• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.26 no.9
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• pp.416-423
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• 2014

To verify different boundary conditions on the borehole wall, which are commonly used for generating g-function, the well-known TRNSYS simulation model, DST (Duct STorage), is employed. By letting the fluid circulation determine the borehole wall conditions, a DST-based g-function is induced with numerical processes proposed in this work. A new TRNSYS module is also developed to accommodate g-function data and predict dynamic outlet fluid temperatures. Results showed that the modified g-function, which is different from Eskilson's original g-function, is closer to the DST-based g-function. This implies that the uniform heat transfer rates over the height can be used for good approximation. In fact, simulations with the modified g-function showed similar results as the DST model, while Eskilson g-function case deviated from the DST model as time progressed.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.595-599
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• 2011

We prove that for any positive integer $g{\geq}3$, there are ${\gg}q^{\frac{l}{2g}}$ real cyclotomic function fields whose conductor has degree ${\leq}l$ and ideal class number is divisible by $\frac{g}{gcd(2,g)}$.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1671-1683
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• 2016

Abstract. In this paper, for $a{\in}C$, we investigate functions $g_a$ and ${\psi}_a$ associated with three term relations. $g_a$ is defined by means of function ${\psi}_a$. By using these functions, we obtain some functional equations related to the Eisenstein series and the Riemann zeta function. Also we find a generalized difference formula of function $g_a$.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.337-345
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• 2023

Different versions of the boundary Schwarz lemma for the 𝒩 (𝜌) class are discussed in this study. Also, for the function g(z) = z+b₂z²+b₃z³+... defined in the unit disc D such that g ∈ 𝒩 (𝜌), we estimate a modulus of the angular derivative of g(z) function at the boundary point 1 ∈ 𝜕D with g'(1) = 1 + 𝜎 (1 - 𝜌), where ${\rho}={\frac{1}{n}}{\sum\limits_{i=1}^{n}}g(c_i)={\frac{g^{\prime}(c_1)+g^{\prime}(c_2)+{\ldots}+g^{\prime}(c_n)}{n}}{\in}g^{\prime}(D)$ and 𝜌≠1, 𝜎 > 1 and c₁, c₂, ..., c_n ∈ 𝜕D. That is, we shall give an estimate below |g"(1)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z ≠ 0. Estimating is made by using the arithmetic average of n different derivatives g'(c₁), g'(c₂), ..., g'(c_n).

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1309-1318
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• 2009

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A Roman k-dominating function on G is a function f : V (G) $\rightarrow$ {0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices $\upsilon_1,\;\upsilon_2,\;{\ldots},\;\upsilon_k$ with $f(\upsilon_i)$ = 2 for i = 1, 2, $\ldot$, k. The weight of a Roman k-dominating function is the value f(V (G)) = $\sum_{u{\in}v(G)}$ f(u). The minimum weight of a Roman k-dominating function on a graph G is called the Roman k-domination number ${\gamma}_{kR}$(G) of G. Note that the Roman 1-domination number $\gamma_{1R}$(G) is the usual Roman domination number $\gamma_R$(G). In this paper, we investigate the properties of the Roman k-domination number. Some of our results extend these one given by Cockayne, Dreyer Jr., S. M. Hedetniemi, and S. T. Hedetniemi [2] in 2004 for the Roman domination number.

• Publications of The Korean Astronomical Society
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• v.25 no.4
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• pp.113-118
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• 2010

The Henyey-Greenstein (H-G) phase function, which is characterized by a single parameter, has been generally used to approximate the realistic dust-scattering phase function in investigating scattering properties of the interstellar dust. Draine (2003) proposed a new analytic phase function with two parameters and showed that the realistic phase function is better represented by his phase function. If the H-G and Draine's phase functions are significantly different, using the H-G phase function in radiative transfer models may lead to wrong conclusions about the dust-scattering properties. Here, we investigate whether the H-G and Draine's phase functions would indeed produce significant differences in radiative transfer calculations for two simple configurations. For the uniformly distributed dust with an illuminating star at the center, no significant difference is found. However, up to ~ 20% of difference is found when the central star is surrounded by a spherical-shell dust medium and the radiation of $\lambda$ < $2000\;{\AA}$ is considered. It would mean that the investigation of dust-scattering properties using the H-G phase function may produce errors of up to ~ 20% depending on the geometry of dust medium and the radiation wavelength. This amount of uncertainty would be, however, unavoidable since the configurations of dust density and radiation sources are only approximately available.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1079-1089
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• 2009

In this paper, we shall show that for any entire function f, the function of the form $f^m(f^n$ - 1)f' has no non-zero finite Picard value for all positive integers m, n ${\in}\;{\mathbb{N}}$ possibly except for the special case m = n = 1. Furthermore, we shall also show that for any two nonconstant meromorphic functions f and g, if $f^m(f^n$-1)f' and $g^m(g^n$-1)g' share the value 1 weakly, then f $\equiv$ g provided that m and n satisfy some conditions. In particular, if f and g are entire, then the restrictions on m and n could be greatly reduced.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.12
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• pp.1914-1924
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• 2016

In this paper, considering virtualized Evolved Packet Core(vEPC) network for 5G mobile network, we propose architecture for supporting Service Function Chaining(SFC) in 5G mobile network. Using SFC in 5G network, dynamic path configuration and providing network services based on subscriber and traffic information. SFC technology provides logical ordered set of network functions and delivers packet through providing logical path over the physical network. Based on the perspective of 5G core network in distributed manner, we design hierarchical SFC architecture to manage SFC for global path including vEPC and SGi-LAN network, and internal path between virtualized network functions in each cloud. In this paper, we define architecture and call flow for establishing data path using SFC. Finally, we design testbed architecture for real implementation based on open source software.

• Journal of the Korean Applied Science and Technology
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• v.37 no.3
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• pp.409-417
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• 2020

The purpose of this study was to investigate the effects of different types of exercise training on ẞ-Amyloid, Brain-Derived Nerurotrophic Factor(BDNF) and cognitive function in mice with Diabetes Mellitus Group(DM.G). 24 male C57BL/6 mice were randomly assigned to the control (C.G. n = 6) and Diabetes Mellitus Group(DM.G. n = 18) groups. After the Diabetes Mellitus induction period, the DM group was subdivided into DM.G. + sedentary (DM.G., n = 6), DM.G. + endurance exercise (A.G, n = 6), and DM.G. + resistance exercise (R.G., n = 6). The A.G. and R.G performed treadmill and ladder climbing exercises 5 times per week for 8 weeks, respectively. After 8 weeks the results are as follows: ẞ-Amyloid showed higher levels of DM.G. than in A.G., R.G., and C.G., but was not statistically significant(p>.05). BDNF was significantly lower in DM.G. than in C.G., A.G., and R.G.(p <0.05). The Y-maze task performance for cognitive function was significantly lower in DM.G. than in C.G., A.G., and R.G.(p <0.05). These results predict that diabetes can negatively affect ẞ-Amyloid, BDNF and cognitive function. It can also be predicted that low-intensity exercise can positively improve ẞ-Amyloid, BDNF and cognitive function regardless of the type of exercise.