• 대한수학회지
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• 제57권1호
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• pp.21-59
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• 2020

Let L_K denote the hypothetical automorphic Langlands group of a number field K. In our recent study, we briefly introduced a certain unconditional non-commutative topological group ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$, called the Weil-Arthur idèle group of K, which, assuming the existence of L_K, comes equipped with a natural topological group homomorphism $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K that we called the "Langlands form" of the global nonabelian norm-residue symbol of K. In this work, we present a detailed construction of ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ and $NR{\frac{\varphi}{K}^{Langlands}}$ : ${\mathfrak{W}}{\mathfrak{A}}{\frac{\varphi}{K}}$ → L_K, and discuss their basic properties.

• 한국수산과학회지
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• 제51권1호
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• pp.95-106
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• 2018

To evaluate appropriate reference genes for the normalization of quantitative reverse transcription PCR (RT-qPCR) data with embryonic and larval samples from Russian sturgeon Acipenser gueldenstaedtii, the expression stability of eight candidate housekeeping genes, including beta-actin (ACTB), elongation factor-1A (EF1A), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), histone 2A (H2A), ribosomal protein L5 (RPL5), ribosomal protein L7 (RPL7), succinate dehydrogenase (SDHA), and ubiquitin-conjugating enzyme E2 (UBE2A), were tested using embryonic samples from 12 developmental stages and larval samples from 11 ontogenic stages. Based on the stability rankings from three statistic software packages, geNorm, NormFinder, and BestKeeper, the expression stability of the embryonic subset was ranked as UBE2A>H2A>SDHA>GAPDH>RPL5>EF1A>ACTB>RPL7. On the other hand, the ranking in the larval subset was determined as UBE2A>GAPDH>SDHA>RPL5>RPL7>H2A>EF1A>AC TB. When the two subsets were combined, the overall ranking was UBE2A>SDHA>H2A>RPL5>GAPDH>EF1A>ACTB>RPL7. Taken together, our data suggest that UBE2A and SDHA are recommended as suitable references for developmental and ontogenic samples of this sturgeon species, whereas traditional housekeepers such as ACTB and GAPDH may not be suitable candidates.

• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• 충청수학회지
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• 제1권1호
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• pp.27-32
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• 1988

In this paper, we study the multipliers of $A^p_q$ into $L^{p^{\prime}}$ when 0 < p' < p. For this purpose, we study the condition on the measure ${\mu}$ satisfying $A^p_q{\subset}A^{p^{\prime}}(d{\mu})$. It turns out that the quotient $k_q={\mu}/v_q$ over hyperbolic ball of radius less than 1 belongs to $L^s_q$, where $\frac{1}{s}+\frac{p^{\prime}}{p}=1$. For the proof, we replace the norm of $k_q$ by the Riemann sum, and then use a result of interpolation theory.

• 대한수학회지
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• 제53권3호
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• pp.597-621
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• 2016

We present regularity conditions for suitable weak solutions of the Navier-Stokes equations with slip boundary data near the curved boundary. To be more precise, we prove that suitable weak solutions become regular in a neighborhood boundary points, provided the scaled mixed norm $L^{p,q}_{x,t}$ with 3/p + 2/q = 2, $1{\leq}q$ < ${\infty}$ is sufficiently small in the neighborhood.

• 대한수학회보
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• 제55권1호
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• pp.297-310
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• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• 충청수학회지
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• 제34권4호
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• Entomological Research
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• 제48권5호
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• pp.390-399
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• 2018

In order to precisely assess gene expression levels, the suitable internal reference genes must be served to quantify real-time reverse transcription polymerase chain reaction (RT-qPCR) data. For armyworm, Mythimna separata, which reference genes are suitable for assessing the level of transcriptional expression of target genes have yet to be explored. In this study, eight common reference genes, including ${\beta}$-actin (${\beta}$-ACT), 18 s ribosomal (18S), 28S ribosomal (28S), glyceraldehyde-3-phosphate (GAPDH), elongation fator-alpha ($EF1{\alpha}$), TATA box binding protein (TBP), ribosomal protein L7 (RPL7), and alpha-tubulin (${\alpha}$-TUB) that in different developmental stages, tissues and insecticide treatments of M. separata were evaluated. To further explore whether these genes were suitable to serve as endogenous controls, three software-based approaches (geNorm, BestKeeper, and NormFinder), the delta Ct method, and one web-based comprehensive tool (RefFinder) were employed to analyze and rank the tested genes. The optimal number of reference genes was determined using the geNorm program, and the suitability of particular reference genes was empirically validated according to normalized HSP70, and MsepCYP321A10 gene expression data. We found that the most suitable reference genes for the different experimental conditions. For developmental stages, 28S/RPL7 were the optimal reference genes, both $RPL7/EF1{\alpha}$ were suitable for experiments of different tissues, whereas for insecticide treatments, $28S/{\alpha}-TUB$ were suitable for normalizations of expression data. In addition, $28S/{\alpha}-TUB$ were the suitable reference genes because they have the most stable expression among different developmental stages, tissues and insecticide treatments. Our work is the first report on reference gene selection in M. separata, and might serve as a precedent for future gene expression studies.

• 호남수학학술지
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• 제6권1호
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.