• Korean Journal of Fisheries and Aquatic Sciences
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• v.8 no.2
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• pp.47-60
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• 1975

For the calculation of population parameter and estimation of recruitment of a fish population, an application of multiple regression method was used with some statistical inferences. Then, the differences between the calculated values and the true parameters were discussed. In addition, this method criticized by applying it to the statistical data of a population of bigeye tuna, Thunnus obesus of the Indian Ocean. The method was also applied to the available data of a population of Pacific saury, Cololabis saira, to estimate its recuitments. A stock at t year and t+1 year is, $N_{0,\;t+1}=N_{0,\;t}(1-m_t)-C_t+R_{t+1}$ where $N_0$ is the initial number of fish in a given year; C, number o: fish caught; R, number of recruitment; and M, rate of natural mortality. The foregoing equation is $$\phi_{t+1}=\frac{(1-\varrho^{-z}{t+1})Z_t}{(1-\varrho^{-z}t)Z_{t+1}}-\frac{1-\varrho^{-z}t+1}{Z_{t+1}}\phi_t-a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}C_t+a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}R_{t+1}......(1)$$ where $\phi$ is CPUE; a', CPUE $(\phi)$ to average stock $(\bar{N})$ in number; Z, total mortality coefficient; and M, natural mortality coefficient. In the equation (1) , the term $(1-\varrho^{-z}t+1)/Z_{t+1}$s almost constant to the variation of effort (X) there fore coefficients $\phi$ and $C_t$, can be calculated, when R is a constant, by applying the method of multiple regression, where $\phi_{t+1}$ is a dependent variable; $\phi_t$ and $C_t$ are independent variables. The values of Mand a' are calculated from the coefficients of $\phi_t$ and $C_t$; and total mortality coefficient (Z), where Z is a'X+M. By substituting M, a', $Z_t$, and $Z_{t+1}$ to the equation (1) recruitment $(R_{t+1})$ can be calculated. In this precess $\phi$ can be substituted by index of stock in number (N'). This operational procedures of the method of multiple regression can be applicable to the data which satisfy the above assumptions, even though the data were collected from any chosen year with similar recruitments, though it were not collected from the consecutive years. Under the condition of varying effort the data with such variation can be treated effectively by this method. The calculated values of M and a' include some deviation from the population parameters. Therefore, the estimated recruitment (R) is a relative value instead of all absolute one. This method of multiple regression is also applicable to the stock density and yield in weight instead of in number. For the data of the bigeye tuna of the Indian Ocean, the values of estimated recruitment (R) calculated from the parameter which is obtained by the present multiple regression method is proportional with an identical fluctuation pattern to the values of those derived from the parameters M and a', which were calculated by Suda (1970) for the same data. Estimated recruitments of Pacific saury of the eastern coast of Korea were calculated by the present multiple regression method. Not only spring recruitment $(1965\~1974)$ but also fall recruitment $(1964\~1973)$ was found to fluctuate in accordance with the fluctuations of stock densities (CPUE) of the same spring and fall, respectively.

• Bulletin of the Korean Chemical Society
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• v.33 no.9
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.11a
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• pp.112-119
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• 2001

Parameter tuning methods by Ziegler-Nickels for control systems are generally classified into Z-N(1) and Z-N(2). The purpose of this paper is to describe what relations exist between methods of Z-N(1) and Z-N(2), or how Z-N(1) method can be originated from Z-N(2) method by analyzing one loop control system of P or PI controller and time delay process. The formulas of Z-N(1) consist of process parameters, L(time delay), $K_m$(gain) and $T_m$(time constant), but Z-N(2) method is based only on the ultimate gain $K_u$ and the ultimate period $T_u$ acquired normally by practical trial without any parameters of Z-N(1). In this paper, for the first step to seek mutual relations, the simple formulas of Z-N(2) are transformed into the formulas composed of the same parameters as Z-N(1) which is derived from the analysis of frequency characteristics. Then, the approximation of the actual ultimate frequency is proposed as important premise in the translation between Z-N(1) and (2). Such equalization and approximation brings a simple approximated formula which can explain how Z-N(1) is originated from the Z-N(2) in the form of formula. And a model system is adopted to compare the approximated formula to Z-N(1) and Z-N(2) methods, the results of which show the effectiveness of the proposals.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.14 no.4
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• pp.253-259
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• 1981

A study was made to find out a new method of calculating the survival rate of a fish population from length composition and growth equation. 1. In the steady state of the fish population, let the total mortality rate be z, the age of complete recruitment a, the oldest age in the catch b and the average between the age of complete recruitment and the oldest age in the catch Ut, then we have $$U_{t}\;=\;\frac{a-b\;{e xp}\{-z(b-a)\}}{1-\;{e xp}\{-z(b-a)\}}+\frac{1}{z}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}$$(1) And let b be infinite, then we obtain $$Z=\frac{1}{U_t-a}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}{\cdots}$$ (2) 2. Calculating numerical value of $U_t$ from age composition table and growth equation, and substitute in (1) for it, we may obtain the value of z and $e^{-z}$. 3. This method is applied to a case of mackerel and horse mackerel in the coastal waters of Korea, with the following results : Total mortality rate-Mackerel : 0.87909, Horse mackerel : 2.22327, Survival rate-Mackerel : 0.41516, Horse Mackerel : 0.10825, 95 percent confidence Interval of survival rate-Mackerel : $0.35966{\sim}0.47264$, Horse mackerel : $0.06897{\sim}0.14974$

