• Title/Summary/Keyword: relative ${\varphi}$-order

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RELATIVE (p, q)-𝜑 ORDER AND RELATIVE (p, q)-𝜑 TYPE ORIENTED GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.243-268
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    • 2019
  • The main aim of this paper is to study some growth properties of composite entire functions on the basis of relative $(p,q)-{\varphi}$ type and relative $(p,q)-{\varphi}$ weak type where p and q are any two positive integers and ${\varphi}(r):[0,+{\infty}){\rightarrow}(0,+{\infty})$ be a non-decreasing unbounded function.

SUM AND PRODUCT THEOREMS OF (p, q)-𝜑 RELATIVE GOL'DBERG TYPE AND (p, q)-𝜑 RELATIVE GOL'DBERG WEAK TYPE OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.28 no.4
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    • pp.819-845
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    • 2020
  • In this paper, we established sum and product theorems connected to (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weak type of entire functions of several complex variables with respect to another one under somewhat different conditions.

SOME GROWTH ESTIMATIONS BASED ON (p, q)-𝜑 RELATIVE GOL'DBERG TYPE AND (p, q)-𝜑 RELATIVE GOL'DBERG WEAK TYPE OF ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

  • Biswas, Tanmay;Biswas, Ritam
    • Korean Journal of Mathematics
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    • v.28 no.3
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    • pp.489-507
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    • 2020
  • In this paper we discussed some growth properties of entire functions of several complex variables on the basis of (p, q)-𝜑 relative Gol'dberg type and (p, q)-𝜑 relative Gol'dberg weal type where p, q are positive integers and 𝜑(R) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

FEW RESULTS IN CONNECTION WITH SUM AND PRODUCT THEOREMS OF RELATIVE (p, q)-𝜑 ORDER, RELATIVE (p, q)-𝜑 TYPE AND RELATIVE (p, q)-𝜑 WEAK TYPE OF MEROMORPHIC FUNCTIONS WITH RESPECT TO ENTIRE FUNCTIONS

  • Biswas, Tanmay
    • The Pure and Applied Mathematics
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    • v.26 no.4
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    • pp.315-353
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    • 2019
  • Orders and types of entire and meromorphic functions have been actively investigated by many authors. In the present paper, we aim at investigating some basic properties in connection with sum and product of relative (p, q)-𝜑 order, relative (p, q)-𝜑 type, and relative (p, q)-𝜑 weak type of meromorphic functions with respect to entire functions where p, q are any two positive integers and 𝜑 : [0, +∞) → (0, +∞) is a non-decreasing unbounded function.

RELATIVE (p, q) - 𝜑 ORDER BASED SOME GROWTH ANALYSIS OF COMPOSITE p-ADIC ENTIRE FUNCTIONS

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.361-370
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    • 2021
  • Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

Lower the Detection Limits of Accelerator Mass Spectrometry

  • John A., Eliades;Song, Jong-Han;Kim, Jun-Gon;Kim, Jae-Yeol;O, Jong-Ju;Kim, Jong-Chan
    • Proceedings of the Korean Vacuum Society Conference
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    • 2013.02a
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    • pp.243-244
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    • 2013
  • Over the past 15 years, several groups have incorporated radio-frequency quadrupole (RFQ) based instruments before the accelerator in accelerator mass spectrometry (AMS) systems for ion-gas interactions at low kinetic energy (<40 eV). Most AMS systems arebased on a tandem accelerator, which requires negative ions at injection. Typically, AMS sensitivity abundance ratios for radioactive-to-stable isotope are limited to Xr/Xs >10^-15, and the range of isotopes that can be analyzed is limited because of theneed to produce rather large negative ion beams and the presence of atomic isobaric interferences after stripping. The potential of using low-kinetic energy ion-gas interactions for isobar suppression before the accelerator has been demonstrated for several negative ion isobar systems with a prototype RFQ system incorporated into the AMS system at IsoTrace Laboratory, Canada (Ontario, Toronto). Requisite for any such RFQ system applied to very rare isotope analysis is large transmission of the analyte ion. This requires proper phase-space matching between the RFQ acceptance and the ion beam phase space (e.g. 35 keV, ${\varphi}3mm$, +-35 mrad), and the ability to control the average ion energy during interactions with the gas. A segmented RFQ instrument is currently being designed at Korea Institute for Science and Technology (한국과학기술연구원, KIST). It will consist of: a) an initial static voltage electrode deceleration region, to lower the ion energy from 35 keV down to <40 eV at injection into the first RFQ segment; b) the segmented quadrupole ion-gas interaction region; c) a static voltage electrode re-acceleration region for ion injection into a tandem accelerator. Design considerations and modeling will be discussed. This system should greatly lower the detection limits of the 6 MV AMS system currently being commissioned at KIST. As an example, current detection sensitivity of 41Ca/Ca is limited to the order of 10^-15 while the 41Ca/Ca abundance in modern samples is typically 41Ca/Ca~10^-14 - 10^-15. The major atomic isobaric interference in AMS is 41K. Proof-of-principal work at IsoTrace Lab. has demonstrated that a properly designed system can achieve a relative suppression of KF3-/41CaF3- >4 orders of magnitude while maintaining very high transmission of the 41CaF3- ion. This would lower the 41Ca detection limits of the KIST AMS system to at least 41Ca/Ca~10^-19. As Ca is found in bones and shells, this would potentially allow direct dating of valuable anthropological archives and archives relevant to our understanding of the most pronounced climate change events over the past million years that cannot be directly dated with the presently accessible isotopes.

