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FLOER MINI-MAX THEORY, THE CERF DIAGRAM, AND THE SPECTRAL INVARIANTS

  • Oh, Yong-Geun
    • Journal of the Korean Mathematical Society
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    • v.46 no.2
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    • pp.363-447
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    • 2009
  • The author previously defined the spectral invariants, denoted by $\rho(H;\;a)$, of a Hamiltonian function H as the mini-max value of the action functional ${\cal{A}}_H$ over the Novikov Floer cycles in the Floer homology class dual to the quantum cohomology class a. The spectrality axiom of the invariant $\rho(H;\;a)$ states that the mini-max value is a critical value of the action functional ${\cal{A}}_H$. The main purpose of the present paper is to prove this axiom for nondegenerate Hamiltonian functions in irrational symplectic manifolds (M, $\omega$). We also prove that the spectral invariant function ${\rho}_a$ : $H\;{\mapsto}\;\rho(H;\;a)$ can be pushed down to a continuous function defined on the universal (${\acute{e}}tale$) covering space $\widetilde{HAM}$(M, $\omega$) of the group Ham((M, $\omega$) of Hamiltonian diffeomorphisms on general (M, $\omega$). For a certain generic homotopy, which we call a Cerf homotopy ${\cal{H}}\;=\;\{H^s\}_{0{\leq}s{\leq}1}$ of Hamiltonians, the function ${\rho}_a\;{\circ}\;{\cal{H}}$ : $s\;{\mapsto}\;{\rho}(H^s;\;a)$ is piecewise smooth away from a countable subset of [0, 1] for each non-zero quantum cohomology class a. The proof of this nondegenerate spectrality relies on several new ingredients in the chain level Floer theory, which have their own independent interest: a structure theorem on the Cerf bifurcation diagram of the critical values of the action functionals associated to a generic one-parameter family of Hamiltonian functions, a general structure theorem and the handle sliding lemma of Novikov Floer cycles over such a family and a family version of new transversality statements involving the Floer chain map, and many others. We call this chain level Floer theory as a whole the Floer mini-max theory.

Measuring the matter energy density and Hubble parameter from Large Scale Structure

  • Lee, Seokcheon
    • The Bulletin of The Korean Astronomical Society
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    • v.38 no.2
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    • pp.57.1-57.1
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    • 2013
  • We investigate the method to measure both the present value of the matter energy density contrast and the Hubble parameter directly from the measurement of the linear growth rate which is obtained from the large scale structure of the Universe. From this method, one can obtain the value of the nuisance cosmological parameter $\Omo$ (the present value of the matter energy density contrast) within 3% error if the growth rate measurement can be reached $z >3.5$. One can also investigate the evolution of the Hubble parameter without any prior on the value of $H_0$ (the current value of the Hubble parameter). Especially, estimating the Hubble parameter are insensitive to the errors on the measurement of the normalized growth rate $f \sigma_8$. However, this method requires the high $z$ ($z >3.5$) measurement of the growth rate in order to get the less than 5% errors on the measurements of $H(z)$ at $z \leq 1.2$ with the redshift bin $\Delta z = 0.2$. Thus, this will be suitable for the next generation large scale structure galaxy surveys like WFMOS and LSST.

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An Experimental Study on the Relation of Compressive Strength and the Equivalent Age according to the Kind of Cement (시멘트종류에 따른 압축강도와 등가재령 관계에 관한 실험적 연구)

  • Na, Chul-Sung;Jang, Jong-Ho;Khil, Bae-Su;Kim, Jung-II;Nam, Jae-Hyun;Kim, Moo-Han
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2003.11a
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    • pp.13-16
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    • 2003
  • There is no study that application of the maturity using H.B.C and H.S.C. Also activation energy has different values according to the cement, admixture and water-cement ratio. Therefore to make accurate explanation for the effect of temperature on concrete strength development properties, it is necessary that activation energy value according to the kind of cement is reviewed. This study compares and estimates equivalent age using activation energy value obtained by this experiment and Freiesleben activation energy value with compressive strength of concrete. As the result of this study, activation energy value obtained by this study has more accurate explanation of temperature's influence on concrete strength development than Freiesleben activation energy value.

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An Experimental Study on the Relation of Compressive Strength and the Equivalent Age according to the Kind of Cement (시멘트종류에 따른 압축강도와 등가재령 관계에 관한 실험적 연구)

  • 나철성;장종호;길배수;김정일;남재현;김무한
    • Proceedings of the Korean Institute of Building Construction Conference
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    • 2003.05a
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    • pp.13.1-16
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    • 2003
  • There is no study that application of the maturity using H.S.C and H.S.C. Also activation energy has different values according to the cement, admixture and water-cement ratio. Therefore to make accurate explanation for the effect of temperature on concrete strength development properties, it is necessary that activation energy value according to the kind of cement is reviewed. This study compares and estimates equivalent age using activation energy value obtained by this experiment and Freiesleben activation energy value with compressive strength of concrete. As the result of this study, activation energy value obtained by this study has more accurate explanation of temperature's influence on concrete strength development than Freiesleben activation energy value.

