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Improved Carleman's Inequality and Improvement of Polya-Knopp's Inequality (칼레만 부등식의 개선 결과들과 폴야-놉 부등식의 개선)

  • Kwon, Ern Gun;Lee, Jinkee
    • East Asian mathematical journal
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    • v.34 no.4
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    • pp.359-369
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    • 2018
  • This note, we first show that the famous Carleman's inequality can be improved if we find a positive sequence $\{c_n\}$ such that $c_n{\sum\limits_{j=n}^{\infty}}{\frac{1}{j\(\prod_{k=1}^{j}ck\)^{\frac{1}{j}}}}$ < e. Then we list a lot of known results in the literature improving Carleman's inequality by this method. These results can be a good source to a further research for interested students. We next consider about similar improvement of Polya-Knopp's inequality, which is a continuous version of Carleman's inequality. We show by a manner parallel to the case of Carleman's inequality that Polya-Knopp's inequality can be improved if we find a positive function c(x) such that $c(x){\int}_{x}^{\infty}\frac{1}{t\;{\exp}\(\frac{1}{t}{\int}_{0}^{t}{\ln}\;c(s)\;ds\)}dt$ < e. But there are no known results improving Polya-Knopp's inequality by this method. Suggesting to find a new method, we lastly show that there is no nice continuous function c(x) that satisfies the inequality.

WEAKTYPE $L^1(R^n)$-ESTIMATE FOR CRETAIN MAXIMAL OPERATORS

  • Kim, Yong-Cheol
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1029-1036
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    • 1997
  • Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

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Oxidation Behavior of U-0.75 wt% Ti Chips in Air at 250-50$0^{\circ}C$

  • Kang, Kweon-Ho;Shin, Hyun-Kyoo;Kim, Chul;Park, Young-Moo
    • Journal of Energy Engineering
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    • v.5 no.2
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    • pp.193-197
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    • 1996
  • A study was conducted on the oxidation behavior of U-0.75 wt% Ti chips (Depleted Uranium, DU chips) using an XRD and a thermogravimetric analyzer in the temperature range from 250 to 500$^{\circ}C$ in air. At the temperature lower than 400$^{\circ}C$, DU chips were converted to UO$_2$, U$_3$O$\_$7/, and U$_3$O$\_$8/ whereas at the temperature higher than 400$^{\circ}C$, DU chips were completely converted to U$_3$O$\_$8/, the most stable form of uranium oxide. The activation energy for the oxidation of DU chips is found, 44.9 kJ/mol and the oxidation rate in terms of weight gain (%) can be expressed as; dW/dt8.4${\times}$10$^2$e(equation omitted) wt%/min (250$\leq$T($^{\circ}C$) $\leq$ 500) where W=weight gain (%), t=time and T=temperature.

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A study on friability test to assess the mechanical impact sensitivity of insensitive explosives (Friability 시험에 의한 둔감화약의 기계적 충격 감도 평가 연구)

  • 박정수;박희덕;김성호;이정관
    • Journal of the Korea Institute of Military Science and Technology
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    • v.4 no.1
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    • pp.20-29
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    • 2001
  • We recently developed a friability test procedure, which will be used as one of substance tests for Extremely Insensitive Detonating Substances(EIDSs) in Test Series 7 of the United Nations. This test was intended to assess the susceptibility of insensitive explosives to the break-up as high strain rate and subsequent ignition characteristics of the deformed material. We designed an air gun system using the hydro code simulation. The projectile velocities of the gun were in good agreement with those predicted by the hydro code with an inert material. Three different types of explosives, melt castable Comp B, castable plastic bonded explosives(PBXs), and pressable PBXs were tested during the development of the test procedure. Two tastable PBXs, i.e. DXD-09 and DXD-10, which are currently under development as candidate formulations of EIDS were classified as EIDS, since test results with these formulations were far better than the criterion of the UN Test Series 7.

