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GENERATING NON-JUMPING NUMBERS OF HYPERGRAPHS

  • Liu, Shaoqiang;Peng, Yuejian
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.1027-1039
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    • 2019
  • The concept of jump concerns the distribution of $Tur{\acute{a}}n$ densities. A number ${\alpha}\;{\in}\;[0,1)$ is a jump for r if there exists a constant c > 0 such that if the $Tur{\acute{a}}n$ density of a family $\mathfrak{F}$ of r-uniform graphs is greater than ${\alpha}$, then the $Tur{\acute{a}}n$ density of $\mathfrak{F}$ is at least ${\alpha}+c$. To determine whether a number is a jump or non-jump has been a challenging problem in extremal hypergraph theory. In this paper, we give a way to generate non-jumps for hypergraphs. We show that if ${\alpha}$, ${\beta}$ are non-jumps for $r_1$, $r_2{\geq}2$ respectively, then $\frac{{\alpha}{\beta}(r_1+r_2)!r_1^{r_1}r_2^{r_2}}{r_1!r_2!(r_1+R_2)^{r_1+r_2}}$ is a non-jump for $r_1+r_2$. We also apply the Lagrangian method to determine the $Tur{\acute{a}}n$ density of the extension of the (r - 3)-fold enlargement of a 3-uniform matching.

Identification of the Maize R Gene Component Responsible for the Anthocyanin Biosynthesis of Kernel Pericarp (옥수수 종피의 안토시아닌 합성을 조절하는 R 유전자 구성요소의 구명)

  • Kim, Hwa-Yeong
    • Korean Journal of Breeding Science
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    • v.42 no.1
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    • pp.50-55
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    • 2010
  • The R-r:standard (R-r:std) allele of maize R gene complex consists of S subcomplex and P component; the S subcomplex regulates anthocyanin pigmentation of seed aleurone layer, and the P component confers pigmentation of the other plant parts. The S subcomplex contains two functional genes, S1 and S2 components. In the presence of Pl gene some alleles of R gene induce anthocyanin pigmentation of pericarp. In the present study, the effects of different R alleles on the anthocyanin pigmentation of pericarp in the presence of Pl gene were analyzed in order to identify the R gene component responsible for pericarp pigmentation. The results show that R-ch and r-ch alleles condition similar degrees of pericarp pigmentation, and that R-r:Ecuador (R-r:Ec) conditions stronger pigmentation. The r-ch allele, which is inferred that its S subcomplex has lost function but the P component is normal, induces pericarp pigmentation in the presence of Pl gene. On the contrary, the R-g:g1111 allele, derived from R-r:Ec and inferred that its S subcomplex functions normal but the P component has lost its function, did not induce pericarp pigmentation in the presence of Pl gene. Moreover, PCR analysis of genomic DNA's of R-ch and r-ch indicate that R-ch maintains both P and S1 components, whereas r-ch lacks for the S1 component. Taken together, The results suggest that the P components of R alleles inducing pericarp pigmentation in the presence of Pl gene are responsible for pericarp pigmentation.

Correlations between Weight, Body Mass Index(BMI) and Risk Factors of Coronary Artery Disease in Men and Women in their Forties and Fifties (40,50대 남녀별 체중, BMI와 관상동맥질환 위험인자 간의 상관 정도 비교)

