• Title/Summary/Keyword: Hyperbolic interval

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INTEGRATION OF BICOMPLEX VALUED FUNCTION ALONG HYPERBOLIC CURVE

  • Chinmay Ghosh;Soumen Mondal
    • Korean Journal of Mathematics
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    • v.31 no.3
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    • pp.323-337
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    • 2023
  • In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex valued functions on rectifiable hyperbolic path. Also we have established bicomplex analogue of the Fundamental Theorem of Calculus for hyperbolic line integral.

CONTRACTION OF HOROSPHERE-CONVEX HYPERSURFACES BY POWERS OF THE MEAN CURVATURE IN THE HYPERBOLIC SPACE

  • Guo, Shunzi;Li, Guanghan;Wu, Chuanxi
    • Journal of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1311-1332
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    • 2013
  • This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

A Study on 2-Dimensional Sound Source Tracking System IV - Mainly on Approximation of the Relative Bearing and Distance - (2차원적 음원추적에 관한 연구IV -음원위치의 근사적 결정법을 중심으로 -)

  • 문성배;전승환
    • Journal of the Korean Institute of Navigation
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    • v.25 no.4
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    • pp.371-379
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    • 2001
  • We have reported the new measurement system which was substituted digital filter for the analog filter in order to develop the optimal system that could find the time delay between each sensors with high accuracy. And also we have confirmed through the experiments that the accuracy of measurements were differentiated by the methods what kind of digital filter had been adopted. This paper suggests two algorithms which approximate the sound source's bearing and distance. One is that sound source's relative bearing can be approximately regarded as the gradient of hyperbolic asymptote, the other is that the source's range can be approximated under the condition of a long range source relative to the sensor's interval. And a series of experiments were carried out with the source's distance 22.42meters and the random bearing interval within the limits of $-90^{\circ}$~$+90^{\circ}$. As a result, we have recognized that the approximation methods could measure the bearing and distance with higher accuracy than the method using trigonometric relation could do.

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Ultrasonic Tracking of Movements of Striped Jack ( Caranx Delicatissimus ) in the Nunoura Bay , Japan (초음파 표지를 이용한 양식어의 유영행동 추적)

  • 신현옥
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.28 no.4
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    • pp.347-359
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    • 1992
  • The movements of three striped jack (Caranx delicatissimus, 24cm of body length) were tracked by ultrasonic telemetry in the Nunoura Bay in August 1990. A school of the striped jack has been released near by the fish farming rafts by Goto branch of the Fisheries Agency and Japan Sea-Farming Association. To investigate the staying area and the swimming pattern of the fish, small size pinger($\Phi$8.5$\times$L35mm, 140dB re 1$\mu$Pa at 1m, 69kHz) was tagged on the dorsal fin without any anesthesia. The movements of three tagged fish are monitored at the same time with four omni-directional hydrophones. The locations of the fish are calculated by the hyperbolic method and tracked by a technique so called time division scheme which uses both the pulse interval and the phase. Three pingers used have the pulse interval of 1.7, 1.8 and 1.9sec, respectively, and the common pulse duration of 15ms. In results it was capable to estimate behavior right after the release, swimming speeds and approximate moving area of the fish. The movements were tracked for a week continuously, and it was found out that the staying area of the fish was around or under the farming rafts. Sometimes they swam together but most of the time they move separately. The average swimming speed of those fish was about two times of the body length.

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Pharmacokinetic/Pharmacodynamic Analysis of Metoprolol in Dogs (실험견에서 Metoprolol 약리효과의 약동/력학적 검토)

  • Oh, Dong-Jin;Jang, In-Jin;Lee, Kyung-Hun;Yim, Dong-Seok;Kim, Hyung-Kee;Shin, Sang-Goo;Park, Chan-Woong;Shin, Jae-Gook
    • The Korean Journal of Pharmacology
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    • v.31 no.2
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    • pp.251-259
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    • 1995
  • Pharmacokinetics and pharmacodynamics of metoprolol, a selective beta-l blocker, were examined for 360 minutes after intravenous bolus administration of metoprolol to 6 dogs. Plasma concentration and excreted amount in the urine metoprolol were measured by liquid chromatography with fluorescence detection. PR interval and heart rate were measured by ECG monitoring. Blood pressure was monitored through intraarterial catheter in femoral artery and cardiac output by thermodilution method using Swan-Ganz catheter. To analyze the effect site concentration-response relationship, plasma concentration and pharmacological effects were simultaneously fitted to a two pharmacokinetic compartment linked to pharmacodynamic model with NONLIN program. Results are as follows. 1) The plasma concentration of metoprolol after intrvenous injection decreased biexponentially. The terminal half-life estimated was $1.33{\pm}0.40$ hours and the volume of distribution at steady state (Vdss) and the total body clearance were $1.04{\pm}0.4\;L/kg,\;6.55{\pm}2.21\;L/hr$, respectively. The central compartment volume of distribution and peripheral compartment volume of distribution were $0.35{\pm}0.14L/kg\;and\;0.69{\pm}0.34L/kg$. The renal clearance and intercompartment clearance were $0.53{\pm}0.25\;L/min\;and\;0.35{\pm}0.19\;L/min$. 2) Simulated biophase concentration-response curve shows hyperbolic relationship and the estimated concentration-effect relationship was best explained by Emax model when the prolongation of PR interval and the reduction of the heart rate were used as pharmacodynamic parameters. Emax and EC50 were estimated to be $26.3{\pm}4.7\;msec\;and\;88.8{\pm}82.3\;g/ml$ for PR interval, and $48.7{\pm}18.8\;beats/min\;and\;113.5{\pm}78.7\;ng/ml$ for heart rate, respectively. 3) The changes of cardiac output-effect site concentration relationship was best fitted by a linear model and the slope of the relationship was $0.005{\pm}0.003$. Diastolic blood pressure-effect site concentration relationship was also explained by the linear model and the slope of the relationship was $0.038{\pm}0.034$.

