• 대한수학회논문집
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• 제22권3호
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• pp.353-357
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• 2007

Let $(g,\;\delta)$ be a Lie bialgebra. Here we give an explicit formula for the Poisson bracket on a subalgebra of $U(g)^{\circ}$ induced by the given cobracket $\delta$.

• 대한수학회보
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• 제50권3호
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• pp.929-934
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• 2013

In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.

• Korean Journal of Mathematics
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• 제28권1호
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

• 대한수학회논문집
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• 제34권2호
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• Advances in Computational Design
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• 제8권2호
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• pp.147-177
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• 2023

Elliptical concrete-filled steel tubular (CFST) column is widely used in modern structures for both aesthetical appeal and structural performance benefits. The ultimate axial load is a critical factor for designing the elliptical CFST short columns. However, there are complications of geometric and material interactions, which make a difficulty in determining a simple model for predicting the ultimate axial load of elliptical CFST short columns. This study aims to propose an efficient adaptive neuro-fuzzy inference system (ANFIS) model for predicting the ultimate axial load of elliptical CFST short columns. In the proposed method, the ANFIS model is used to establish a relationship between the ultimate axial load and geometric and material properties of elliptical CFST short columns. Accordingly, a total of 188 experimental and simulation datasets of elliptical CFST short columns are used to develop the ANFIS models. The performance of the proposed ANFIS model is compared with that of existing design formulas. The results show that the proposed ANFIS model is more accurate than existing empirical and theoretical formulas. Finally, an explicit formula and a Graphical User Interface (GUI) tool are developed to apply the proposed ANFIS model for practical use.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.881-892
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• 1999

In this paper we consider a polling system with two classes of stations; high priority and low priority. High priority stations are polled more frequently than low priority stations. We derive an exact and explicit formula for computing the mean waiting times for a message when the arrival processes are batch Poisson. In general the formula requires to solve two sets of simultaneous equations By specializing them to the case of two priority classes we greatly reduce the number equations and provide a simple formula for mean waiting times. We apply the results to a data communication processing system and show that the overall mean waiting time can be reduced by using priority polling.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.1186-1190
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• 1995

This paper is focused on the formulation of explicit closed-form functions describing the performance measures of the general flexible manufacturing system (FMS)according to the strategy of material handling system(MHS). the performance measures such as the production rate, the production lead-time and the utilization rate of the general FMS are expressed, respectively, as the explicit closed-form functions of the part processing time, the service rate of the material handling system (MHS) and the number of machine tools in the FMS. For this, the gensral FMS is presented as a generalized stochastic Petri net model, then, the moment generating function (MGF) based approach is applied to obtain the steady-state probabity formulation. Based on the steady-state formulation, the explicit closed-form functions for performance measures of the probability FMS can be obtained. Finally, the analytical results are compared with the Petri net simulation results to verify the validity of the suggested method. The paper is of significance in the sense that it provides a comprehensive formula for performance measures of the FMS even to the industry engineers and academic reademic resuarchers who have no background on Markov chain analysis method or Petrinet modeling

• 대한수학회지
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• 제42권2호
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• pp.203-222
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• 2005

Thompson series is a Hauptmodul for a genus zero group which lies between $\Gamma$o(N) and its normalizer in PSL2(R) ([1]). We construct explicit ring class fields over an imaginary quadratic field K from the Thompson series $T_g$($\alpha$) (Theorem 4), which would be an extension of [3], Theorem 3.7.5 (2) by using the Shimura theory and the standard results of complex multiplication. Also we construct various class fields over K, over a CM-field K (${\zeta}N + {\zeta}_N^{-1}$), and over a field K (${\zeta}N$). Furthermore, we find an explicit formula for the conjugates of Tg ($\alpha$) to calculate its minimal polynomial where $\alpha$ (${\in}{\eta}$) is the quotient of a basis of an integral ideal in K.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1073-1086
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• 2009

This paper considers the problems of martingale measures and risk-minimizing hedging strategies in the market with restricted information. By constructing a general restricted information market model, the explicit relation of arbitrage and the minimal martingale measure between two different information markets are discussed. Also a link among all equivalent martingale measures under restricted information market is given. As an example of restricted information markets, this paper constitutes a jump-diffusion process model and presents a risk minimizing problem under different information. Through $It\hat{o}$ formula and projection results in Schweizer[13], the explicit optimal strategy for different market information are given.

• 대한수학회논문집
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• 제34권1호
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• pp.333-349
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• 2019

The paper study the curvature theory of a line-trajectory of constant Disteli-axis, according to the invariants of the axodes of moving body in spatial motion. A necessary and sufficient condition for a line-trajectory to be a constant Disteli-axis is derived. From which new proofs of the Disteli's formulae and concise explicit expressions of the inflection line congruence are directly obtained. The obtained explicit equations degenerate into a quadratic form, which can easily give a clear insight into the geometric properties of a line-trajectory of constant Disteli-axis with the theory of line congruence. The degenerated cases of the Burmester lines are discussed according to dual points having specific trajectories.