• Title/Summary/Keyword: t$\frac{1}{2}$

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Subclasses of Starlike and Convex Functions Associated with Pascal Distribution Series

  • Frasin, Basem Aref;Swamy, Sondekola Rudra;Wanas, Abbas Kareem
    • Kyungpook Mathematical Journal
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    • v.61 no.1
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    • pp.99-110
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    • 2021
  • In the present paper, we determine new characterisations of the subclasses ����∗��(α, β; γ) and ������(α, β; γ) of analytic functions associated with Pascal distribution series ${\Phi}^m_q(z)=z-{\sum_{n=2}^{\infty}}(^{n+m-2}_{m-1})q^{n-1}(1-q)^mz^n$. Further, we give necessary and sufficient conditions for an integral operator related to Pascal distribution series ${\mathcal{G}}^m_qf(z)={\int_{0}^{z}}{\frac{{\Phi}^m_q(t)}{t}}dt$ to belong to the above classes. Several corollaries and consequences of the main results are also considered.

A Study on the System Principle of PID Module Implementation (PID Module 구현 원리 시스템에 대한 연구)

  • 위성동;김태성;최창주;권병무
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1999.05a
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    • pp.183-192
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    • 1999
  • The derivative equation measured of a ${\Delta}MV=Kp*{(EVn-EVn-1)+\frac{1}{Ki/S}* EVn+(Kd/S)*(2PVn-1-PVn-PVn-1)}$ is used on the machine apparatus of industrial field, but this par doesn\`t able to educate now, because we didn\`t have the implementation device of PID module, so the principle implementation system of the PID Module is manufactured and developed. Through this system, the implementation system of PID Module is practiced with that the SV and the set of P, I, D is set on the derivative equation measured of PID. A things to be known of this experiment result is flow. 1)PID module is known that had to be used with the module of A/D and D/A. 2) In process of PV is approached to the SV to follow Kp, Ti and Td to cause a constant of set value on the $MVp=Kp*EV, MV=\frac{1}{Ki}{\int}EVdt, MVd=Td\frac{d}{dt}EV$, the variable rate of E and Kp, Td, Ti in that table 1 is analysed, is same as flow. (1)If Kp is high, PV is near fast to the SV, but Kp is small, PV is near slowly to the SV. (2)If Ki is shot, PV is close fast to the SV, but Ti is high, PV is close slowly to the SV (3)If Td is high, the variable rate of E press hardly when because it doesn\`t increase, but Td is small, the variable rate of E press not hardly, upper with 1), 2), PID module is supposed that be able to do the A/S and an implementation of that apparatus, and getting a success of aim that an engineer want, on control of temperature, tension, velocity, amount of flow, power of wind end so on, to get the principle of automatic implementation in industrial field with cooperation of A/D and D/A module.

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Filtering Rate Model of Farming Oyster, Crassostrea gigas with effect of Water Temperature and Size (수온과 크기의 영향을 고려한 양식굴, Crassostrea gigas의 여수율 모형)

  • KIM Yong-Sool
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.28 no.5
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    • pp.589-598
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    • 1995
  • Filtering rates of Crassostrea gigas were experimentally investigated with reference to effects of water temperature and size. Absorptiometric determinations of filtering rates with oysters being fed diatom Chaetoceros calcirtans were carried out in a closed system. Optical density of 675nm in path length 100mm cell used as the indication of food particles absorption was appeared directly In proportion with the concentration of diatom pigment $chlorophyll-\alpha$. In the closed system where $C_0$ is $OD_{675}$ at initial time 0, $C_t$, at time t, and Z is the decreasing coefficient of OD as meaning of instantaneous removal speed, then $C_t=C_0{\cdot} e^{-2t}$, $Z=In(C_t/C_0)/t$. On the assumption that the filtering rate is constant, then removal rate per unit time (d) is $d=-e^{-z}$. If t is used to time unit of hour (hr), the filtering rate (FR) in I/hr is given by $FR=V{\cdot}d=V(1-e^{-z})$, where V is the water volume (I) of the experimental vessel. Filtering rate increased as exponential function with increasing temperature while not over critical limit. The critical temperature for filtering rate was assumed to be between $28^{\circ}C$ and $29^{\circ}C$. And the weight exponent for filtering rate is 0.223. The model formula derived from the results as FR, $Ihr^{-1}$ = $Exp(0.208{\cdot}T-4.324){\cdot} (DW)^{0.223}$ (T<29 $^{\circ}C)$ where T is water temperature $(^{\circ}C

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THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS

  • Jang, Lee-Chae
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1181-1188
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    • 2010
  • q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

Pharmacokinetics of oxytetracycline in rabbits after intravenous and intramuscular administrations (토끼에서 oxytetracycline의 정맥 및 근육 투여시의 약물동태학)

