• Title/Summary/Keyword: Relative alpha

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A NOTE ON THE INTEGRAL REPRESENTATIONS OF GENERALIZED RELATIVE ORDER (𝛼, 𝛽) AND GENERALIZED RELATIVE TYPE (𝛼, 𝛽) OF ENTIRE AND MEROMORPHIC FUNCTIONS WITH RESPECT TO AN ENTIRE FUNCTION

  • Biswas, Tanmay;Biswas, Chinmay
    • The Pure and Applied Mathematics
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    • v.28 no.4
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    • pp.355-376
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    • 2021
  • In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

SUM AND PRODUCT THEOREMS RELATING TO GENERALIZED RELATIVE ORDER (𝛼, 𝛽) AND GENERALIZED RELATIVE TYPE (𝛼, 𝛽) OF ENTIRE FUNCTIONS

  • Biswas, Tanmay;Biswas, Chinmay;Saha, Biswajit
    • The Pure and Applied Mathematics
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    • v.28 no.2
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    • pp.155-185
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    • 2021
  • Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (𝛼, 𝛽), generalized relative type (𝛼, 𝛽) and generalized relative weak type (𝛼, 𝛽) of entire functions with respect to another entire function where 𝛼, 𝛽 are continuous non-negative functions on (-∞, +∞).

GENERALIZED RELATIVE ORDER (α, β) BASED SOME GROWTH ANALYSIS OF COMPOSITE ENTIRE FUNCTIONS

  • Biswas, Tanmay;Biswas, Chinmay
    • The Pure and Applied Mathematics
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    • v.29 no.2
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    • pp.125-139
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    • 2022
  • In this paper we wish to establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized relative order (α, β) and generalized relative lower order (α, β) where α and β are continuous non-negative functions defined on (-∞, +∞).

A Study on the Correlation Analysis of EEG and Vibraimage due to Auditory and Olfactory Stimulation (청각 및 후각자극에 의한 뇌파(EEG)와 진동이미지기술의 상관성 분석에 관한 연구)

  • Kim, Jung-Min;Kim, Myung-Ho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.6
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    • pp.4291-4297
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    • 2015
  • EEG has been used to measure the emotion of amenity and discomfort in the interior space. EEG is limited to the experiment, because it is a equipment of contact type. However, Vibraimage can measure the emotion with a web camera. Because Vibraimage is a equipment of non-contact type, it is more suitable for the interior space than EEG. Therefor, it tries to find a correlation variable between EEG and Vibraimage to measure the human emotions. In this study, it were analyzed correlation of EEG and vibraimage due to variation of loudness 60[dB], 90[dB] and rosemary, jasmine scents. Check the health status of subjects who were selected 3 male students, and the period of this experiment was about months. The condition of the environmental test room was in temperature 25[$^{\circ}C$], relative humidity 50[RH%], air current speed 0.02[m/s] and illuminance 1000[lux]. It were analyzed correlation of twenty-three index of EEG(absolute ${\theta}$, relative ${\theta}$, absolute $S{\alpha}$, relative $S{\alpha}$, absolute ${\alpha}$, relative ${\alpha}$, absolute ${\beta}$, relative ${\beta}$, absolute $\gamma$, relative $\gamma$, absolute $F{\alpha}$, relative $F{\alpha}$, absolute SMR, relative SMR, $SMR/{\theta}$, $SMR+M{\beta}/{\theta}$, absolute $H{\beta}$, relative $H{\beta}$, $H{\beta}/{\alpha}$, absolute $M{\beta}$, relative $M{\beta}$, SEF50, ASEF50) and ten index of Vibraimage(Aggression, Stress, Tension/Anxiety, Suspect, Balance, Charm, Energy, Self regulation, Inhibition, Neuroticism). As a result, I was found that relative ${\gamma}$ index of EEG and neuroticism index of Vibraimage have a high correlation as (${\pm}$).414 and (${\pm}$).424.

CLOSED IDEALS IN A SEMIFINITE, INFINITE VON NEUMANN ALGEBRA, ARISING FROM RELATIVE RANKS OF ITS ELEMENTS

  • Lee, Sa-Ge;Kim, Sang-Moon;Chi, Dong-Pyo
    • Bulletin of the Korean Mathematical Society
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    • v.21 no.2
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    • pp.107-113
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    • 1984
  • Throughout the paper let A be a semifinite, infinite von Neumann algebra acting on a Hilbert space H, .alpha. an infinite cardinal. The main purpose of our work is to give several characterizations of a class of closed ideals in A, by introducing the notions of relative ranks of elements in A and the relative .alpha.-topology on H. The relative .alphi.-topology is an analogue to the .alpha.-topology that we have defined in ([7], [8]). The present work is regarded as an extension of [7], [8] and motivated by works of M. Breuer ([1], [2]), V. Kaftal ([5], [6]) and M.G. Sonis [9].

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SOME REMARKS ON THE GROWTH OF COMPOSITE p-ADIC ENTIRE FUNCTION

  • Biswas, Tanmay;Biswas, Chinmay
    • Korean Journal of Mathematics
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    • v.29 no.4
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    • pp.715-723
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    • 2021
  • In this paper we wish to introduce the concept of generalized relative index-pair (𝛼, 𝛽) of a p-adic entire function with respect to another p-adic entire function and then prove some results relating to the growth rates of composition of two p-adic entire functions with their corresponding left and right factors.

