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VIABILITY FOR SEMILINEAR DIFFERENTIAL EQUATIONS OF RETARDED TYPE

  • Dong, Qixiang;Li, Gang
    • Bulletin of the Korean Mathematical Society
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    • v.44 no.4
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    • pp.731-742
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    • 2007
  • Let X be a Banach space, $A:D(A){\subset}X{\rightarrow}X$ the generator of a compact $C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$, D a locally closed subset in X, and $f:(a,b){\times}C([-q,0];X){\rightarrow}X$ a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the semi linear differential equation of retarded type $$u#(t)=Au(t)+f(t,u_t),\;t{\in}[t_0,\;t_0+T],{u_t}_0={\phi}{\in}C([-q,0];X)$$ is the tangency condition $$\limits_{h{\downarrow}0}^{lim\;inf\;h^{-1}d(S(h)v(0)+hf(t,v);D)=0}$$ for almost every $t{\in}(a,b)$ and every $v{\in}C([-q,0];X)\;with\;v(0){\in}D$.

Influence of histologic chorioamnionitis and funisitis on the level of peripheral blood C-reactive protein at birth in preterm infants (조산아에서 조직학적 융모양막염 및 제대 혈관염이 출생 직후 말초 혈액 C-반응성 단백의 농도에 미치는 영향)

  • Kim, Do-Hyun;Lee, Heun Ji;Kim, Hee Sup;Yoo, Byoung Hoon
    • Clinical and Experimental Pediatrics
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    • v.53 no.1
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    • pp.33-40
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    • 2010
  • Purpose : The objective of this study is to determine the change of C-reactive protein (CRP) levels in the peripheral blood of preterm infants at birth according to the stage of intrauterine inflammation. Methods : A total of 187 infants (<32 weeks of gestation) were divided into a "no histologic chorioamnionitis" [HCAM (-), n=85] group and a "histologic chorioamnionitis" [HCAM (+), n=102] group according to placental pathologic findings. Furthermore, the HCAM (+) group was subdivided into a "funisitis" [F (+), n=49] group and a "no funisitis" [F (-), n=53] group and also into a "funisitis/amnionitis" [FA (+), n=58] group and an "isolated chorio-deciduitis" [FA (-), n=44] group. High-sensitivity CRP levels in the peripheral blood at birth were measured.Results : Peripheral blood CRP levels were significantly higher in the HCAM (+), F (+), F (-), and FA (+) groups than in the HCAM (-) group, but were not significantly different between the FA (-) and HCAM (-) groups. In addition, peripheral blood CRP levels were significantly higher in the F (+) and FA (+) groups than in the F (-) and FA (-) groups, respectively. For identification of amnionitis or funisitis, a cut-off value of 0.02 mg/dL was chosen. Clinical chorioamnionitis, proven early onset sepsis, histologic chorioamnionitis, and funisitis had higher incidences in infants with peripheral blood CRP levels higher than 0.02 mg/dL. Conclusion : The present study shows that peripheral blood CRP levels at birth in preterm infants born before 32 weeks' gestation is significantly increased in amnionitis or funisitis and might reflect the progress of histologic chorioamnionitis.

Identifying and Sequencing of the Elementary Minor Concepts of the Highest Common Factor (H.C.F.) and the Lowest Common Multiple (L.C.M.) of Numbers

  • Alam, S. K. Samsul
    • Research in Mathematical Education
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    • v.13 no.1
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    • pp.49-61
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    • 2009
  • In this paper some attempts have been made: (a) To identify all the elementary minor concepts of the Highest Common Factor (H.C.F.) and the Lowest Common Multiple (L.C.M.), and (b) To find the sequential order of these elementary concepts. Total 385 elementary minor concepts have been identified and sequenced.

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A Study on Managing High-Speed Railway Links and Rolling Stocks Based on the Level of Service (서비스수준(LOS)을 감안한 고속철도 노선 및 차량관리방안)

  • Oh, Jae Kyoung;Kim, Si Gon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.37 no.6
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    • pp.1025-1032
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    • 2017
  • In this paper, the level of service (LOS) is defined for high-speed railway links and rolling stocks. Based on this LOS, how to manage high-speed railway facility is also suggested. The LOS is divided into 6 levels from A to F. The measurement of effectiveness (MOE) for railway links is derived from the relationship between a total delay time and a railway link utilization ratio. Another MOE, volume over capacity (V/C), is also proposed. On the other hand, the LOS for high-speed railway rolling stocks is based on the density of people in a rolling stock. Above all, LOS D is defined to the total number of seats. Then, LOS A is 50% of the LOS D, LOS B is 70% of the LOS D, LOS C is 90% of the LOS D and LOS D~F is defined as the maximum seats and standing people at the level of each. Finally, a method to manage high-speed railway links and rolling stocks is proposed in order to keep the level of service at the target by the government.