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Calculation of Unit Hydrograph from Discharge Curve, Determination of Sluice Dimension and Tidal Computation for Determination of the Closure curve (단위유량도와 비수갑문 단면 및 방조제 축조곡선 결정을 위한 조속계산)

  • 최귀열
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.7 no.1
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    • pp.861-876
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    • 1965
  • During my stay in the Netherlands, I have studied the following, primarily in relation to the Mokpo Yong-san project which had been studied by the NEDECO for a feasibility report. 1. Unit hydrograph at Naju There are many ways to make unit hydrograph, but I want explain here to make unit hydrograph from the- actual run of curve at Naju. A discharge curve made from one rain storm depends on rainfall intensity per houre After finriing hydrograph every two hours, we will get two-hour unit hydrograph to devide each ordinate of the two-hour hydrograph by the rainfall intensity. I have used one storm from June 24 to June 26, 1963, recording a rainfall intensity of average 9. 4 mm per hour for 12 hours. If several rain gage stations had already been established in the catchment area. above Naju prior to this storm, I could have gathered accurate data on rainfall intensity throughout the catchment area. As it was, I used I the automatic rain gage record of the Mokpo I moteorological station to determine the rainfall lntensity. In order. to develop the unit ~Ydrograph at Naju, I subtracted the basic flow from the total runoff flow. I also tried to keed the difference between the calculated discharge amount and the measured discharge less than 1O~ The discharge period. of an unit graph depends on the length of the catchment area. 2. Determination of sluice dimension Acoording to principles of design presently used in our country, a one-day storm with a frequency of 20 years must be discharged in 8 hours. These design criteria are not adequate, and several dams have washed out in the past years. The design of the spillway and sluice dimensions must be based on the maximun peak discharge flowing into the reservoir to avoid crop and structure damages. The total flow into the reservoir is the summation of flow described by the Mokpo hydrograph, the basic flow from all the catchment areas and the rainfall on the reservoir area. To calculate the amount of water discharged through the sluiceCper half hour), the average head during that interval must be known. This can be calculated from the known water level outside the sluiceCdetermined by the tide) and from an estimated water level inside the reservoir at the end of each time interval. The total amount of water discharged through the sluice can be calculated from this average head, the time interval and the cross-sectional area of' the sluice. From the inflow into the .reservoir and the outflow through the sluice gates I calculated the change in the volume of water stored in the reservoir at half-hour intervals. From the stored volume of water and the known storage capacity of the reservoir, I was able to calculate the water level in the reservoir. The Calculated water level in the reservoir must be the same as the estimated water level. Mean stand tide will be adequate to use for determining the sluice dimension because spring tide is worse case and neap tide is best condition for the I result of the calculatio 3. Tidal computation for determination of the closure curve. During the construction of a dam, whether by building up of a succession of horizontael layers or by building in from both sides, the velocity of the water flowinii through the closing gapwill increase, because of the gradual decrease in the cross sectional area of the gap. 1 calculated the . velocities in the closing gap during flood and ebb for the first mentioned method of construction until the cross-sectional area has been reduced to about 25% of the original area, the change in tidal movement within the reservoir being negligible. Up to that point, the increase of the velocity is more or less hyperbolic. During the closing of the last 25 % of the gap, less water can flow out of the reservoir. This causes a rise of the mean water level of the reservoir. The difference in hydraulic head is then no longer negligible and must be taken into account. When, during the course of construction. the submerged weir become a free weir the critical flow occurs. The critical flow is that point, during either ebb or flood, at which the velocity reaches a maximum. When the dam is raised further. the velocity decreases because of the decrease\ulcorner in the height of the water above the weir. The calculation of the currents and velocities for a stage in the closure of the final gap is done in the following manner; Using an average tide with a neglible daily quantity, I estimated the water level on the pustream side of. the dam (inner water level). I determined the current through the gap for each hour by multiplying the storage area by the increment of the rise in water level. The velocity at a given moment can be determined from the calcalated current in m3/sec, and the cross-sectional area at that moment. At the same time from the difference between inner water level and tidal level (outer water level) the velocity can be calculated with the formula $h= \frac{V^2}{2g}$ and must be equal to the velocity detertnined from the current. If there is a difference in velocity, a new estimate of the inner water level must be made and entire procedure should be repeated. When the higher water level is equal to or more than 2/3 times the difference between the lower water level and the crest of the dam, we speak of a "free weir." The flow over the weir is then dependent upon the higher water level and not on the difference between high and low water levels. When the weir is "submerged", that is, the higher water level is less than 2/3 times the difference between the lower water and the crest of the dam, the difference between the high and low levels being decisive. The free weir normally occurs first during ebb, and is due to. the fact that mean level in the estuary is higher than the mean level of . the tide in building dams with barges the maximum velocity in the closing gap may not be more than 3m/sec. As the maximum velocities are higher than this limit we must use other construction methods in closing the gap. This can be done by dump-cars from each side or by using a cable way.e or by using a cable way.

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