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A Study on the Effects of Temperature Rise of Irrigation Water Passed Through the Warm Water Pool. (온수지에 의한 관개용수의 수온상승 효과에 관한 연구)

  • 연규석;최예환
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.19 no.1
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    • pp.4323-4337
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    • 1977
  • The study was to estimate the effect of the rise of water temperature in the warm water pool and to make contribution to the establishment of reducing to a damage of cool water as well as to the planning for warm water pool. This observation was performed in Wudu warm water pool located at Wudu-Dong of Chuncheon for two years from 1975 to 1976. The results were showed as follows; 1. The daily variation of water temperature was the least for inset (No.1; 0.6$^{\circ}C$) the second for middle overflow (No2: 3$^{\circ}C$, No.3; 2.3$^{\circ}C$) and another for outflet (No.4; 3.6$^{\circ}C$, No.5; 3.8$^{\circ}C$) And the highest reaching time of water temperature in each block was later about 1 hour than the time at which air temperature happend in the daytime. So, the variation of water temperature was sensitive to the variation of air temperature 2. The monthly variation of water temperature at each measuring point was plotted to be increased with increase in air temperature till August (Mean monthly rising degree; No.1; 1.15$^{\circ}C$, No.2; 1.7$^{\circ}C$, No.3; 1.73$^{\circ}C$, No.4; 2.08$^{\circ}C$, No.5; 2.0$^{\circ}C$), and expressed gradually descended influence upon water temperature after August. 3. The mean temperature of inflow folwed in warm Water pool was 7.5∼12.5$^{\circ}C$, and outflow temperature was described as 13.4∼22.5$^{\circ}C$ to be climbed. And So, the rising interval of water temperature was shown as 6.7∼10.4$^{\circ}C$. 4. The correlation between the rising of water temperature and the weather condition was found out highly significant. As the result, their correlation coefficents of water temperature depending on mean air temperature, ground temperature, wind velocity and relative humidity were to be 0.93, 0.90, - 0.83 and 0.71 respectively. But there was no confrimation of the correlation on the clouds, sunlight time, volume of evaporation, and heat capacity of horizontal place. 5. The water temperature of balance during the period of rice growing in Chuncheon district was shown as table 10, and the mean of whole period was calculated as about 23.7$^{\circ}C$. 6. The observed value of the outflow temperature passed through the warm water pool was higher than that of computed, the mean difference between two value was marked as 1.15$^{\circ}C$ for blockl, 1.18$^{\circ}C$ for block2, and 0.47$^{\circ}C$ for block3, respectivly. Therefore, the ratio on the rising degree between the observed and computed were shown as 53%, 44%, and 18%, mean 38% through each block warm water pool (referring item $\circled9$ of table 11,12, and 13). Accordingly, formula (4) in order to fit for each block warm water pool was transfromed as follow; {{{{ { theta }_{w } - { theta }_{ 0} =[1-exp LEFT { { 1-(1+2 varphi )} over {cp } CDOT { A} over { q} RIGHT } ] TIMES ( { theta }_{w } - { theta }_{ 0}) TIMES C }}}} Here, correction coefficinent was computed 1.38, and being substituted 1.38 for C in preceding formula, the expected water temperature will be calculated to be able to irrigate the rice paddy. As the result, we can apply the coefficient in order to plan and to construct a new warm water pool.

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