• Korean Journal of Mathematics
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• v.16 no.3
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• pp.425-437
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• 2008

Let P be a poset and G = G(P) be the incomparability graph of P. Stanley [7] defined the chromatic symmetric function $X_{G(P)}$ which generalizes the chromatic polynomial ${\chi}_G$ of G, and showed all coefficients are nonnegative in the e-expansion of $X_{G(P)}$ for a poset P of rank 1. In this paper, we construct a sign reversing involution on the set of special rim hook P-tableaux with some conditions. It gives a combinatorial proof for (3+1)-free conjecture of a poset P of rank 1.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.635-648
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• 2022

In this paper, we establish an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_P)$ averaging over ℙ_2g+1 and over ℙ_2g+2 as g → ∞ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_u)$ averaging over 𝓘_g+1 and over 𝓕_g+1 as g → ∞ in even characteristic.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1139-1151
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• 2022

This paper studies the eigenvalues of the G(·)-Laplacian Dirichlet problem $$\{-div\;\(\frac{g(x,\;{\mid}{\nabla}u{\mid})}{{\mid}{\nabla}u{\mid}}{\nabla}u\)={\lambda}\;\(\frac{g(x,{\mid}u{\mid})}{{\mid}u{\mid}}u\)\;in\;{\Omega}, \\u\;=\;0\;on\;{\partial}{\Omega},$$ where Ω is a bounded domain in ℝ^N and g is the density of a generalized Φ-function G(·). Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.

• The Journal of Korean Medicine
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• v.30 no.3
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• pp.28-38
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• 2009

Background : Peripheral nerve injuries are a commonly encountered clinical problem and often result in a chronic pain and severe functional deficits. Objective : The aim of this study was to evaluate the effects of Gentianae Macrophyllae Radix (G. M. Radix) on the pain control and the recovery of the locomotor function that results from the sciatic crushed nerve injury in rats. Method : Using rats, we crushed their sciatic nerve, and then orally administered the aqueous extract of G. M. Radix. The effects of G. M. Radix on the recovery locomotor function were investigated by walking track analysis. The effects of G. M. Radix on pain control were investigated by brain-derived neurotrophic factor (BDNF) expression in the sciatic nerve, and c-Fos expression in the paraventricular nucleus (PVN) of the hypothalamus and in the ventrolateral periaqueductal gray (vlPAG). Result : G. M. RADIX facilitates motor function from the locomotor deficit, and thereby increased BDNF expression and suppressed painful stimuli in the PVN and vlPAG after sciatic crushed nerve injury. Conclusion : It is suggested that G. M. Radix might aid recovery locomotor function and control pain after sciatic crushed nerve injury. Further studies on identifying specific the component in G.M. Radix associated with enhanced neural activity in the peripheral nerve injury may be helpful to develop therapeutic strategies for the treatment of peripheral nerve injury.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.837-844
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• 2002

In this paper, we obtain the Hyers-Ulam Stability for the difference equations of the form f(x + 1) = $\Gamma$(x)f(x), which is the reciprocal functional equation of the double gamma function.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.26 no.6
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• pp.263-268
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• 2014

Eskilson's g-function, a well-known geothermal heat response factor, is widely used for sizing of the ground heat exchangers. Unlike the Eskilson's original model that uses common temperature boundaries for all boreholes and along the borehole height, an analytical-solution-based g-function uses a uniform heat transfer rate over the height with variable heat transfer rates for respective boreholes. To evaluate the impact of such a boundary difference on g-function and the design length, a simple case study was carried out on the cooling-dominant commercial buildings. The results show that the design lengths given by the boundary of uniform heat transfer rates are longer than those given by Eskilson's boundary for all cases tested. The difference in length is more important when the bore field is composed of more boreholes with shorter length of each borehole.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.191-198
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• 2005

In this paper, we introduce a length function for elements of the imprimitive complex reflection group G(m, 1, n) and study its properties. Furthermore, we show that every conjugacy class of G(m, 1, n) can be represented by an admissible diagram. The corresponding results for Weyl groups are well known.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.247-257
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• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.243-254
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• 1991

For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.