east Asia. The oak forests, which is dominated by Quercus mongolica var. grosseserrata in Japanse islands, seem to be developed from different climatic and edaphic conditions, especially in the amount and sharing pattern of precipitation in a year, and weak acid brown forest soil, volcanic ash soil and sandy soil. On the all-inclusive phytogeographical view-point, Hokkaido is situated at northernmost region of F a g e t e a c r e n a t a e (cool-temperate zone)neighboring with subarctic and subalpine vegetation, vegetation, but the evergreen broad-leaved forest (C a m e l l i e t e a j a p o n i c a e, warm-temperate zone) is abscent.

• Journal of the Korean Society of Groundwater Environment
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• v.5 no.2
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• pp.88-100
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• 1998

Since fractures may serve as major conduits of groundwater flow in crystalline rocks, characterization of conductive fractures is especially important for interpretation of flow system. In this study, characterization of fractures to investigate hydraulically conductive fractures in gneisses at an abandoned mine area was performed. The orientation, width, length, movement sense, infilling materials, spacing, aperture, roughness of both joints and faults and intersection and connectivity to other joints were measured on outcrops. In addition, characteristics of subsurface fractures were examined by core logging in five boreholes, of which the orientations were acquired by acoustic televiewer logging from three boreholes. The dominant fracture sets were grouped from outcrops; GSet 1: N50-82$^{\circ}$E/55-90$^{\circ}$SE, GSet 2: N2-8$^{\circ}$E/56-86$^{\circ}$SE, GSet 3: N46-72$^{\circ}$W/60-85$^{\circ}$NE, GSet 4:Nl2-38$^{\circ}$W/15-40$^{\circ}$SW and from subsurface; HSet 1: N50-90$^{\circ}$E/55-90$^{\circ}$SE, HSet 2: N10-30$^{\circ}$E/50-70$^{\circ}$SE, HSet 3: N20-60$^{\circ}$W/50-80$^{\circ}$NE, HSet 4: N10-50$^{\circ}$E/$\leq$40$^{\circ}$NW. Among them, GSet 1, GSet 3 and HSet 1, HSet 3 are the most intensely developed fracture sets in the study area. The mean fracture spacings of HSet 1 are 30-47cm and code 1 fractures, such as faults and open fractures, comprise 21.0-42.9 percent of the whole fractures in each borehole. HSet 3 shows the mean fracture spacings of 55-57cm and the ratio of code 1 fractures is 15.4-26.9 percent. In spite of the mean fracture spacing of 239cm, code 1 fractures of HSet 4 have the highest ratio of 54.5 percent. From the fact that faults or open fractures have high hydraulic conductivity, it can be inferred that the three fracture sets of N55-85$^{\circ}$E/50-80$^{\circ}$SE, N20-60$^{\circ}$W/50-75$^{\circ}$NE and N10-30$^{\circ}$E/$\leq$30$^{\circ}$NW from a fracture system of relatively high conductivity. It is indirectly verified with geophysical loggings and constant injection tests performed in the boreholes.

• Archives of Pharmacal Research
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• v.21 no.6
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• pp.764-768
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• 1998

In connection with the development of new anticonvulsant agents with a broad spectrum, we reported that N-Cbz-alpha-aminoglutarimides, combining common structures of othe r anticonvulsants such as N-CO-C-N and cyclic imides in a single molecule, showed significant anticonvulsant activities in the MES (maximal electroshock seizure) and PTZ (pentylenetetrazole induced seizure) tests. In these studies, a series of (R) and (S) N-alkyloxycarbonyl-alpha-aminoglutarimides 7a-7e and 8a-8e, which were substituted with various alkyloxycarbonyl group instead of Cbz group, were prepared from the corresponding (R) and (S) N-Cbz-glutamic acid 3 and 4, and were evaluated with their anticonvulsant activities against the MES and PTZ tests, including neurotoxicity, in order to define the effect of N-alkyloxycarbonyl group on the anticonvulsant activities of N-alkyloxycarbonyl-${\alpha}$-aminoglutarimides. Among them, (S)N-4-nitrobenzyloxycarbonyl-${\alpha}$-amino-N-methylglutarimide 8e was the most active in MES ($ED_{50}$=35.6mg/kg, PI=2.7) and PTZ tests ($ED_{50}$=15.6, PI=6.1). Interestingly, (R) and (S) N-4-nitrobenzyloxycarbonyl-${\alpha}$-amino-N-methylglutarimide 7e and 8e and (R) N-phenoxycarbonyl-${\alpha}$-amino-N-methylglutrimide 7d showed significant anti-convulsant activities in both the MES and PTZ tests and other compounds showed anticonvulsant activities in only the PTZ test. In addition, it was found that their anticonvulsant activities were dependent on their stereochemistries and N-substituted alkyloxycarbonyl groups.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.493-503
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• 2014

We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.