  • Kim, Eun-jung;Yun, Hyo-in;Park, Seung-chun;Oh, Tae-kwang;Cho, Chun-hyung
    • Korean Journal of Veterinary Research
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    • v.34 no.2
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    • pp.259-266
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    • 1994
  • The study was carried out to determine the pharmacokinetic parameters after intravenous(iv) and intramuscular(im) administration (10mg/kr) in healthy rabbits. The results obtained through the experiments were summarized as follows: 1. Bioassay (Bacillus cereus 11778) was evaluated very useful for the determination of oxytetracycline(OTC) in the rabbit serum and tissues, with the detection limit of $0.125{\mu}g/ml$. 2. The pharmacokinetic profiles of OTC (10mg/kg, iv) in rabbits were best described with a two compartment open model $(C=29.5e^{-4,3t}{\pm}3.6^{-0.2t})$, whereas that of OTC (10mg/kg, im) showed a one compartment curve fitting. 3. Following iv administration, a rapid distribution phase was predominant [$t_{\frac{1}{2}}({\alpha}):1.43{\pm}0.98hr$ (♂), $0.5{\pm}0.1hr$(♀)], and then more slow elimination phase ensued [$t_{\frac{1}{2}}({\beta}):4.52{\pm}0.76hr$(♂), $7.32{\pm}2.52hr$(♀)]. Other computer generated pharmacokinetic values were as follows:C1 [$67.76{\pm}18.59ml/kg/h$(♂), $76.03{\pm}22.98ml/kg/h$ (♀)] Vd [$257.74{\pm}180.47ml/kg$ (♂), $92.33{\pm}23.62$ (♀)] AUC [$25.6{\pm}4.44mgh/L$ (♂), $39.6{\pm}12.13mgh/l$ (♀)]. There were no statistical significance between both sexes for all the parameters at the confidence level of 95%. 4. After im administaration, the absorption from the injection sites was very rapid [ Ka:$0.18{\pm}0.03h^{-1}$ (♂), $0.24{\pm}0.02h^{-1}$ (♀)] followed by a monoexponential elimination fashion. The time to peak blood level (Tmax) were calculated $1.64{\pm}0.15hr$ and $1.34{\pm}0.24hr$, in the male and female, respectively. The peak levels (Cmax) at the corresponding time were $1.69{\pm}0.23{\mu}g/ml$ (♂) and $2.08{\pm}0.16{\mu}g/ml$ (♀), with no statistical differences (p>0.05).

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Development of Mathematical Model for the Hydrolysis Fish Oil (물고기 기름의 가수분해에 대한 수학적 모형개발)

  • Kim Won-Ho;Lee Yong-Hoon;Park Ji-Suk;Hur Byung-Ki
    • KSBB Journal
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    • v.20 no.2 s.91
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    • pp.106-111
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    • 2005
  • The functional relationship between the number of mole of an i-fatty acid (Si) included in fish oil and the hydrolysis time(t) was expressed as a mathematical model, $S_i=-{\alpha_i}1n(t)+\beta_i$. The average errors of calculated values on the basis of the measured values were distributed in the range of less than $5\%$ for all the 15 fatty aids composing of fish oil. The equation of hydrolysis rate of each fatty acid was deduced as $v_i={\gamma_i}exp(\frac{S_i}{\alpha_i})$ from the above-mentioned $S_i=-{\alpha_i}ln(t)+{\beta_i}$. Therefore the hydrolysis yields of fatty acids were analyzed using the equation of $S_i\;Vs.\;t.$. The 15 fatty acids were categorized into 4groups from the view point of hydrolysis yield. The hydrolysis yields of the first group, including C14:0, C16:0, C16:1, C18:0, C18:1 (n-7) and 1l8:1 (n-9), were higher than $70\%$ at 48 hr of hydrolysis. Those of the second group, C20:1, C22:1, C18:3, C20:4 and C20:5, were distributed from $40\%,\;to\;60\%$, and third group were around $30\%$. The final group containing only C22:6 was very hard to be hydrolyzed and the yield was less than $20\%$ at the same time.

The Relationship between the Storage Humidity and the Sorption Rate of Red-Pepper Powder (고춧가루의 저장습도(貯藏濕度)와 흡습속도(吸濕速度)와의 관계(關係))

  • Chun, Jae-Kun;Suh, Chung-Sik
    • Applied Biological Chemistry
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    • v.23 no.1
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    • pp.1-6
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    • 1980
  • The sorption characteristics of red pepper powder were analyzed in respect to its storing humidities and the types of powder product. The sorption rate of the powder was affected by the humidity values under which it was stored. At low relative humidity values below 70% RH the sorption equilibrium was easily attained, but at the higher humidity over 75% RH the equilibrium state was not reached even after a long period of storage. From the estimation of the sorption rate at arbitrary humidity an empirical equation was obtained; In ${\frac{dw}{dt}}=n\;ln(t)+ln\;c$, where w is moisture content(%) absorbed, t is time (hour) and n and c are empirical constants which were determined from empirical data. Particle sizes and drying methods of red pepper showed little effect on the sorption behavior.

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NONRELATIVISTIC LIMIT OF CHERN-SIMONS GAUGED FIELD EQUATIONS

  • Chae, Myeongju;Yim, Jihyun
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.871-888
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    • 2018
  • We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

REEB FLOW INVARIANT UNIT TANGENT SPHERE BUNDLES

  • Cho, Jong Taek;Chun, Sun Hyang
    • Honam Mathematical Journal
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    • v.36 no.4
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    • pp.805-812
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    • 2014
  • For unit tangent sphere bundles $T_1M$ with the standard contact metric structure (${\eta},\bar{g},{\phi},{\xi}$), we have two fundamental operators that is, $h=\frac{1}{2}{\pounds}_{\xi}{\phi}$ and ${\ell}=\bar{R}({\cdot},{\xi}){\xi}$, where ${\pounds}_{\xi}$ denotes Lie differentiation for the Reeb vector field ${\xi}$ and $\bar{R}$ denotes the Riemmannian curvature tensor of $T_1M$. In this paper, we study the Reeb ow invariancy of the corresponding (0, 2)-tensor fields H and L of h and ${\ell}$, respectively.