• Title/Summary/Keyword: F-ratio

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RELATIVE CLASS NUMBER ONE PROBLEM OF REAL QUADRATIC FIELDS AND CONTINUED FRACTION OF $\sqrt{m}$ WITH PERIOD 6

  • Lee, Jun Ho
    • East Asian mathematical journal
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    • v.37 no.5
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    • pp.613-617
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    • 2021
  • Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number Hd(f) of K of discriminant d is the ratio of class numbers 𝒪K and 𝒪f, where 𝒪K is the ring of integers of K and 𝒪f is the order of conductor f given by ℤ + f𝒪K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number Hd(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

A New HF/$NH_4F$/Glycerine Aqueous Solution for Protection of Al Layers During Sacrificial Etching of PSG Films (PSG 희생층 식각시 Al층을 보호하기 위한 새로운 HF/$NH_4F$/Glycerine 혼합 식각액)

  • Kim, Sung-Un;Paik, Seung-Joon;Kim, Im-Jung;Lee, Seung-Ki;Cho, Dong-Il
    • Journal of Sensor Science and Technology
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    • v.8 no.5
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    • pp.414-420
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    • 1999
  • The oxide sacrificial layer technology is one of the key technologies in surface micromachining. However, the commonly used aqueous HF solutions, including the $NH_4F$ buffered HF solutions (BHF), are known to attack the Al metal layers during the oxide sacrificial etch. A mixed $NH_4F$/HF/glycerine aqueous solution of 4:1:2 ratio is known to have the best etch selectivity between oxide and AI, but even this sacrificial etchant has a significant etch rate for AI. This paper reports an extensive experimental study on various concentration ratios for HF, $NH_4F$ and glycerine, and develops the optimal mixture ratio for sacrificial etching. At the $NH_4F$/HF/glycerine ratio of 2:1:4, the etch selectivity between PSG and Al improves by approximately 6 times over the previously known best selectivity, to a value of 7,700. At this condition, the measured etch rate of PSG film is approximately $2.1\;{\mu}m/min$, which is sufficiently fast. The developed sacrificial etchant allows the addition of a Al metal layer in surface micromachining, without the worry of Al layer erosion during sacrificial etch.

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Effect of AlF3 addition to the plasma resistance behavior of YOF coating deposited by plasma-spraying method (플라즈마-스프레이법에 의해 코팅한 옥시불화이트륨(YOF) 증착층의 플라즈마 내식성에 미치는 불화알루미늄(AlF3) 첨가 효과)

  • Young-Ju Kim;Je Hong Park;Si Beom Yu;Seungwon Jeong;Kang Min Kim;Jeong Ho Ryu
    • Journal of the Korean Crystal Growth and Crystal Technology
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    • v.33 no.4
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    • pp.153-157
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    • 2023
  • In order to manufacture a semiconductor circuit, etching, cleaning, and deposition processes are repeated. During these processes, the inside of the processing chamber is exposed to corrosive plasma. Therefore, the coating of the inner wall of the semiconductor equipment with a plasma-resistant material has been attempted to minimize the etching of the coating and particle contaminant generation. In this study, we mixed AlF3 powder with the solid-state reacted yttrium oxyfluoride (YOF) in order to increase plasma-etching resistance of the plasma spray coated YOF layer. Effects of the mixing ratio of AlF3 with YOF powder on crystal structure, microstructure and chemical composition were investigated using XRD and FE-SEM. The plasma-etching ratios of the plasma-spray coated layers were calculated and correlation with AlF3 mixing ratio was analyzed.