The Estimation Method and Application of UV-cut effect in Lens (렌즈에서 UV 차단효과의 평가방법 및 적용)

  • Kim, Yong-Geun
    • Journal of Korean Ophthalmic Optics Society
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    • v.6 no.1
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    • pp.107-110
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    • 2001
  • In order to estimate the UV-A line's cut efficiency it lens, it was measured the light transmittance in the 320~400nm wavelength regions. We obtained the area to integrate the light transmittance of standard CR-39 and sample in the 320~400nm wavelength regions and established ${\alpha}$, ${\beta}$ of UV-A line's cut efficiency by contrast its area. We obtained the absolute cut efficiency ${\alpha}$ CR=0.59 value of CR-39 Lens, and if ${\alpha}$ was the absolute cut efficiency value of the lens to estimate UV-A cut effect, the relative cut efficiency ${\beta}$ was $1.69{\alpha}$. It was obtained the absolute and the relative UV exclusion index through each $a=(1-{\alpha}){\times}100%$, $b=(1-{\beta}){\times}100%$.

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THE EFFECT OF INDOMETHACIN ON PROSTAGLANDINS IN 4-NITROQUINOLINE-N-OXIDE (4-NQO) INDUCED PALATAL CARCINOMA OF ALBINO RATS (Indomethacin이 4-Nitroquinoline-N-Oxide(4-NQO) 유도 백서 구개암 발암과정에서 prostaglandins에 미치는 영향에 관한 연구)

  • Kim, Young-Soo
    • Maxillofacial Plastic and Reconstructive Surgery
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    • v.11 no.1
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    • pp.187-202
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    • 1989
  • This study was undertaken to investigate the effect of indomethacin on prostaglandins in 4-Nitroquinoline-N-Oxide (4-NQO) induced palatal carcinoma of albino rats. 128 Sprague-Dawley strain albino rats-about 100g in body weight-were used in this study, divided into as belows; 1. Normal group (16-albino rats) with no treatment, 2. Control group (16-albino rats) treated with prophylene application onto palatal mucosa 3 times a week. 3. Experimental group I (48-albino rats) treated with 0.5% 4-NQO in prophylene application onto palatal mucosa 3 times a week. 4. Experimental group II (48-albino rats) treated with 0.5% 4-NQO in prophylene application with administered $20{\mu}g/ml$ of indomethacin in drinking water ad. lib. Four animals were sacrificed 7th, 13th, 19th, and 25th week respectively in normal and control group, and 7th, 9th, 11th, 13th, 15th, 17th, 19th, 21st, 23rd, 25th, 27th and 29th week respectively in experimental group I and II at each time. The palatal and lingual tissues were excised and kept frozen at $-70^{\circ}C$. Densitometer scan and Beta-counting counter were used for the thin layer chromatography of the arachidonic acid metabolites. The obtained results were as belows; 1. In normal and control group, there was little change of the arachidonic acid metabolites during experiment period, and the tissue homogenates included prostaglandin $D_2$, 6-keto-prostaglandin $F_{1{\alpha}}$, prostaglandin $E_2$, thromboxane $B_2$, prostaglandin $F_{2{\alpha}}$ in that order of relative abundances. 2. In experimental group I, prostaglandin $D_2$, and prostaglandin $E_2$ were increased, while 6-keto-prostaglandin $F_{1{\alpha}}$ and thromboxane $B_2$ were decreased in relative abundances of arachidonic acid metabolites. And there was little change in prostaglandin $F_{1{\alpha}}$ 3. In experimental group II, prostaglandin $D_2$, and prostaglandin $E_2$ were increased, while 6-keto-prostaglandin $F_{1{\alpha}}$ and thromboxane $B_2$ were decreased in relative abundances of arachidonic acid metabolites. And there was little change in prostaglandin $F_{2{\alpha}}$ also. 4. In the range of increase in prostaglandin $D_2$, and prostaglandin $E_2$, and that of decrease in 6-keto-prostaglandin $F_{1{\alpha}}$ and thromboxane $B_2$, in relative abundances, there was wider in experimental group I than in group II. 5. In the range of increase in prostaglandin $D_2$, and prostaglandin $E_2$, and that of decrease in 6-keto-prostaglandin $F_{1{\alpha}}$ and thromboxane $B_2$, in relative abundances, there was wider in palatal mucosa than in lingual mucosa in experimental group I and II.

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Preshear Influence for Liquefaction Resistance in Sand (사질지반에서 액상화 저항에 대한 선행전단응력의 영향)

  • 윤여원;김한범;김방식
    • Proceedings of the Korean Geotechical Society Conference
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    • 2003.03a
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    • pp.315-322
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    • 2003
  • Cyclic simple shear tests were performed to find out the effect of preshear on dynamic strength of the sandy soil. Tests were performed for the specimens with 40% and 60% of relative density, under three different effective vertical stress of 50, 100 and 200kPa. For 50 and 100kPa, preshear ratios 0.00, 0.08, 0.12 and 0.16 were given, respectively, For low and high relative densities, two different results are shown in dynamic tests. Under the dense conditions, the maximum shear stress ratio($\tau$$\_$cyc//$\sigma$$\_$vo/) and the cyclic shear stress ratio($\tau$$\_$cyc//$\sigma$$\_$vo/) causing a certain shear strain increase with augmenting preshear ratio(${\alpha}$). However, the maximum shear stress ratio and the cyclic shear stress ratio increase or decrease with increasing preshear ratio under the loose conditions. Correction factor(K$\_$${\alpha}$/) for preshear increases at an early stage and then decreases with increasing preshear ratio at loose condition and increase with increasing preshear ratio at dense condition. Correction factor (K$\_$${\alpha}$,Max/) for preshear increases with the increasing preshear ratio irrespective of relative density, and the value of has same behavior as K$\_$${\alpha}$/.

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