• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.407-417
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• 2020

Let (R, m) be a d-dimensional Cohen-Macaulay local ring with infinite residue field. Let I be an ideal of R that has analytic spread ℓ(I) = d, satisfies the G_d condition, the weak Artin-Nagata property AN^-_d-2 and m is not an associated prime of R/I. In this paper, we show that if j₁(I) = λ(I/J) + λ[R/(J_d-1 :_RI+(J_d-2 :_RI+I):_R m^∞)] + 1, then I has almost minimal j-multiplicity, G(I) is Cohen-Macaulay and r_J(I) is at most 2, where J = (x₁, _…, x_d) is a general minimal reduction of I and J_i = (x₁, _…, x_i). In addition, the last theorem is in the spirit of a result of Sally who has studied the depth of associated graded rings and minimal reductions for m-primary ideals.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.7
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• pp.462-469
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• 2015

This study was carried out to examine characteristics of various acoustic indicators evaluating speech intelligibility such as reverberation time(T₃₀), D₅₀, C₅₀ and speech transmission index(STI) in Korean elementary school classrooms. Results showed that mean T₃₀ at middle frequencies(500 Hz to 2000 Hz) measured in 9 classrooms was about 0.75 s, which exceeds a regulation specified on American National Standards(ANSI); 0.60 s. Mean D₅₀, C₅₀ and STI were 60 % to 66 %, +2 dB to +3 dB, and 0.65, respectively. The maximum difference in D₅₀ and C₅₀ according to different receiver points in a classroom was 13 % and 2.5 dB, while the maximum difference in T₃₀ was 0.03 s. Whereas STI measured in classrooms has relatively low correlation with other indicators, correlation between D₅₀ and C₅₀ was high, R²=.9964. In addition, T₃₀ and C₅₀ were fitted well as logarithmic regression curve with R²=.9610. It was +3.73 dB in C₅₀ and 68 % in D₅₀ which are the value corresponding to 0.60 s in T₃₀ on this curve.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.185-196
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• 2024

In this article, we investigate the growth of meromorphic solutions of $${\alpha}(z)(\frac{{\Delta}_c{\eta}}{{\eta}})^2\,+\,(b_2(z){\eta}^2(z)\;+\;b_1(z){\eta}(z)\;+\;b_0(z))\frac{{\Delta}_c{\eta}}{{\eta}} \atop =d_4(z){\eta}^4(z)\;+\;d_3(z){\eta}^3(z)\;+\;d_2(z){\eta}^2(z)\;+\;d_1(z){\eta}(z)\;+\;d_0(z),$$ where a(z), b_i(z) for i = 0, 1, 2 and d_j (z) for j = 0, ..., 4 are given functions, △_cη = η(z + c) - η(z) with c ∈ ℂ\{0}. In particular, when the a(z), the b_i(z) and the d_j(z) are polynomials, and d₄(z) ≡ 0, we shall show that if η(z) is a transcendental entire solution of finite order, and either deg a(z) ≠ deg d₀(z) + 1, or, deg a(z) = deg d₀(z) + 1 and ρ(η) ≠ ½, then ρ(η) ≥ 1.

• Biomolecules & Therapeutics
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• v.32 no.1
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• pp.56-64
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• 2024

Biased signaling or functional selectivity refers to the ability of an agonist or receptor to selectively activate a subset of transducers such as G protein and arrestin in the case of G protein-coupled receptors (GPCRs). Although signaling through arrestin has been reported from various GPCRs, only a few studies have examined side-by-side how it differs from signaling via G protein. In this study, two signaling pathways were compared using dopamine D₂ receptor (D₂R) mutants engineered via the evolutionary tracer method to selectively transduce signals through G protein or arrestin (D₂G and D₂Arr, respectively). D₂G mediated the inhibition of cAMP production and ERK activation in the cytoplasm. D₂Arr, in contrast, mediated receptor endocytosis accompanied by arrestin ubiquitination and ERK activation in the nucleus as well as in the cytoplasm. D₂Arr-mediated ERK activation occurred in a manner dependent on arrestin3 but not arrestin2, accompanied by the nuclear translocation of arrestin3 via importin1. D₂R-mediated ERK activation, which occurred in both the cytosol and nucleus, was limited to the cytosol when cellular arrestin3 was depleted. This finding supports the results obtained with D₂Arr and D₂G. Taken together, these observations indicate that biased signal transduction pathways activate distinct downstream mechanisms and that the subcellular regions in which they occur could be different when the same effectors are involved. These findings broaden our understanding on the relation between biased receptors and the corresponding downstream signaling, which is critical for elucidating the functional roles of biased pathways.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.711-720
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• 2021

Let R denote a commutative noetherian ring, and let 𝐱 := x1, …, xd be an R-regular sequence. Suppose that 𝖆 denotes a monomial ideal with respect to 𝐱. The first purpose of this article is to show that 𝖆 is irreducible if and only if 𝖆 is a generalized-parametric ideal. Next, it is shown that, for any integer n ≥ 1, (x1, …, xd)n = ⋂P(f), where the intersection (irredundant) is taken over all monomials f = xe11 ⋯ xedd such that deg(f) = n - 1 and P(f) := (xe1+11, ⋯, xed+1d). The second main result of this paper shows that if 𝖖 := (𝐱) is a prime ideal of R which is contained in the Jacobson radical of R and R is 𝖖-adically complete, then 𝖆 is a parameter ideal if and only if 𝖆 is a monomial irreducible ideal and Rad(𝖆) = 𝖖. In addition, if a is generated by monomials m1, …, mr, then Rad(𝖆), the radical of a, is also monomial and Rad(𝖆) = (ω1, …, ωr), where ωi = rad(mi) for all i = 1, …, r.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• Analytical Science and Technology
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• v.35 no.5
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• pp.205-211
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• 2022