Studies on Combining Ability and Inheritance of Major Agronomic Characters in Naked Barley (과맥의 주요형질에 대한 조합능력 및 유전에 관한 연구)

  • Kyung-Soo Min
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.23 no.2
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    • pp.1-24
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    • 1978
  • To obtain basic information on the breeding of early maturing, short culm naked-barley varieties, the following 10 varieties, Ehime # 1, Shikoku #42, Yamate hadaka, Eijo hadaka, Kagawa # 1, Jangjubaeggwa, Baegdong, Cheongmaeg, Seto-hadaka and Mokpo #42 were used in diallel crosses in 1974. Heading date, culm length and grain yield per plant for the parents, $F_1's$ and $F_2's$ of the 10X10 partial diallel crosses were measured in 1976 for analysis of their combining ability, heritability and inheritance. The results obtained are summarized below; 1. Heritabilities in broad sense for heading date, culm length and grain yield per plant were 0.7831, 0.7599 and 0.6161, respectively. Narrow sense heritabilities for heading date were 0.3972 in $F_1$ and 0.7789 in $F_2$ and for culm length 0.6567 in $F_1$ and 0.6414 in $F_2.$ These values suggest that earliness and culm length could be successfully selected for in the early generations. Narrow sense heritability for grain yield was 0.3775 in $F_1$ and 0.4170 in $F_2.$ 2. GCA effects of the $F_1$ and $F_2$ generations for days to heading were high in the early direction for early-heading varieties, while for late-heading varieties the GCA effects were high in the late direction. Absolute values for GCA effects in $F_1$ were higher than in $F_2.$ SCA effects of the $F_1$ and $F_2$ generations were high in the early-heading direction for Shikoku # 42 x Mokpo # 42, Ehime # 1 x Yamate hadaka, Shikoku # 42 x Yamate hadaka and Shikoku #42 x Eijo hadaka. 3. The GCA effects for culm length in the $F_1$ and $F_2$ generations for tall varieties were high in the tall direction while short varieties were high in the short direction. Absolute values for the GCA effects in $F_1$ were higher than in $F_2.$ SCA effects were high in the short direction for the combinations of Mokpo # 42 with Ehime # 1, Yamate had aka and Eijo hadaka. 4. The GCA effects for grain yields per plant in the $F_1$ and $F_2$ generations for varieties with high yields per plant were high in the high yielding direction, while varieties with low yields per plant were high in the low yielding direction. Absolute values of the $F_1$ GCA effects were higher than the $F_2$ effects. The combinations with high SCA effects were Mokpo # 42 x Shikoku # 42, Mokpo # 42 x Seto hadaka and Mokpo # 42 x Cheongmaeg. 5. Mean heading dates of the $F_1$ and $F_2$ generations were earlier than those of mean mid-parent. Mean heading date of the $F_1$ generation was earlier than the $F_2$ generation. Crosses involving early-heading varieties showed a greater $F_1, $ mid-parent difference than crosses involving late-heading varieties. 6. Heading date was controlled by a partial dominance effect. Nine varieties excluding Mokpo # 42 showed allelic gene action. Ehime # 1, Shikoku # 42, Kagawa # 1 and Mokpo # 42 were recessive to the other tested varieties. 7. The $F_2$ segregations of the 45 crosses for days to heading showed that 33 cosses were of such complexity that they could not be explained by simple genetic inheritance. One cross showed a 3 : 1 ratio where earliness was dominant. Another cross showed a 3 : 1 ratio where lateness was dominant. Four other crosses showed a 9 : 7 ratio for earliness while six crosses showed a 9 : 7 ratio for lateness. 8. Many transgressive segregants for earliness were found in the following crosses; Eijo hadaka x Baegdong, Ehime # 1 x Seto hadaka, Yamate had aka x Kagawa # 1, Kagawa # 1 x Sato hadaka, Shikoku # 42 x Kagawa # 1, Ehime # 1 x Kagawa # 1, Ehime # 1 x Shikoku # 42, Ehime # 1 x Eijo hadaka. 9. Mean culm length of the F, and F. generations were usually taller than the mid-parent where tall parent were used. These trends were high in the short varieties, but low in the tall varieties. 10. Culm length was controlled by partial dominace which was gonverned by allelic gene(s). Culm length showed a high degree of control by additive genes. Mokpo # 42 was recessive while Baegdong was dominant. 11. The F_2 frequency for culm length was in large part normally distributed around the midparent value. However, some combinations showed transgressive segregation for either tall or short culm length. From combinations between medium tall varieties, Ehime # 1, Shikoku # 42, Eijo hadaka and Seto hadaka, many short segregants could be found. 12. Mean grain yields per plant of the F_1 and F_2 generations were 6% and 5% higher than those of mid-parents, respectively. The varieties with high yields per plant showed a low rate of yield increase in their F_1's and F_2's while the varieties with low yields per plant showed a high rate of yield increase in their F_1's and F_1's. 13. Grain yields per plant showed over-dominnee effects, governed by non-allelic genes. Mokpo # 42 showed recessive genetic control of grain yield per plant. It remains difficult to clarify the inheritance of grain yields per plant from these data.