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Effect of Body Fat on Thermophysiological Responses at a Hot Environment (체지방률이 서열환경하의 온열생리에반응에 미치는 효과)

  • Kim, Hee-Eun;Kim, Seong-Suk
    • Fashion & Textile Research Journal
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    • v.6 no.4
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    • pp.515-521
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    • 2004
  • The Purpose of this study was to investigate the effect of body fat on thermophysiological responses and subjective sensations under hot environment. Fifteen female college students volunteered as subjects. Subjects were organized into three groups - low body fat group(L group : less than 20% of body fat), medium body fat group(M group : 20%~30% of body fat) and high body fat group(H group : More than 30% of Body fat). The experiment was carried out in a climate chamber of $32^{\circ}C$, 60%RH with the repeat of having 'Exercise' and 'Rest' period. The results of this study are as follows ; Rectal temperature maintained higher in M group and L group than in H group in the period of exercise 1. High body fat was so effective in keeping the core temperature, it seems that as was usually the case in cold environment. The mean skin temperature was the lowest value in H group but the ratio of mean skin temperature change was clearly high value in H group. The above facts indicated that thermophysiological response occurs rapidly in H group. Blood pressure, pulse rate and metabolic rate of H group showed the highest values and those of L group showed the lowest value in all period of experiment. Effective of sweating rate was higher in H group than other groups. In subjective sensations, The H group felt more pleasant and comfortable than M group. With these results in mind, people of H group responses more actively for thermal regulation in a hot environment, and these leads H group to feel more pleasant and comfortable.

Degradation of toxic azo dye (AO7) using Fenton's process

  • Sharma, Ashish;Verma, Manisha;Haritash, A.K.
    • Advances in environmental research
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    • v.5 no.3
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    • pp.189-200
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    • 2016
  • This study aimed at advanced oxidation of hetero tri-functional reactive dye Acid orange 7 using photo-Fenton conditions in a lab-scale experiment. Decolourisation of Acid Orange 7 dye by Fenton's process was dependent on concentration of Hydrogen peroxide, Ferrous sulphate, pH, and contact time. A $2^3$ factorial design was used to evaluate the effects of these key factors: pH, Fe(II), and $H_2O_2$ concentration, for a dye concentration of 50 mg/L with COD of 340 mg/L at pH 3.0. The response function was removal of colour under optimised conditions; pH 3.0, [Fe(II)] 40.83 mg/L, [$H_2O_2$] 4.97 mmol/L; 13.6 min. of treatment resulting in 100% colour removal. The final COD of treated wastewater was nil suggesting that AOP is a potentially useful process of color removal and dye degradation/mineralisation of effluent having AO7. Minimum contact time for complete decolourisation was at 5 mmol/l $H_2O_2$ concentration. Increase in $FeSO_4$ (mg/l) concentration resulted in decrease of time for complete decolourisation. Box-Behnken Design was used to optimize the process variables. Maximum and minimum levels of pH (3-5), $H_2O_2$ (4-6 mmol/l), $FeSO_4$ (30-46 mg/l) and contact time (5-15 minutes) were used. The statistical analysis revealed a value of 0.88 for coefficient of regression ($R^2$) indicating a good fit of model. Calculated F-value was found higher than the tabulated value confirming to significance of the model. Based on student's t-test, Ferrous sulphate, pH, and contact time have a positive effect on the percent decolourisation of Acid Orange 7.

Functional Properties and Antioxidant Effects of Solanum nigrum-Ethanol Extract (까마중-에탄올 추출물의 기능적 특성과 항산화 효과)

  • Jeong, Kap-Seop;Lee, Nahm-Gull
    • Journal of Environmental Science International
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    • v.18 no.11
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    • pp.1207-1214
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    • 2009
  • Functional properties of Solanium nigrum-ethanol extract were investigated, nitrite scavenging ability(NSA) and antioxidant activities based on thiobarbituric acid(TBA) value were measured. The contents of potassium in fruit and root, calcium in leaf were the highest mineral components in each parts of Solanium nigrum. Total aromatics contents(TAC) was order of fruit>root>leaf, total flavonoid contents(TFC) in leaf was 6 and 10 times, total phenolic compounds contents(TPC) in leaf was 15 and 30 times of those in fruit and root, respectively, and TFC was high with TPC increase. NSA of leaf-ethanol extract was 61.9% on pH 1.2, 53.5% on pH 3.0, 54.8% on pH 4.0 and 14.3% on pH 6.0, where as NSA of root and fruit-ethanol were considerably low to 3.5~7.9% over pH 1.2~6.0. TBA value of soybean oil with the dosage of leaf-extract showed few differences from control within 3 days, but it fairly decreased with considerable antioxidant effect to 47.6% of the control in 8 days.

