• Title/Summary/Keyword: degU

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Distance Eccentric Connectivity Index of Graphs

  • Alqesmah, Akram;Saleh, Anwar;Rangarajan, R.;Gunes, Aysun Yurttas;Cangul, Ismail Naci
    • Kyungpook Mathematical Journal
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    • v.61 no.1
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    • pp.61-74
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    • 2021
  • Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

Influence of Anisotropic Property Ratio of Orthotropic Material on Stress Components and Displacement Components at Crack tip Propagating with Constant Velocity Under Dynamic Mode I (동적모드 I 상태에서 직교 이방성체의 이방성비가 등속전파 균열선단의 응력성분과 변위성분에 미치는 영향)

  • 이광호;황재석;최선호
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.19 no.1
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    • pp.87-98
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    • 1995
  • When the crack in orthotropic material is propagating under dynamic model I load, influences of anisotropic property ratio $E_{L}$/ $E_{T}$ on stress and displacement around propagating crack tip are studied in this paper. When M<0.55 and .alpha.=90.deg.(.alpha.; the angle of fiber direction with crack propagating direction, M; crack propagation velocity/shear stress wave velocity), the influence of $E_{L}$/ $E_{T}$ on stress .sigma.$_{x}$, .sigma.$_{y}$, .tau.$_{xy}$ and .sigma.$_{\theta}$ is the greast on .sigma.$_{y}$. Except M<0.55 and .alpha.=90.deg., it is the greast on .sigma.$_{x}$ in any situation. Increasing $E_{L}$/ $E_{T}$, stress components are increased or decreased. When maximum stress is based, the stress .sigma.$_{x}$(.alpha.=90.deg.), .sigma.$_{y}$(.alpha.=0.deg.) and .tau.$_{xy}$ (.alpha.=90.deg.) are decreased with increment of $E_{L}$/ $E_{T}$ in M=0. any stresses except .sigma.$_{*}$x/(.alpha.=0.deg.) are decreased with increment of $E_{L}$/ $E_{T}$ in M=0.9. When .alpha.=90.deg., the influence of $E_{L}$/ $E_{T}$ on displacement U and V is V>U in any velocities of crack propagation, when .alpha.=0.deg., it is VU in M>0.75 and when $E_{L}$/ $E_{T}$ is increased, U and V are decreased in any conditions.sed in any conditions.tions.tions.tions.

EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX

  • Ghalavand, Ali;Ashrafi, Ali Reza;Sharafdini, Reza;Ori, Ottorino
    • The Pure and Applied Mathematics
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    • v.26 no.3
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    • pp.177-188
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    • 2019
  • Suppose G is a molecular graph with edge set E(G). The hyper-Zagreb index of G is defined as $HM(G)={\sum}_{uv{\in}E(G)}[deg_G(u)+deg_G(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, all chemical trees of order $n{\geq}12$ with the first twenty smallest hyper-Zagreb index are characterized.

The Overexpression of Subtilisin Enzyme Using Mutations on Transition State Regulatory Proteins of AprE Promoter and Development of Bacillus subtilis Host System (AprE Promoter전이상태 조절인자 변이주를 이용한 공업적 효소의 과발현과 고초균 숙주계의 개발)

  • 류성호;박승환김병기
    • KSBB Journal
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    • v.11 no.1
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    • pp.8-14
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    • 1996
  • Bacillus subtillis strains with transition state regulator mutations and a spore mutation were developed for the overexpression of apsE and for the enhancement of expression level. Among the many regulator genes, degU and hpr were chosen as a representative positive and negative regulator for the aprE, respectively. Spo II G was used for the construction of asporogeneous strains. All the mutants were constructed from two protease-deleted strain DB104 and the apsE gene was transformed with an integration vector pMK101. DB104(deg$U^h$(32) $his^+$)::pMK101(Cm) and DB104($\Delta$her(Em))::pMKl01(Cm) show 7-fold and about 2-fold increase in aprE expression level, respectively. But the effect of transition state regulator mutation on the aprE expression was diminished when the integrated aprE gene was amplified by the high concentration of chloramphenicol, i. e. 30 $\mu\textrm{g}$/ml. DB104($\Delta$spoIIG(Pm) degUh(32) his+)::pMK101(Cm) and DB104($\Delta$spoIIG(Pm) $\Delta$hpr(Em))::pMK101 double mutant show 10-fold and 3-fold increase in aprE expression level, respectively. The results suggest that sporulation mutation and transition state regulator mutation have independent and additive effect on the aprE expression, and the same gene dosage effect on the transition state regulator mutation was also identified.

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A Study on the Development of High Permeability and Low Coercivity Ni-Zn Ferrite (고투자율, 저보자력을 갖는 Ni-Zn Ferrite의 개발에 관한 연구)

  • 고재귀
    • Journal of the Korean Magnetics Society
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    • v.7 no.1
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    • pp.13-18
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    • 1997
  • The effects of the various raw material composition and sintered temperature on the physical properties of Ni-Zn ferrite have been investigated. They turned out to be spinel structure by X-ray diffraction and the size of grain from microscope was from 6 ${\mu}{\textrm}{m}$ to 16 ${\mu}{\textrm}{m}$. As the sintering temperature was increased from 1030 $^{\circ}C$ to 1070 $^{\circ}C$, the initial permeability and magnetic induction has increased and the both of Q factor and coercive force has decreased. The coercive force and curie temperature were almost the same at each specimen. Their values were about 0.20 Oe and 220 $^{\circ}C$. The frequency of specimen will used in the range from 400 kHz to 20 MHz. The basic composition of $Ni_{0.14}Zn_{0.64}Cu_{0.22}Fe_2O_4$ (specimen B) sintered at 1050 $^{\circ}C$ shows the best results at magnetic induction($B_r & B_m$).

