• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.623-635
• /
• 2006

In this paper, we derive an elementary formula for the linearization coefficients of the product of two Legendre polynomials. Our main purpose is to study the method which can be used to derive the formula, which is straightforward from the integration and their orthogonality.

• Journal of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.485-501
• /
• 2001

In this paper we express analytic Feynman integral of the first variation of a functional F in terms of analytic Feynman integral of the product F with a linear factor and obtain an integration by parts formula of the analytic Feynman integral of functionals on abstract Wiener space. We find the Fourier-Feynman transform for the product of functionals in the Fresnel class F(B) with n linear factors.

• Kyungpook Mathematical Journal
• /
• v.56 no.1
• /
• pp.131-136
• /
• 2016

The main object of this paper is to present two general integral formulas whose integrands are the integrand given in the integral formula (3) and a finite product of the generalized Bessel function of the first kind.

• Journal of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.265-294
• /
• 2004

In this paper, using a simple formula, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products of cylinder type functions, and show that the conditional Fourier-Feynman transform of the conditional convolution product is expressed as a product of the conditional Fourier-Feynman transforms. Also, we evaluate the conditional Fourier-Feynman transforms of the functions of the forms exp {$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))ds}$\Phi$($\chi$(T)), exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}, exp{$\int_{O}^{T}$ $\theta$(s,$\chi$(s))d${\zeta}$(s)}$\Phi$($\chi$(T)) which are of interest in Feynman integration theories and quantum mechanics.

• Asian-Australasian Journal of Animal Sciences
• /
• v.19 no.10
• /
• pp.1490-1495
• /
• 2006

The purpose of this research was to develop an optimum composition model for a new synbiotic fermented dairy product with high probiotic cell counts, and to experimentally verify this model. The optimum composition model indicated the growth promoter ratio that could provide the highest growth rate for probiotics in this fermented product. Different levels of growth promoters were first blended with milk to improve the growth rates of probiotics, and the optimum composition model was determined. The probiotic viabilities and chemical properties were analyzed for the samples made using the optimal formula. The optimal combination of the growth promoters for the synbiotic fermented milk product was 1.12% peptides, 3% fructooligosaccharides (FOS), and 1.87% isomaltooligosaccharides (IMO). A product manufactured according to the formula of the optimum model was analyzed, showing that the model was effective in improving the viability of both Lactobacillus spp. and Bifidobacterium spp.

• Journal of Korean Institute of Industrial Engineers
• /
• v.25 no.1
• /
• pp.125-129
• /
• 1999

The Little's formula, $L={\lambda}W$, expresses a fundamental principle of queueing theory: Under very general conditions, the average queue length is equal to the product of the arrival rate and the average waiting time. This useful formula is now well known and frequently applied. In this paper, we demonstrate that the Little's formula has much more power than was previously realized when it is properly decomposed into what we call the microscopic Little's formula. We use the M/G/1 queue with server vacations as an example model to which we apply the microscopic Little's formula. As a result, we obtain a transform-free expression for the queue length distribution. Also, we briefly summarize some previous efforts in the literature to increase the power of the Little's formula.

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1255-1274
• /
• 2008

The purpose of this paper is to discuss the constant term appearing in the BFK-gluing formula for the zeta-determinants of Laplacians on a complete Riemannian manifold when the warped product metric is given on a collar neighborhood of a cutting compact hypersurface. If the dimension of a hypersurface is odd, generally this constant is known to be zero. In this paper we describe this constant by using the heat kernel asymptotics and compute it explicitly when the dimension of a hypersurface is 2 and 4. As a byproduct we obtain some results for the value of relative zeta functions at s=0.

• Journal of the Korean Mathematical Society
• /
• v.57 no.4
• /
• pp.1059-1059
• /
• 2020

• Journal of applied mathematics & informatics
• /
• v.34 no.3_4
• /
• pp.207-220
• /
• 2016

Our goal is to construct a two-frequency-dependent formula $I_N$ which interpolates a product f of two functions with different frequencies at some N points. In the beginning, it is not clear to us that the formula $I_N$ satisfies $I_N=f$ at the points. However, it is later shown that $I_N$ satisfies the above equation. For this theoretical development, a one-frequency-dependent formula is introduced, and some of its characteristics are explained. Finally, our newly constructed formula $I_N$ is compared to the classical Lagrange interpolating polynomial and the one-frequency-dependent formula in order to show the advantage that is obtained by generating the formula depending on two frequencies.

• Journal of the Korean Mathematical Society
• /
• v.45 no.6
• /
• pp.1635-1646
• /
• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.