Characterization of the Morphology and Corrosion Resistance in Electroless Ni-P-PTFE Composite Coating Prepared by Different pH Value (pH에 따른 무전해Ni-P-PTFE 복합도금의 표면형상 및 내식성에 대한 특성 연구)

  • Byoun, Young-Min;Seo, Sun-Kyo;Yoon, Jin-doo;Ryu, Chanh-Hwan;Na, Sang-Jo;Hwang, Hwan-il
    • Journal of Surface Science and Engineering
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    • v.52 no.3
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    • pp.156-162
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    • 2019
  • Electroless Ni-P coatings are widely used in the chemical, mechanical, and electronic industries because of their excellent wear and abrasion resistance. In this study, The influence of pH values on properties of Ni-P-PTFE composite coatings was investigated. To improve mold lubrication, Ni-P-PTFE composite coatings at different pH value were studied. The morphology and phase structure of Ni-P-PTFE composite coatings were analyzed by scanning electron microscopy(SEM) and X-ray diffractometry(XRD). The result showed that Ni-P-PTFE composite coating is composed of Ni, P and PTFE. It exhibits an amorphous structure and good Corrosion Resistance to the substrate. Ni-P-PTFE composite coatings have higher open circuit potential than that of the substrate, which obtained at pH value of 5.0 optimal integrated properties.

Acidic Pelvic Drainage as a Predictive Factor For Anastomotic Leakage after Surgery for Patients with Rectal Cancer

  • Yang, Liu;Huang, Xin-En;Xu, Lin;Zhou, Xin;Zhou, Jian-Nong;Yu, Dong-Sheng;Li, Dong-Zheng;Guan, Xin
    • Asian Pacific Journal of Cancer Prevention
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    • v.14 no.9
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    • pp.5441-5447
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    • 2013
  • Purpose: To demonstrate the value of sequential determinations of pelvic drainage in the identification of increased risk of anastomotic leakage (AL) after anterior resection for rectal cancer with a double stapling technique. Patients and Methods: Between January 2004 and December 2011, data for the daily postoperative pH of pelvic drainage fluid in 753 consecutive patients with rectal cancer who initially underwent anterior resection with a double stapling technique were reviewed. All patients experienced a total mesorectal excision. Patients with anastomotic leakage (Group AL, n=57) were compared to patients without leakage (Group nAL, n=696). Patients with perioperatively abdominopelvic implants that were likely to affect pH value (determined at $25^{\circ}C$) other than leakage were excluded. Mean postoperative values were compared. Results: Anastomotic leakage was noted in 57 (7.6%) of 753 patients with rectal cancer. The diagnosis of AL was made between the $6^{th}$ and $12^{th}$ postoperative day (POD; mean $8^{th}$ POD). There was no significance of the daily average values of pH on POD1 & 2 in group AL while a significantly sharp declining mean pH value reached its diagnostic point of AL (p<0.001) on POD3. A cut-off value of 6.978 on the $3^{rd}$ POD maximized the sensitivity (98.7.0%) and specificity (94.7%) in assessing the risk of leakage. Conclusion: According to these results, an early and persistent declining of pH value of pelvic drainage fluid after rectal surgery with anastomosis, is a marker of AL. A cut-off value of 6.798 determined at $25^{\circ}C$ on POD3 maximizes sensitivity and specificity.

A Study of Ferrite Formation by Aerial Oxidation of Fe$(OH)_2$ Suspension of Aqueous Solution Containing Heave Metal Ions (水酸化鐵 懸濁液에서 空氣酸化에 의한 중금속이온의 Ferrite 생성에 관한 연구)

  • Lee, Sung Ho;Hyun, Yong Bum;Kim, Soo Saeng
    • Journal of Environmental Health Sciences
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    • v.12 no.1
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    • pp.1-14
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    • 1986
  • This investigation was carried out on the study of Ferrite formation by aerial oxidation of Fe $(OH)_2$ suspension of aqueous solution containing heavy metal ions. In this study the optimum reactionary condition of the Ferrite formation in Batch reactor wa studied by aerial oxidation which are subjected to various reaction time and temperature, under the different kinds of R(2NaOH/$FeSO_4$) Values, pH, Air flow rate, and $Fe^2+/M^2+$ mole ratio. The optimum condition for the Ferrite formation in Batch reactor was such that residence Time was 90 min., Temperature $65{\circ}$C, pH 11.0, Air flow rate 2.0l/min and $Fe^{2+}/M^{2+}$ mole ratio 4.0, which was observed by X-Ray diffraction analysis. The relation R-value, pH and ORP affecting the formation of Ferrite is that the jump step in pH 11.0, when a amount of NaOH is added, is steady state to the formation of Ferrite. Effect of R-value of $FeSO_4$ and $FeCl_2$ on the formation of Ferrite in different from each other the optimum condition of the in different from each other the optimum condition of the $FeCl_2$ is R-value 0.7, pH 11.0 and the $FeSO_4$ R-value 1.2, pH 11.0.

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