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Effect of the Brain Death on Hemodynamic Changes and Myocardial Damages in Canine Brain Death Model -Hemodynamic and Electrocardiographic Changes in the Brain Death Model Caused by Sudden Increase of Intracranial Pressure- (잡견을 이용한 실험적 뇌사모델에서 뇌사가 혈역학적 변화와 심근손상에 미치는 영향 -제1보;급격한 뇌압의 상승에 의한 뇌사모델에서의 혈역학적 및 심전도학적 변화-)

  • 조명찬
    • Journal of Chest Surgery
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    • v.28 no.5
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    • pp.437-442
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    • 1995
  • We developed an experimental model of brain death using dogs. Brain death was caused by increasing the intracranial pressure[ICP suddenly by injecting saline to an epidural Foley catheter in five female mongrel dogs[weight, 20-25Kg .Hemodynamic and electrocardiographic changes were evaluated continuously during the process of brain death. 1. Abrupt rise of ICP after each injection of saline followed by a rapid decline to a new steady-state level within 15 minutes and the average volume required to induce brain death was 7.6$\pm$0.8ml.2. Body temperature, heart rate, mean pulmonary arterial pressure, left ventricular[LV enddiastolic pressure and cardiac output was not changed significantly during the process of brain death, but there was an increasing tendency.3. Mean arterial pressure and LV maximum +dP/dt increased significantly at the time of brain death.4. Hemodynamic collapse was developed within 140 minutes after brain death.5. Marked sinus bradycardia followed by junctional rhythm was seen in two dogs and frequent VPB`s with ventricular tachycardia was observed in one dog at the time of brain death. Hyperdynamic state develops and arrhythmia appears frequently at the time of brain death. Studies on the effects of brain death on myocardium and its pathophysiologic mechanism should be followed in the near future.

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Optimization of Measuring Cardiac Output by Both Hands Electrode Impedance Method (양손 전극의 임피던스법을 이용한 심박출량 측정의 최적화)

  • Jung, Sang-O;Sim, Myeong-Heon;Jung, Woon-Mo;Kim, Min-Yong;Yoon, Chan-Sol;Yoon, Hyung-Ro
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.60 no.9
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    • pp.1770-1776
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    • 2011
  • In this study, a new method that can estimate ICG data from a subject's both hands to measure Cardiac Output under convenient sensor environment. With this aim, a grip-type electrode was implemented to measure ICG. To improve the accuracy of measurement, the regression equation was extracted using multiple bio-parameters and our result was compared with the thoracic ICG equipment(Physio Flow$^{(R)}$, PF104D, Manatec Biomedical, France), which is being used in clinics. The subjects consist of 26 men and 4 women(age in $22.0{\pm}3.32$). They are no cardiac disease. Parameters available for regression model were used gender, BMI, MBP, LVET, dZ/dt(max), distance between the measured electrodes, body impedance, and PTT. As a result of analyzing the ICG measurement value on thorax and both hands, the correlation with stroke volume, heart rate, and cardiac output was $R^2$=0.853, $R^2$=0.958 and $R^2$=0.899, respectively.

Examination of Cavitation-Induced Surface Erosion Pitting of a Mechanical Heart Valve Using a Solenoid-Actuated Apparatus

  • Lee, Hwan-Sung;Hwang, Sung-Won;Katsuyuki Yamamoto
    • Journal of Mechanical Science and Technology
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    • v.17 no.9
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    • pp.1339-1348
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    • 2003
  • Several factors, including peak dp/dt of the ventricular pressure and maximum closing velocity of leaflet have been studied as indices of the cavitation threshold. In the present study, just before closing velocity of the leaflet has been studied as indices of the cavitation threshold, and cavitation erosion on the surface of a mechanical valve was examined by focusing on squeeze flow and the water hammer phenomenon during the closing period of the valve. A simple solenoid-actuated test device that can directly control the valve closing velocity was developed, and opening-closing tests of 3,000 and 40,000 cycles were performed at various closing velocities. There was a closing velocity threshold to occur erosion pitting of valve surface, and its value was about 0.4 m/s in this study. Cavitation-induced erosion pits were observed only in regions where squeeze flow occurred immediately before valve closure On the other hand, the number of the pits was found to be closely related to an area of water hammer-induced pressure wave below the critical pressure defined by water vapor pressure. Therefore, it was concluded that cavitation is initiated and augmented by the two pressure drops due to squeeze flow and water hammer phenomenon, respectively.