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Numerical Analysis of Natural Convection from a Horizontal Surface Immersed in Cold Water (저온의 물속에 잠겨있는 수평 평면에 의하여 야기되는 자연대류의 수치해석)

  • 유갑종;예용택;권혁용
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.6
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    • pp.1195-1204
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    • 1992
  • The natural convection from upward and downward facing horizontal isothermal plate immersed in water is studied numerically. The temperature of the plate is from 0.0 .deg. C to 8.0 .deg. C and the ambient water temperature is from 1.0 .deg. C to 10.0 .deg. C. Numerical results are presented for the velocity profiles, temperature profiles, local heat transfer coefficients, and average Nusselt numbers over the entire flow fields. Flow patterns are shown in the upward and downward facing surfaces at different ambient water temperatures. For the upward facing surface, there are upflow and unsteady flow. And the regions of the ambient water temperatures which give rise to the upflow are more extensive as the temperatures of the isothermal surface become more distant from the density extremum temperature. For the downward facing surface, only the downflow region is shown. For the upward facing horizontal isothermal surface, the average Nusselt number(= N $u_{1}$$^{*}$) is 28.86(Ra)$^{0.01}$. And for the downward facing surface, the average Nusselt number(= N $u_{2}$$^{*}$) is $C_{2}$(Ra)$^{0.2}$ and the values of $C_{2}$ are enlarged in the range of 0.785 .leq. $C_{2}$ .leq. 1.250 as increasing of the temperatures of the isothermal surface.ace.ace.

Experimental investigation of flow parameters influencing the calibration of five-hole probes (5공프로우브의 보정에 영향을 주는 유동변수들에 대한 실험적 연구)

  • Lee, Sang-U;Yun, Tae-Jin
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.5
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    • pp.637-649
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    • 1997
  • Effects of cone angle, pressure-hole orientation and Reynolds number on the five-hole probe calibration have been investigated for eight large-scale conical five-hole probes, which have either perpendicular pressure holes or forward-facing pressure holes for the cone angles of 45 deg, 60 deg, 75 deg and 90.deg. Pitch and yaw angles are changed from -40 deg to +40 deg with an interval of 5 deg, respectively, when the probe Reynolds numbers are 1.77*10$^{4}$, 3.53*10$^{4}$ and 7.06*10$^{4}$. The result shows that larger cone angle results in more sensitive changes in the calibration coefficients. In the case that the cone angle is 45 deg, the pitch-angle and yaw-angle coefficients of the five-hole probe with the perpendicular pressure holes show a very different trend compared with those of the five-hole probe with the forward-facing pressure holes. On the other hand, when the cone angle is more than 60 deg, each calibration coefficient is nearly independent of the pressure-hole orientation. Additionally, the effects of the Reynolds number on the calibration coefficients are also reported in detail.

A Study on the Crystallization of Amorphous Pb-Sb-Au Alloys (비정질 Pb-Sb-Au합금의 결정화 과정에 관한 연구)

  • 김종오
    • Electrical & Electronic Materials
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    • v.2 no.2
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    • pp.137-142
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    • 1989
  • Piston and anvil법으로 제작한 (P $b_{0.75S}$ $b_{0.25}$)$_{45}$A $u_{55}$ 비정질의 결정화 과정을 시차열분석(DTA), X-선 회절, 전기저항의 온도 및 시간변화를 측정하여 결정화과정을 조사하였다. 두단계의 상변태를 거쳐 결정화가 되는데 첫번째 변태온도는 52.deg.C이며 A $u_{2}$Pb의 결정상이 나타난다. 두번째 변태온도는 253.deg.C이며 AuS $b_{2}$의 결정상이 나타난다. 일차변태는 핵생성 및 성장 반응에 의하여 이루어졌으며 이때의 활성화 에너지는 1.38Kcal/mol이다.다.

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Application of Grobner bases to some rational curves

  • Cho, Young-Hyun;Chung, Jae-Myung
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.595-601
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    • 1997
  • Let $C_d$ be the rational curve of degree d in $P_k ^3$ given parametrically by $x_0 = u^d, X_1 = u^{d - 1}t, X_2 = ut^{d - 1}, X_3 = t^d (d \geq 4)$. Then the defining ideal of $C_d$ can be minimally generated by d polynomials $F_1, F_2, \ldots, F_d$ such that $degF_1 = 2, degF_2 = \cdots = degF_d = d - 1$ and $C_d$ is a set-theoretically complete intersection on $F_2 = X_1^{d-1} - X_2X_0^{d-2}$ for every field k of characteristic p > 0. For the proofs we will use the notion of Grobner basis.

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A Research of the Flow-Field Measurement Above the Flight Deck on LHP by PIV System (입자영상유속계를 이용한 대형수송함(LPH) 갑판 상부의 유동장 측정 연구)

  • Shim, Hojoon;Chung, Jindeog;Cho, Taehwan;Lee, Seunghoon;Song, Gisu
    • Journal of the Society of Naval Architects of Korea
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    • v.59 no.4
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    • pp.225-234
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    • 2022
  • The flow field measurement above whole area of the flight deck on 'Landing Platform Helicopter (LPH)' was performed by using PIV system in wind tunnel. In various heading angle conditions (0deg, -30deg, -45deg, -60deg, -75deg and ±90deg), the velocity fields such as U velocity & V velocity were measured at three different height above flight deck. Due to the geometrical characteristics of several bodies like deck, crane and super-structure, various vortex were generated. When the heading angle is 0deg, the deck edge vortex by flight deck and massive separation by super-structure were clearly observed by visualization with smoke and PIV, respectively. In other heading angles, the acceleration of flow in space between crane and super-structure were detected. And area with flow separation by super-structure is directly related to the heading angle of vessel.