• Proceedings of the Korean Geotechical Society Conference
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• 1999.03a
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• pp.3-46
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• 1999

A new method called SRICOS is proposed to predict the scour depth z versus time t around a cylindrical bridge pier of diameter D founded in clay. The steps involved are ; 1. taking samples at the bridge pier site, 2. testing them in an Erosion Function Apparatus called the EFA to obtain the scour rate z versus the hydraulic shear stress applied $\tau$, 3. predicting the maximum shear stress r max which will be induced around the pier by the water flowing at ν Ο before the scour hole starts to develop, 4. using the measured z versus r curve to obtain the initial scour rate zi corresponding to r max , 5. predicting the maximum depth of scour zmax for the pier, 6. using zi and zmarx to develop the hyperbolic function describing the scour depth z versus time t curve, and 7. reading the z vs. t curve at a time corresponding to the duration of the flood to find the scour depth which will develop around the pier. A new apparatus is developed to measure the z vs t curve of step 2, a series of advanced numerical simulations are performed to develop an equation for the $\tau$ max value of step 3, and a series of flume tests are performed to develop an equation for the zmax value of step 5. The method is evaluated by comparing predictions and measurements in 42 flume experiments.

• Journal of the Korean GEO-environmental Society
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• v.13 no.10
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• pp.33-42
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• 2012

The efficiency of the current design methods for computing pile resistances is analyzed using field load-settlement tests results. Twelve load-settlement test data for drilled shafts and bored piles were obtained from the literature. These load-test data were fitted using the t-z method. Subsequently, the ultimate resistances were evaluated based upon the failure criteria from following methods: (1) the Davisson's approach and (2) settlement corresponding to 5% or 10% shaft diameter approach. The ultimate resistances for these drilled shafts and bored piles were also predicted using methods based on the design code from North America (United States, Canada), Europe, and Asia (Japan). The pile resistances determined from field load-settlement tests were compared with those calculated using the design codes. The comparisons show that most design codes predict a conservative resistance for drilled shafts and bored piles. However, in the case of drilled shafts, we find that some of the design codes can over-predict the resistance and, therefore, should be applied cautiously. This research also shows that the t-z method can be successfully used to predict the ultimate resistance and the load transfer mechanism for a single pile.

• Proceedings of the KIEE Conference
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• 1996.11a
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• pp.49-51
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• 1996

The z-transform method is a basic mathematical tool in analyzing and designing sampled-data control systems. However, since the z-transform method relates only the sampling-instants signals, another mathematical tool is necessary to describe the continous signals between the sampling instants. For this purpose the delayed and the modi fled z-transform methods were developed. The definition of the modi fled z-transform includes a sample in the interval [-T,0] of the original signal in its series expression, where the signal value is always zero for any physical system. From this reason one step skew of the time index always appears in its application formulas. This introduces an unnecessary operation and a gap in linking the mathematical formula and its physical interpretation. Considering the conceptual difficulty and application inconvenience, a method of using the advanced z-transform in analysis of sampled-data control systems is developed as a replacement of the modi fled z-transform. With one formulation of the advanced z-transform, now it is possible to relate both the signals of the sampling instants and those in between without any complication and conceptual difficulty.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.293-303
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• 2020

The present work aims to analyzed the transient thermoelastic stress analysis of a thin circular plate with uniform internal heat generation. Initially, the plate is characterized by a parabolic temperature distribution along the z-direction given by T = T₀(r, z) and perfectly insulated at the ends z = 0 and z = h. For times t > 0, the surface r = a is subjected to convection heat transfer with convection coefficient h_c and fluid temperature T_∞. The integral transform method used to obtain the analytical solution for temperature, displacement, and thermal stresses. The associated thermoelastic field is analyzed by making use of the temperature and thermoelastic displacement potential function. Numerical results are carried out with the help of computational software PTC Mathcad Prime-3.1 and shown in figures.

• Journal of Electrical Engineering and Technology
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• v.11 no.6
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• pp.1769-1776
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• 2016

For on-line partial discharge (PD) monitoring of rotating machines, a novel sensor is proposed, which can be installed on the power lead inside the terminal box of the machine. The sensor has been designed to have high capacitance, and minimal reflection of measured pulses. As a sensitivity of the sensor, transfer impedance $Z_t$ has been measured and compared to conventional coupler-type sensors. A simple method is presented for measuring $Z_t$ of coupler sensors, using a vector network analyzer and a practical lead-cable of rotating machine. Through this method, it became possible to measure the $Z_t$ of coupler sensors including the installation environment of them. The $Z_t$ of the proposed sensor is higher than that of same sized other conventional couplers at frequencies between 30 and 92 MHz. Another sensitivity test has been performed using a PD calibrator as a test pulse source. The proposed sensor has higher measured peak voltage than the conventional coupler type sensors when the same charges were input.