Deuterium (D) is an isotope with one more neutron number than hydrogen (H). Heavy elements rarely change their chemical properties with little effect even if the number of neutrons increases, but low-mass elements change their vibration energy, diffusion rate, and reaction rate because the effect cannot be ignored, which is called an isotope effect. Recently, in the semiconductor and display industries, there is a trend to replace hydrogen gas (H₂) with deuterium gas (D₂) in order to improve process stability and product quality by using the isotope effect. In addition, as the demand for D₂ in industries increases, domestic gas producers are making efforts to produce and supply D₂ on their own. In the case of high purity D₂, most of them are produced by electrolysis of heavy water (D₂O), and among D₂, hydrogen deuteride (HD) molecules are present as isotope impurities. Therefore, in order to maximize the isotope effect of hydrogen in the electronic industry, HD, which is an isotope impurity of D₂ used in the process, should be small amount. To this end, purity analysis of D₂ for industrial processing is essential. In this study, HD quantitative analysis of D₂ for high purity D₂ purity analysis was established and hydrogen isotope RM (Reference material) was developed. Since hydrogen isotopes are difficult to analyze with general gas analysis instrument, they were analyzed using a high-precision mass spectrometer (Gas/MS, Finnigan MAT271). High purity HD gas was injected into Gas/MS, sensitivity was determined by a signal according to pressure, and HD concentrations in two bottles of D₂ were quantified using the corresponding sensitivity. The amount fraction of HD in each D₂ was (4518 ± 275) μmol/mol, (2282 ± 144) μmol/mol. D₂, which quantifies HD amount using the developed quantitative analysis method, will be manufactured with hydrogen isotope RM and distributed for quality management and maintenance of electronic industries and gas producers in the future.

• Nutrition Research and Practice
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• v.18 no.1
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• pp.1-18
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• 2024

BACKGROUND/OBJECTIVES: Endoplasmic reticulum (ER) stress in adipose tissue causes an inflammatory response and leads to metabolic diseases. However, the association between vitamin D and adipose ER stress remains poorly understood. In this study, we investigated whether 1,25-dihydroxyvitamin D₃ (1,25(OH)₂D₃) alleviates ER stress in adipocytes. MATERIALS/METHODS: 3T3-L1 cells were treated with different concentrations (i.e., 10-100 nM) of 1,25(OH)₂D₃ after or during differentiation (i.e., on day 0-7, 3-7, or 7). They were then incubated with thapsigargin (TG, 500 nM) for an additional 24 h to induce ER stress. Next, we measured the mRNA and protein levels of genes involved in unfold protein response (UPR) and adipogenesis using real-time polymerase chain reaction and western blotting and quantified the secreted protein levels of pro-inflammatory cytokines. Finally, the mRNA levels of UPR pathway genes were measured in adipocytes transfected with siRNA-targeting Vdr. RESULTS: Treatment with 1,25(OH)₂D₃ during various stages of adipocyte differentiation significantly inhibited ER stress induced by TG. In fully differentiated 3T3-L1 adipocytes, 1,25(OH)₂D₃ treatment suppressed mRNA levels of Ddit3, sXbp1, and Atf4 and decreased the secretion of monocyte chemoattractant protein-1, interleukin-6, and tumor necrosis factor-α. However, downregulation of the mRNA levels of Ddit3, sXbp1, and Atf4 following 1,25(OH)₂D₃ administration was not observed in Vdr-knockdown adipocytes. In addition, exposure of 3T3-L1 preadipocytes to 1,25(OH)₂D₃ inhibited transcription of Ddit3, sXbp1, Atf4, Bip, and Atf6 and reduced the p-alpha subunit of translation initiation factor 2 (eIF2α)/eIF2α and p-protein kinase RNA-like ER kinase (PERK)/PERK protein ratios. Furthermore, 1,25(OH)₂D₃ treatment before adipocyte differentiation reduced adipogenesis and the mRNA levels of adipogenic genes. CONCLUSIONS: Our data suggest that 1,25(OH)₂D₃ prevents TG-induced ER stress and inflammatory responses in mature adipocytes by downregulating UPR signaling via binding with Vdr. In addition, the inhibition of adipogenesis by vitamin D may contribute to the reduction of ER stress in adipocytes.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.843-867
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• 2022

Maynard proved that there exists an effectively computable constant q1 such that if q ≥ q1, then $\frac{{\log}\;q}{\sqrt{q}{\phi}(q)}Li(x){\ll}{\pi}(x;\;q,\;m)<\frac{2}{{\phi}(q)}Li(x)$ for x ≥ q8. In this paper, we will show the following. Let 𝛿1 and 𝛿2 be positive constants with 0 < 𝛿1, 𝛿2 < 1 and 𝛿1 + 𝛿2 > 1. Assume that L ≠ ℚ is a number field. Then there exist effectively computable constants c0 and d1 such that for dL ≥ d1 and x ≥ exp (326n𝛿1L(log dL)1+𝛿2), we have $$\|{\pi}_C(x)-\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)\|\;{\leq}\;\(1-c_0\frac{1og\;d_L}{d^{7.072}_L}\)\;\frac{{\mid}C{\mid}}{{\mid}G{\mid}}Li(x)$$.