Comparison of Bentgrass Recovery Speed on Golf Green Followed by Methods of Ball Mark Repair Practise (골프장 그린의 볼마크 수리방법에 따른 벤트그래스의 회복속도 비교)

  • Park, Jong-Hwa;Lee, Jae-Phil;Kim, Doo-Hwan;Joo, Young-Kyoo
    • Asian Journal of Turfgrass Science
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    • v.24 no.2
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    • pp.211-217
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    • 2010
  • This study was conducted to investigate a proper method of ball mark repair by comparing the creeping bentgrass recovery speed on golf course green treated by various methods of ball mark repair. Nine general repairing methods were tested and compared; control (no repair, A type), two common methods of USGA (B type) and GCSAA (C type), three methods with fork shaped hand set performing at Korean golf courses (Ansung Benest, D; Sky72, E; Lakeside, F type), and three methods using the repair machine with 6, 8, or 14 teeth (G, H, I type, respectively). Three creeping bentgrass cultivar of 'Penncross', 'T-1', and 'CY-2' were tested in this field experiment. This test was carried out from September to November in 2009 at the nursery on the Seoul Lakeside Golf course. The average speed of turfgrass recovery after various ball mark repairing methods have been ranked as in the order of E, D, C, B, F, I, H, G, and A. The methods of hand practise showed more effective results than repair method using machines. The ball mark recovery speeds of 'Penncross' were in the order of E, D, B, C, F, I, H, and A. In the case of 'T1' and 'CY-2', similar orders were showed as D, E, B, F, C, H, I, A, G and the order of D, E, C, F, B, H, G, I, A, respectively. The ball mark recovery speed among creeping bentgrass cultivar resulted in the order of 'CY-2', 'Penncross', and 'T-1'. The most proper method of ball mark repair was repair method using a hand set tool especially the method of the Sky72 Golf course (E type). At the first, remove a damaged grass area with fork and tap. And then gather the side grasses into the center area with pulling the grasses with fork. After that, make harden and flat on the turf surface by pounding and rolling with the round wooden stick. The final Nstep, water the repaired grass surface. This ball mark repairing practise showed a most rapid and proper recovery method on creeping bentgrass green.

Synthesis of Polyurethane Foam/Organonanoclay/Phosphates Composites and its Characterization (폴리우레탄폼/유기나노점토/포스페이트 복합체의 합성과 그 특성)

  • Park, Kyeong-Kyu;Lee, Sang-Ho
    • Elastomers and Composites
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    • v.46 no.4
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    • pp.343-351
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    • 2011
  • We prepared polyurethane foam/cloisite30B/phosphates composites and characterized their rise time, density, cell morphology, and thermal properties. The composites were synthesized with polyadipatediol-cloisite30B composite (f=2.0), polyether-polyol (f=4.6), polymeric 4,4-diphenyl methane diisocyanate (f=2.5), and D-580 (phenyl polyoxyalkenyl phosphate). As a blowing agent, cyclopentane and distilled water were used at various concentrations of D-580 from 0 to 2.81 wt%. The rise times of PUF/Closite30B/Phosphate composites blown with distilled water were faster than those blown with cyclopentane by 30%. The composites blown with cyclopentane had spherical-shape cells and the cell diameter was decreased with increasing D-580 wt%. While $T_g$ of the composites blown with cyclopentane linearly decreased with increasing the D-580 content, the $T_g$ of the composites blown with distilled water increased with the D-580 content. All PUF/Closite30B/Phosphate composites began to decompose from $250^{\circ}C$. The composites blown with cyclopentane showed the second thermal decomposition at temperatures higher than $500^{\circ}C$. The thermal stability of all composites increased with the D-580 content. The effect of D-580 on the thermal stability of the composites was measured higher at the composites blown with distilled water.

EVERY POLYNOMIAL OVER A FIELD CONTAINING 𝔽16 IS A STRICT SUM OF FOUR CUBES AND ONE EXPRESSION A2 + A

  • Gallardo, Luis H.
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.5
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    • pp.941-947
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    • 2009
  • Let q be a power of 16. Every polynomial $P\in\mathbb{F}_q$[t] is a strict sum $P=A^2+A+B^3+C^3+D^3+E^3$. The values of A,B,C,D,E are effectively obtained from the coefficients of P. The proof uses the new result that every polynomial $Q\in\mathbb{F}_q$[t], satisfying the necessary condition that the constant term Q(0) has zero trace, has a strict and effective representation as: $Q=F^2+F+tG^2$. This improves for such q's and such Q's a result of Gallardo, Rahavandrainy, and Vaserstein that requires three polynomials F,G,H for the strict representation $Q=F^2$+F+GH. Observe that the latter representation may be considered as an analogue in characteristic 2 of the strict representation of a polynomial Q by three squares in odd characteristic.

Ulam Stability Generalizations of 4th- Order Ternary Derivations Associated to a Jmrassias Quartic Functional Equation on Fréchet Algebras

  • Ebadian, Ali
    • Kyungpook Mathematical Journal
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    • v.53 no.2
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    • pp.233-245
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    • 2013
  • Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.