• 대한수학회보
• /
• 제54권6호
• /
• pp.1981-1990
• /
• 2017

Let R be a root system in $\mathbb{R}^d$ with Coxeter-Weyl group W and let k be a nonnegative multiplicity function on R. The generalized volume mean of a function $f{\in}L^1_{loc}(\mathbb{R}^d,m_k)$, with $m_k$ the measure given by $dmk(x):={\omega}_k(x)dx:=\prod_{{\alpha}{\in}R}{\mid}{\langle}{\alpha},x{\rangle}{\mid}^{k({\alpha})}dx$, is defined by: ${\forall}x{\in}\mathbb{R}^d$, ${\forall}r$ > 0, $M^r_B(f)(x):=\frac{1}{m_k[B(0,r)]}\int_{\mathbb{R}^d}f(y)h_k(r,x,y){\omega}_k(y)dy$, where $h_k(r,x,{\cdot})$ is a compactly supported nonnegative explicit measurable function depending on R and k. In this paper, we prove that for almost every $x{\in}\mathbb{R}^d$, $lim_{r{\rightarrow}0}M^r_B(f)(x)= f(x)$.

• 대한수학회보
• /
• 제53권4호
• /
• pp.1071-1085
• /
• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

• 한국자기학회지
• /
• 제8권5호
• /
• pp.271-274
• /
• 1998

자장중 정렬된(Nd1-xRx)2Fe14B (R=Y, Pr) 다결정 분말을 사용하여 스핀재배열현상과 결정자기이방성을 연구하였다. 이 화합물에서 스핀재배열온도(TSR)는 R=Pr인 경우 0$\leq$x$\leq$0.75 의 조성범위에서 Pr 치환량이 증가함에 따라 $\Delta$TSR=-1.35 K/Pr at.%의 비율로 단순 감소하였으나 R=Y인 경우에는 초기 소량의 감소 후 다시 약간 증가한다. 4.2 K에서 스핀재배열각(SRA)은 Y과 Pr 치환량의 증가에 따라 0$\leq$x$\leq$0.5의 범위에서 $\Delta$SRA=-0.073$^{\circ}$/T at.%와 $\Delta$SRA=-0.258$^{\circ}$/Pr at.% 비율로 감소한다. 4.2 K에서 결정자기이방성상수의 조사결과 R=Y인 경우 x=0.9 이상에서 R=Pr인 경우에는 x=0.8 이상에서 스핀재배열현상이 사라질 것으로 예측되었다.

• 한국토양비료학회지
• /
• 제50권4호
• /
• pp.259-274
• /
• 2017

To get some informations for sustainable paddy use, the productivities of soils with two years of cropping systems were estimated through pot experiment using two pretreated groups of not autoclaved 'natural'- and 'autoclaved'-soils without any fertilization. And then the relationship between the productivities, called yield potentials, and the characteristics of soils as affected by cropping systems, such as rice-rice (R-R), ricebarley-rice-barley (R-B-R-B), rice-barley-rice-wheat (R-B-R-W), soybean-barley-soybean-barley (S-B-S-B), of which barley and wheat were composted at a level of $10MT\;ha^{-1}$, and S-B-S-B without compost, was analyzed. These treatments were established in mid-mountainous loam paddy, which contained exchangeable Ca of $11.8cmol_c\;kg^{-1}$, located at the altitude of 285 m above sea level in Sangju of Korea. Crops for the estimation of soil productivity were rice cv. 'Seolemi' and soybean cv. 'Chamol'. As a result, under the natural soils condition, rice grain and straw were highly produced in composted S-B-S-B soils (p < 0.05) and lowly in R-R soils (p < 0.05). While soybean grain and stem were higher in R-R soils (p < 0.05) than other soils which not significantly different each other. In case of autoclaved soils, the yield potentials of rice and soybean were high together in either composted R-B-R-B/W or S-B-S-B soils compared to R-R and uncomposted S-B-S-B soils (p < 0.05). In especial, these yield potentials under the natural soils condition were commonly influenced by soil porosity showing negative correlation for rice (p < 0.01); positive for soybean (p < 0.05). And the porosity possibly reversed even the symbiotic contribution of indigenous Bradyrhizobium japonicum for soybean. Under autoclaved soils condition the potentials of rice and soybean showed negative correlations with soil C:N ratio (p < 0.05) similarly to the case of rice in the natural soils.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.949-968
• /
• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• 대한수학회지
• /
• 제34권1호
• /
• pp.43-55
• /
• 1997

Suppose that D is a domain in the extended complex plane $\overline{C} = C \cup {\infty}$. For each $z_0 \in C$ and $C < r < \infty$, we let $B(z_0, r) = {z \in C : $\mid$z - z_0$\mid$ < r}$ and $S(z_0, r) = \partial B(z_0, r)$. For non-empty sets A, $B \subset \overling{C}$, diam (A) is the diameter of A and d(A, B) is the distance of A and B.