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Behavior of $CaF_2$ at the Initial Adsorption Stage on Si(114)

  • Dugerjav, Otgonbayar;Duvjir, Ganbat;Li, Huiting;Kim, Hui-Dong;Seo, Jae-Myeong
    • Proceedings of the Korean Vacuum Society Conference
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    • 2012.02a
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    • pp.242-242
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    • 2012
  • From the combined studies of STM and synchrotron photoemission, it has been found that a $CaF_2$ molecule is dissociated to Ca and F atoms on the $Si(114)-2{\times}1$ held at $500^{\circ}C$ at the initial adsorption stage. The Ca atoms form isolated and unique shapes of silicide molecules as shown in Fig. (a), while the F atoms are desorbed from the surface. On the other hand, beyond a $CaF_2$ coverage of 0.3 monolayer, as shown in Fig. (b), in addition to these silicide molecules, a 1-D facet [composed of (113) and (115) faces] adjacent to an etch pit has been observed, and F atoms are also detected from photoemission. These results imply that F atoms act as an etchant on Si(114) and CaF is adsorbed selectively on the (113) face of this facet. From the present studies, it has been concluded that, an insulating $CaF_2$ layer like that on Si(111) cannot be formed on Si(114), but a CaF-decorated nanofacet with a high aspect-ratio can be grown.

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Effects of Resin Compositions and Additives on Gelation Properties and Bonding Characteristics of Urea-Melamine-Formaldehyde resin adhesives (요소·멜라민 수지 접착제의 겔화성 및 접착특성에 미치는 수지조성과 첨가물의 영향)

  • Roh, Jeang-Kwan
    • Journal of the Korean Wood Science and Technology
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    • v.27 no.1
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    • pp.72-78
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    • 1999
  • To accelerate the curing and to improve the bonding properties of urea-melamine-formaldehyde (UMF) resin adhesives for plywood, the effects of resin compositions and additives on gelation time and bonding strength were discussed. The gelation time of UMF resin prepared by simultaneous reaction with urea(U), melamine(M) and formaldehyde(F) at M/U molar ratio 0.2 was shortened as the molar ratio of formaldehyde to urea was increased. However, at F/U molar ratios higher than 2.5, the amounts of free fomaldehyde of resin could not satisfy with KS standard, Therefore, it was difficult to increase the amount of formaldehyde in resin composition for the purpose of fast gelation time. With increasing the molar ratio of melamine to urea(M/U) from 0.3 to 0.6 at constant F/U molar ratio 3.4, the gelation time of UMF resin was slightly decreased, while gradually increased at M/U molar ratio higher than 0.6. The gelation properties of UMF resin and bonding strength of UMF-bonded plywood could be enhanced by using ammonium chloride and p-toluene sulfonic acid as a curing-agent together with wheat flour and corngluten powder as a extender.