Changing Patterns of Communicable Diseases in Korea (우리나라 전염성 질환의 변화 양상)

  • Lim, Hyun-Sul
    • Journal of Preventive Medicine and Public Health
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    • v.38 no.2
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    • pp.117-124
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    • 2005
  • Before twentieth centuries and during early twentieth centuries, communicable diseases were the major cause of morbidity and mortality in Korea. But reliable data are not available. After 1975, the overall morbidity and mortality from communicable diseases, rapidly declined. Recently many new pathogenic microbes were recognized: L. monocytogenes, Hantaan virus, Y. pseudotuberculosis, P. multocida, L. pneumophilia, Human immunodeficiency virus (HIV), G. seoi, H. capsulatum, C. burnetii, V. cholerae O139, C. parvum, F. tularensis, E. coli O157:H7, B. burgdorferi, S. Typhimurium DT104, Rotavirus, hepatitis C virus and so on. Since the first HIV infection recognized in 1985, the reported cases of infection and deaths from HIV/AIDS have been steady increased each year. Legionnaire's disease, E. coli O157:H7 colitis, listeriosis and crytosporidiasis have been occurring just sporadically among immunocompromized cases. Many re-emerging communicable diseases were occurred in Korea: leptospirosis, malaria, endemic typhus, cholera, tsutsugamushi disease, salmonellosis, hepatitis A, shigellosis, mumps, measles, acute hemorrhagic conjunctivitis, brucellosis and so on. Leptospirosis and tsutsugamushi diseases have been noticed as major public health problems since 1980s. The malaria that had been virtually disappeared for a decade has reappeared from 1993 with striking increase of patients in recent 3-4 years. The distributions of salmonella and shigella serotypes have been changed a lot in recent few decades. Furthermore rapid emergence of antibiotic-resistant bacterial strains induces more difficult and complex problems in control of communicable diseases. We must recognize on the importance of environment and ecosystem conservation and careful prescription of anti-microbial agent in order to prevent communicable diseases.

Oviposition Behavior of Ooencyrtus kuvanae (Howard) (Hymenoptera : Encyrtidae), Egg Parasitoid of Lymantria dispar L. (Lepidoptera : Lymantriidae) (매미나방알좀벌, Ooencyrtus kuvanae (Hymenoptera : Encyrtidae)의 매미나방 난에 대한 산란행동)

  • 이해풍;이장훈
    • Korean journal of applied entomology
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    • v.28 no.4
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    • pp.221-228
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    • 1989
  • The oviposition behavior of Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyridae) was examined in a small petri dish containing eggs of gypsy moth, Lymantrt'a dt'spar L. The behavioral sequence from initial searching movement toward the host egg through oviposition, departure, and auxiliary phase activities such as resting, glooming, and host feeding were described. Oviposition experience shortened the approach time to subsequent eggs. The time spent for contacting the host egg also decreased with oviposition experience. Oviposition experience may play an important role in host recognition and increasing oviposition efficiency.

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Stabilization Control of the Nonlinear System using A RVEGA ~. based Optimal Fuzzy Controller (RVEGA 최적 퍼지 제어기를 이용한 비선형 시스템의 안정화 제어에 관한 연구)

  • 이준탁;정동일
    • Journal of Advanced Marine Engineering and Technology
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    • v.21 no.4
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    • pp.393-403
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    • 1997
  • In this paper, we proposed an optimal identification method of identifying the membership func¬tions and the fuzzy rules for the stabilization controller of the nonlinear system by RVEGA( Real Variable Elitist Genetic Algo rithm l. Although fuzzy logic controllers have been successfully applied to industrial plants, most of them have been relied heavily on expert's empirical knowl¬edge. So it is very difficult to determine the linguistic state space partitions and parameters of the membership functions and to extract the control rules. Most of conventional approaches have the drastic defects of trapping to a local minima. However, the proposed RVEGA which is similiar to the processes of natural evolution can optimize simulta¬neously the fuzzy rules and the parameters of membership functions. The validity of the RVEGA - based fuzzy controller was proved through applications to the stabi¬lization problems of an inverted pendulum system with highly nonlinear dynamics. The proposed RVEGA - based fuzzy controller has a swing -. up control mode(swing - up controller) and a stabi¬lization one(stabilization controller), moves a pendulum in an initial stable equilibrium point and a cart in an arbitrary position, to an unstable equilibrium point and a center of the rail. The stabi¬lization controller is composed of a hierarchical fuzzy inference structure; that is, the lower level inference for the virtual equilibrium point and the higher level one for position control of the cart according to the firstly inferred virtual equilibrium point. The experimental apparatus was imple¬mented by a DT -- 2801 board with AID, D/A converters and a PC - 586 microprocessor.

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