• 대한수학회논문집
• /
• 제25권3호
• /
• pp.349-364
• /
• 2010

P. M. Cohn called a ring R reversible if whenever ab = 0, then ba = 0 for a, $b\;{\in}\;R$. Commutative rings and reduced rings are reversible. In this paper, we extend the reversible condition of a ring as follows: Let R be a ring and $\alpha$ an endomorphism of R, we say that R is right (resp., left) $\alpha$-shifting if whenever $a{\alpha}(b)\;=\;0$ (resp., $\alpha{a)b\;=\;0$) for a, $b\;{\in}\;R$, $b{\alpha}{a)\;=\;0$ (resp., $\alpha(b)a\;=\;0$); and the ring R is called $\alpha$-shifting if it is both left and right $\alpha$-shifting. We investigate characterizations of $\alpha$-shifting rings and their related properties, including the trivial extension, Jordan extension and Dorroh extension. In particular, it is shown that for an automorphism $\alpha$ of a ring R, R is right (resp., left) $\alpha$-shifting if and only if Q(R) is right (resp., left) $\bar{\alpha}$-shifting, whenever there exists the classical right quotient ring Q(R) of R.

• Molecules and Cells
• /
• 제45권3호
• /
• pp.122-133
• /
• 2022

The aim of this study was to investigating whether lncRNA H19 promotes myocardial fibrosis by suppressing the miR-29a-3p/miR-29b-3p-VEGFA/TGF-β axis. Patients with atrial fibrillation (AF) and healthy volunteers were included in the study, and their biochemical parameters were collected. In addition, pcDNA3.1-H19, si-H19, and miR-29a/b-3p mimic/inhibitor were transfected into cardiac fibroblasts (CFs), and proliferation of CFs was detected by MTT assay. Expression of H19 and miR-29a/b-3p were detected using real-time quantitative polymerase chain reaction, and expression of α-smooth muscle actin (α-SMA), collagen I, collagen II, matrix metalloproteinase-2 (MMP-2), and elastin were measured by western blot analysis. The dual luciferase reporter gene assay was carried out to detect the sponging relationship between H19 and miR-29a/b-3p in CFs. Compared with healthy volunteers, the level of plasma H19 was significantly elevated in patients with AF, while miR-29a-3p and miR-29b-3p were markedly depressed (P < 0.05). Serum expression of lncRNA H19 was negatively correlated with the expression of miR-29a-3p and miR-29b-3p among patients with AF (r_s = -0.337, r_s = -0.236). Moreover, up-regulation of H19 expression and down-regulation of miR-29a/b-3p expression facilitated proliferation and synthesis of extracellular matrix (ECM)-related proteins. SB431542 and si-VEGFA are able to reverse the promotion of miR-29a/b-3p on proliferation of CFs and ECM-related protein synthesis. The findings of the present study suggest that H19 promoted CF proliferation and collagen synthesis by suppressing the miR-29a-3p/miR-29b-3p-VEGFA/TGF-β axis, and provide support for a potential new direction for the treatment of AF.

• 미생물학회지
• /
• 제45권4호
• /
• pp.425-429
• /
• 2009

Bacillus cereus 설사독소 전사조절유전자인 plcR 및 papR의 특이적 프라이머 쌍을 사용한 PCR로 설사 독소유전자 함유 B. cereus 균의 검출 가능성을 조사하였다. 적어도 한 종류 이상의 독소유전자들(hblACD, nheABC, cytK)을 함유한 96균주의 B. cereus를 대상으로 plcR-papR 유전자에 특이적인 프라이머들을 이용하여 PCR을 한 결과 모두 양성을 나타냈다. 그러나 독소 유전자를 함유하지 않은 48균주의 Bacillus들로 같은 분석을 한 결과 모두 음성을 보였다. PCR에 의한 plcR-papR 유전자 검출법은 설사독소 유전자를 함유한 B. cereus를 확인하는데 간편하면서도 정확한 결과를 제공하였다.

• 대한수학회논문집
• /
• 제12권2호
• /
• pp.393-401
• /
• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.