• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.667-677
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• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.905-915
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• 2000

In this article we discuss some aspects of operational Tau Method on delay differential equations and then we apply this method on the differential delay equation defined by $\omega(u)\;=\frac{1}{u}\;for\;1\lequ\leq2$ and $(u\omega(u))'\;=\omega(u-1)\;foru\geq2$, which was introduced by Buchstab. As Khajah et al.[1] applied the Recursive Tau Method on this problem, they had to apply that Method under the Mathematica software to get reasonable accuracy. We present very good results obtained just by applying the Operational Tau Method using a Fortran code. The results show that we can obtain as much accuracy as is allowed by the Fortran compiler and the machine-limitations. The easy applications and reported results concerning the Operational Tau are again confirming the numerical capabilities of this Method to handle problems in different applications.

• Proceedings of the Korea Water Resources Association Conference
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• 2000.05a
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• pp.37-47
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• 2000

The method of delays is widely used fur reconstructing chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d{\;}or{\;}{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m is increased.

• Journal of Korea Water Resources Association
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• v.33 no.S1
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• pp.37-47
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• 2000

The method of delays is widely used for reconstruction chaotic attractors from experimental observations. Many studies have used a fixed delay time ${\tau}_d$ as the embedding dimension m is increased, but this is not necessarily the best choice for obtaining good convergence of the correlation dimension. Recently, some researchers have suggested that it is better to fix the delay time window ${\tau}_w$ instead. Unfortunately, ${\tau}_w$ cannot be estimated using either the autocorrelation function or the mutual information, and no standard procedure for estimating ${\tau}_w$ has yet emerged. However, a new technique, called the C-C method, can be used to estimate either ${\tau}_d\;or\;{\tau}_w$. Using this method, we show that, for small data sets, fixing ${\tau}_w$, rather than ${\tau}_d$, does indeed lead to a more rapid convergence of the correlation dimension as the embedding dimension m in increased.

• Proceedings of the KOSOMBE Conference
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• v.1989 no.05
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• pp.35-37
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• 1989

A new MR angiography technique using a composite sequence for the suppression of static sample signals is proposed and verified with experiments. When the composite [$90^{\circ}-{\tau}-180^{\circ}-2{\tau}-180^{\circ}-{\tau}$] sequence is applied, the large signal from the static sample is sufficiently suppressed but the signal from fresh inflow sample of which amplitude. is observed without suppression. These properties are appropriate for angiographic applications. In this paper, a modified line scan method (Block line scan angiography) incorporated with the composite [$90^{\circ}-{\tau}-180^{\circ}-2{\tau}-180^{\circ}-{\tau}$] sequence is used to obtain flow-only images, i.e., angiograms. The block line scan method improves the resolution in the flow-direction at the expense of imaging time. With the composite sequence, there is no need for subtraction procedure as in the most conventional angiographic methods. Experimental results for a phantom and a normal volunteer with KAIS 2.0 Tesla MRI system are shown.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.8 no.4
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• pp.197-201
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• 1975

다랭이 주낚의 양승방식에는 방향의 양승(On-tracing retrieve)방식과 역방향의 양승(Back-tracing retrieve) 방식의 두가지 방식이 있다. 순방향의 양승은 최초에 투승된 주낙끝에서부터 양승하기 시작하여 투승한 순과 같은 순으로 양승하는 것이고 역방향의 양승은 최후에 투승된 주낚끝에서부터 양승하기 시작하며 투승한 순과 반대순으로 양승하는 것이다. 주낚의 조업소요시간을 변갱하지 않고 양승방식만 변갱한다면 주낚의 평균침지시간은 변하지 않고 다만 침지시간의 분포구간만 변한다. 투승작업시간을 $\tau_1$, 투승작업이 끝나고 양승작업을 시작하기까지의 대기시간을 $\tau_2$, 양승작업시간을 $\tau_3$하면 주낚의 침지시간분포범위는 양승방식에 따라 다음과 같이 서로 다르다. $\tau_2$부터 $\tau_1+\tau_2+\tau_3$까지의 범위 역방향으로 양승할 때 $\tau_1+\tau_2$부터 $\tau_2+\tau_3$까지의 범위 임의시의 낚시 어획성능은 $F_0\varrho-^{-zt}$ ($F_0$는 초기어획성능, z는 감소계수, t는 투승후 경과시간)으로 나타낼 수 있고 침지시간 t인 낚시 Hro의 어획미수는 $H_{F_0}\frac{1-\varrho^{-zt}}{z}$로 나타낼 수 있으므로 주낙조업에서 낚시수 $H_G$개 이고 침지시간이 $\tau_\alpha$와 $\tau_\beta$ 범위내에서 분포하면 어획미수는 $C_G$는 다음과 같이 나타낼 수 있다. $$C_G=\frac{H_G}{\tau_\beta-\tau_\alpha}{\cdot}\frac{F_0}{Z}\int^{\tau_\beta}_{\tau_\alpha}(1-\varrho^{-zt})dt$$ $\tau_\alpha,\;\tau_\beta$의 값은 순방향의 양승에 있어서는 $\tau_\alpha=\tau_1+\tau_2,\;\tau_\beta=\tau_2+\tau_3$, 역방향은 양승에 있어서는 $\tau_\alpha=\tau_2,\;\tau_\beta=\tau_1+\tau_2+\tau_3$. 따라서 다랭이 주낚의 어획미수는 그 양승방식에 따라 차가 있고 순방향의 양승으로 더 많은 어획미수를 얻을 수 있다.

• The KIPS Transactions:PartB
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• v.9B no.4
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• pp.421-428
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• 2002

The local prediction method utilizing embedding vector loses the prediction power when the parameter r estimation is not exact for predicting the chaos time series induced from the high order differential equation. In spite of the fact that there have been a lot of suggestions regarding how to estimate the delay time ($\tau$), no specific method is proposed to apply to any time series. The inclinded linear model, which utilizes inclinded netter, yields satisfying degree of prediction power without estimating exact delay time ($\tau$). The usefulness of this approach has been indicated not only theoretically but also in practical situation when the method w8s applied to economical time series analysis.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.25-42
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• 2007

A direct solver for the Legendre tau approximation for the two-dimensional Poisson problem is proposed. Using the factorization of symmetric eigenvalue problem, the algorithm overcomes the weak points of the Schur decomposition and the conventional diagonalization techniques for the Legendre tau approximation. The convergence of the method is proved and numerical results are presented.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1715-1725
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• 1998

A two-dimensional transient inverse heat conduction problem involving the estimation of the unknown location, ($X^*$, $Y^*$), and timewise varying unknown strength, $G({\tau})$, of a line heat source embedded inside a rectangular bar with insulated boundaries has been solved simultaneously. The regular conjugate gradient method, RCGM and the modified conjugate gradient method, MCGM with adjoint equation, are used alternately to estimate the unknown strength $G({\tau})$ of the source term, while the parameter estimation approach is used to estimate the unknown location ($X^*$, $Y^*$) of the line heat source. The alternate use of the regular and the modified conjugate gradient methods alleviates the convergence difficulties encountered at the initial and final times (i.e ${\tau}=0$ and ${\tau}={\tau}_f$), hence stabilizes the computation and fastens the convergence of the solution. In order to examine the effectiveness of this approach under severe test conditions, the unknown strength $G({\tau})$ is chosen in the form of rectangular, triangular and sinusoidal functions.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.