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The Effects of the Microstructural Change of Dual Phase Steel on Fatigue Fracture Propagation (복합조직강의 미시조직변화가 피로파괴전파에 미치는 영향)

  • Oh, Sae-Wook;Kim, Ung-Jip
    • Journal of Ocean Engineering and Technology
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    • v.5 no.2
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    • pp.58-66
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    • 1991
  • Not only difference of fatigue crack growth and propagation behavior resulted from the grain size, the hardness ratio and volume fraction in M.E.F. dual phase steel composed of martensite in hard phase and ferrite in soft phase, but also the effects of the plastic constraint were investigated by fracture mechanics and microstructural method. The main results obtained are as follows: 1) The fatigue endurance of M.E.F. steel increases with decreasing the grain size, increasing the ratio of hardness and volume fraction. 2) The initiation of slip and crack occures faster as the stress level goes higher. These phenomena result from the plastic constraint effect of the second phase. 3) The crack propagation rate in the constant stress level is faster as the grain size gets larger, the ratio of hardness lower and volume fraction smaller.

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A Study on the Prediction of Fatigue Damage in 2024-T3 Aluminium Alloy Using Neural Networks (신경회로망을 이용한 AI 2024-T3합금의 피로손상예측에 관한 연구)

  • Cho, Seok-Swoo;Jang, Deuk-Yul;Joo, Won-Sik
    • Journal of the Korean Society for Precision Engineering
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    • v.16 no.7
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    • pp.168-177
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    • 1999
  • Fatigue damage is the phenomena which is accumulated gradually with loading cycle in material. It is represented by fatigue crack growth rate da/dN and fatigue life ratio $N/N_{f}$. Fracture mechanical parameters estimating large crack growth behavior can calculate quantitative amount of fatigue crack growth resistance in engineering material. But fatigue damage has influence on various load, material and environment. Therefore, In this study, we propose that artificial intelligent fatigue damage model can predicts fatigue crack growth rate da/dN and fatigue life ratio $N/N_{f}$ simultaneously using fracture mechanical and nondestructive parameters.

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Estimation of Gauge R&R by Variance Components of Measurement ANOVA (측정 ANOVA의 분산성분에 의한 게이지 R&R 추정)

  • Choi, Sung-woon
    • Journal of the Korea Safety Management & Science
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    • v.12 no.1
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    • pp.199-205
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    • 2010
  • The research proposes the three-factor random measurement models for estimating the precision about operator, part, tool, and various measurement environments. The combined model with crossed and nested factors is developed to analyze the approximate F test by degrees of freedom given by Satterthwaite and point estimation of precisions from expected mean square. The model developed in this paper can be extended to the three useful models according to the type of nested designs. The study also provides the three-step procedures to evaluate the measurement precisions using three indexes such as SNR(Signal-To-Noise Ratio), R&R TR(Reproducibility&Repeatability-To-Total Precision Ratio), and PTR(Precision-To-Tolerance Ratio), The procedures include the identification of resolution, the improvement of R&R reduction, and the evaluation of precision effect.

A Study on the Mechanical Properties of Wool Fabrics -The effect of the structural conditions of the fabrics- (모직물의 역학적 특성에 관한 연구)

  • 박정순
    • Journal of the Korean Home Economics Association
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    • v.27 no.1
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    • pp.1-8
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    • 1989
  • In order to investigate the mechanical properties such as tensile, bending, shearing, thickness and weight of the wool fabrics were measured by KES-F system. Samples were classified into blend ratio, weave type, fabric count. Blend ratio was classified into two groups, which are P/W blended fabric (p=63~65%, w=35~37%) and all wool fabric. Weave type was classified into four groups, which are plain, 3 harness twill, 4harness twill, satin. Cloth count was classified into three groups, which are loose, medium, tight. Statistical analysis was performed using T-test, F-test. The results were as follows; 1. There was significant difference in the thickness, tensile, bending, shearing according to the blend ratio. 2. According the weave, there was significant difference in the bending, weight and thickness in the P/W blended fabrics. There was significant difference in the tensile, weight, thickness, bending, shearing, shearing hysterisis (2HG) in the all wool fabrics. 3. There was significant difference in the shearing properties according to the fabric count.

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