  • 김희승;정혜선;한경실
    • Journal of Korean Academy of Nursing
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    • v.28 no.1
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    • pp.184-192
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    • 1998
  • This study was done to examine the correlations between weight, BMI and risk factors of coronary heart disease in men and women in their forties and fifties. The subjects were 412 adults. who had regular health examinations between January and December of 1996 at S-Hospital in Seoul. The data were analyzed using ANOVA, Scheffe test, and Pearson correlation coefficient. The results are as follows : 1. The men between 50 and 59 years of age had higher levels for BMI, weight, systolic blood pressure, diastolic blood pressure, total cholesterol. LDL-cholesterol, triglyceride, fasting blood sugar, plasminogen activator-1, and hemoglobin A,C than the group of women in their forties. Yet. HDL-cholesterol was lower than in the former group. 2. In the group of men in their forties, weight was significantly correlated to diastolic blood pressure(r=.22), LDL-cholesterol(r=.20), plasminogen activator-inhibitor-1(r=.35) HDL-cholesterol(r=-.19). Their BMI was significantly correlted to systolic blood pressure(r=.27), diastolic blood pressure (r=.33), total cholesterol(r=.23), LDL-cholesterol (r=.26), plasminogen activator-1(r=.36) and HDL-cholesterol(r=-.25). 3. As for the group of women in their forties weight was significantly correlated to systolic blood pressure(r=.20), diastolic blood pressure(r=.22), triglyceride(r=.32) , plasminogen activator inhibitor-1 (r=.30) and HDL-cholesterol(r= -.37). Their BMI was significantly correlated to diastolic blood pressure (r=.25) triglyceride(r=.47), plasminogen activator-1 (r=.35), fibrinogen(r=.27) and HDL-cholesterol(r=-.47). 4. In the group of men in their fifties. weight was significantly correlated to total cholesterol (r=32), LDL-cholesterol(r=.29). plasminogen activator inhibitor-1(r=.26). Their BMI was significantly correlated to systolic blood pressure(r=.24), diastolic blood pressure (r=.22), total cholesterol (r=.34), LDL-cholesterol (r=.32), and plasminogen activator-1(r=.25). 5. In the group of women in their fifties, weight was significantly correlated to diastolic blood pressure(r=.33), total cholesterol(r=.21), LDL-cholesterol(r=.20), plasminogen activator inhibitor-1 (r=.43) and HDL-cholesterol(r=-.21). Their BMI was significantly correlated to systolic blood pressure(r=.25), diastolic blood pressure(r=.40), total cholesterol(r=.24), LDL-cholesterol(r=.24), triglyceride(r=22), and HDL-cholesterol (r=-.30). The above findings indicate that the BMI was more predictive than weight as a risk factor for coronary artery disease for men and women in their forties and fifties.

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A Roentgenographic Study on the Development of Human Permanent Posterior Teeth (영구 구치 발육에 관한 방사선학적 연구)

  • Young-Ku Kim
    • Journal of Oral Medicine and Pain
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    • v.16 no.1
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    • pp.73-84
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    • 1991
  • 저자는 연령을 추정하기 위한 기본자료를 얻기 위하여 상하악의 대구치, 소구치의 발육정도를 평가하였다. Orthopantomograph를 촬영한 722명의 3,464개 치아를 대상으로 crown-root ratio를 측정하여 발육정도를 평가하였으며, 다음과 같은 결론을 얻었다. 1. 완전히 형성된 치아의 crown-root ration에는 남녀간에 유의한 차이가 없었다. 2. 발육중인 치아의 crown-root ratio에는 좌우측간에 유의한 차이가 없었다. 3. 각 치아의 crown-root ratio를 이용한 연령추정의 회귀방정식은 다음과 같다. 남자: 여자 : 하악좌측 제 2대구치 : Y=4.599X+7.832(r=0.8337) 하악 좌측 제 2대구치 : Y=4.857X+7.429(r=0.8975) 제 1대구치 : Y=5.179X+2.324(r=0.7948) 제 1대구치 : Y=5.919X+2.018(r=0.8144) 제 2소구치 : Y=3.863X+7.432(r=0.8638) 제 2소구치 : Y=3.679X+7.275(r=0.8819) 제 1소구치 : Y=3.472X+7.120(r=0.8352) 제 1소구치 : Y=4.001X+6.544(r=0.9024) 하악우측 제 2대구치 : Y=4.447X+7.938(r=0.8045) 하악 우측 제 2대구치 : Y=4.653X+7.365(r=0.8598) 제 1대구치 : Y=5.954X+1.495(r=0.7777) 제 1대구치 : Y=5.449X+2.012(r=0.7553) 제 2소구치 : Y=3.894X+7.253(r=0.8689) 제 2소구치 : Y=3.772X+7.025(r=0.8719) 제 1소구치 : Y=4.189X+6.717(r=0.8370) 제 1소구치 : Y=4.327X+6.193(r=0.8524) 상악좌측 제 2대구치 : Y=4.430X+7.722(r=0.7538) 상악 좌측 제 2대구치 : Y=4.876X+7.606(r=0.8311) 제 1대구치 : Y=4.645X+2.886(r=0.6894) 제 1대구치 : Y=6.754X+1.891(r=0.5378) 제 2소구치 : Y=4.391X+6.686(r=0.7700) 제 2소구치 : Y=1.245X+10.575(r=0.1908) 제 1소구치 : Y=5.564X+6.037(r=0.9032) 제 1소구치 : - 상악우측 제 2대구치 : Y=4.587X+7.966(r=0.7882) 상악 우측 제 2대구치 : Y=4.454X+7.803(r=0.8443) 제 1대구치 : Y=4.047X+4.124(r=0.6352) 제 1대구치 : Y=6.336X+2.911(r=0.4688) 제 2소구치 : Y=2.920X+8.089(r=0.7277) 제 2소구치 : Y=3.105X+8.082(r=0.6381) 제 1소구치 : Y=3.264X+6.970(r=0.7292) 제 1소구치 : - 4. Orthopantomograph상의 crown-root ratio를 이용한 연령의 추정에는 상악치아들 보다 하악치아들이 더 정확하게 사용될 수 있다.

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이중 경사 자장 에코와 일반 경사 자장 에코 펄스열로부터의 $\Delta{R}_1$$\Delta{R}_2$에 대한 컴퓨터 가상 실험

  • 김대홍;김은주;서진석
    • Proceedings of the KSMRM Conference
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    • 2002.11a
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    • pp.102-102
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    • 2002
  • 목적:$\Delta{R}_1$$\Delta{R}_2\;^{*}$$T_1$, $T_2\;^{*}$로부터 직접 구해야 하지만, 시간 해상도 때문에 각각 $T_1$, $T_2\;^{*}$ 강조영상으로부터 구하는 것이 일반적이다. $T_1$, $T_2\;^{*}$ 강조영상으로부터 얻은 $\Delta{R}_1$$\Delta{R}_2\;^{*}$ 과 이중 경사 자장에코 펄스열로부터 얻은 $\Delta{R}_1$$\Delta{R}_2\;^{*}$ 를 컴퓨터 가상 실험을 통해서 비교한다. 강조 영상의 신호 세기만으로는 정확한 관류 정보를 얻을 수 없음을 보이고자 한다. 대상 및 방법: 알려진 $\Delta{R}_1$$\Delta{R}_2\;^{*}$ 값을 이용하여 강조영상으로부터 구할 수 있는 $\DeltaR_1$$\Delta{R}_2\;^{*}$ 을 농도에 따라서 가상실험으로 구하고, 이 값과 이중 경사 자장 에코 펄스열로부터 구할 수 있는 $\Delta{R}_1$$\Delta{R}_2\;^{*}$를 가상실험으로 구해서 비교한다.

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Studies on the Estimation of Theromodynamic Properties for the Non-Azeotropic Refrigerant Mixtures (혼합냉매의 열역학적 물성치 추산에 관한 연구)

  • 김민수;김동섭;노승탁;김욱중;윤재호
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.14 no.5
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    • pp.1337-1348
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    • 1990
  • Estimations of the thermodynamic properties are made for the selected binary non-azeotropic refrigerant mixtures including R13B1/R114, R22/R114, R12/R114, R152a/R114, R13B1/R152a and R13B1/R12 using the Peng-Robinson equation of state and mixing rules. In this study, we find that the binary interaction coefficients for the above mixtures have an effect upon the vapor-liquid equilibria and the thermodynamic properties. As the binary interaction coefficient becomes larger, the deviation from the idealized model, say, Raoult`s rule, is obvious. A correlation is proposed to relate the binary interaction coefficient to the difference between the dipole moments op each pure refrigerant. Vapor-liquid equilibrium are also accurately estimated using the binary interaction coefficient. Pressure-enthalpy and temperature-entropy relations are plotted for a certain composition ratio of each refrigerant mixture. Results show that the estimating method in this study can be applied to the investigation of the thermodynamic properties for the binary non-azeotropic refrigerant mixtures.

ON 3-ADDITIVE MAPPINGS AND COMMUTATIVITY IN CERTAIN RINGS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • Communications of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.41-51
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    • 2007
  • Let R be a ring with left identity e and suitably-restricted additive torsion, and Z(R) its center. Let H : $R{\times}R{\times}R{\rightarrow}R$ be a symmetric 3-additive mapping, and let h be the trace of H. In this paper we show that (i) if for each $x{\in}R$, $$n=<<\cdots,\;x>,\;\cdots,x>{\in}Z(R)$$ with $n\geq1$ fixed, then h is commuting on R. Moreover, h is of the form $$h(x)=\lambda_0x^3+\lambda_1(x)x^2+\lambda_2(x)x+\lambda_3(x)\;for\;all\;x{\in}R$$, where $\lambda_0\;{\in}\;Z(R)$, $\lambda_1\;:\;R{\rightarrow}R$ is an additive commuting mapping, $\lambda_2\;:\;R{\rightarrow}R$ is the commuting trace of a bi-additive mapping and the mapping $\lambda_3\;:\;R{\rightarrow}Z(R)$ is the trace of a symmetric 3-additive mapping; (ii) for each $x{\in}R$, either $n=0\;or\;<n,\;x^m>=0$ with $n\geq0,\;m\geq1$ fixed, then h = 0 on R, where denotes the product yx+xy and Z(R) is the center of R. We also present the conditions which implies commutativity in rings with identity as motivated by the above result.

miR-140 inhibits porcine fetal fibroblasts proliferation by directly targeting type 1 insulin-like growth factor receptor and indirectly inhibiting type 1 insulin-like growth factor receptor expression via SRY-box 4

  • Geng, Hongwei;Hao, Linlin;Cheng, Yunyun;Wang, Chunli;Wei, Wenzhen;Yang, Rui;Li, Haoyang;Zhang, Ying;Liu, Songcai
    • Asian-Australasian Journal of Animal Sciences
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    • v.33 no.10
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    • pp.1674-1682
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    • 2020
  • Objective: This study aimed to elucidate the effect of miR-140 on the proliferation of porcine fetal fibroblasts (PFFs) and identify the target genes of miR-140 in PFFs. Methods: In this study, bioinformatics software was used to predict and verify target genes of miR-140. Quantitative polymerase chain reaction and western blot were used to detect the relationship between miR-140 and its target genes in PFFs. Dual luciferase reporter gene assays were performed to assess the interactions among miR-140, type 1 insulin-like growth factor receptor (IGF1R), and SRY-box 4 (SOX4). The effect of miR-140 on the proliferation of PFFs was measured by CCK-8 when PFFs were transfected with a miR-140 mimic or inhibitor. The transcription factor SOX4 binding to promoter of IGF1R was detected by chromatin immunoprecipitation assay (ChIP). Results: miR-140 directly targeted IGF1R and inhibited proliferation of PFFs. Meanwhile, miR-140 targeted transcription factor SOX4 that binds to promoter of porcine IGF1R to indirectly inhibit the expression of IGF1R. In addition, miR-140 inhibitor promoted PFFs proliferation, which is abrogated by SOX4 or IGF1R knockdown. Conclusion: miR-140 inhibited PFFs proliferation by directly targeting IGF1R and indirectly inhibiting IGF1R expression via SOX4, which play an important role in the development of porcine fetal.

The Line n-sigraph of a Symmetric n-sigraph-V

  • Reddy, P. Siva Kota;Nagaraja, K.M.;Geetha, M.C.
    • Kyungpook Mathematical Journal
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    • v.54 no.1
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    • pp.95-101
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    • 2014
  • An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

A NOTE ON THE MIXED VAN DER WAERDEN NUMBER

  • Sim, Kai An;Tan, Ta Sheng;Wong, Kok Bin
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1341-1354
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    • 2021
  • Let r ≥ 2, and let ki ≥ 2 for 1 ≤ i ≤ r. Mixed van der Waerden's theorem states that there exists a least positive integer w = w(k1, k2, k3, …, kr; r) such that for any n ≥ w, every r-colouring of [1, n] admits a ki-term arithmetic progression with colour i for some i ∈ [1, r]. For k ≥ 3 and r ≥ 2, the mixed van der Waerden number w(k, 2, 2, …, 2; r) is denoted by w2(k; r). B. Landman and A. Robertson [9] showed that for k < r < $\frac{3}{2}$(k - 1) and r ≥ 2k + 2, the inequality w2(k; r) ≤ r(k - 1) holds. In this note, we establish some results on w2(k; r) for 2 ≤ r ≤ k.