• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.395-407
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.565-586
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• 2017

In this paper we continue to investigate the Super Vertex Mean behaviour of all graphs up to order 5 and all regular graphs up to order 7. Let G(V,E) be a graph with p vertices and q edges. Let f be an injection from E to the set {1,2,3,${\cdots}$,p+q} that induces for each vertex v the label defined by the rule $f^v(v)=Round\;\left({\frac{{\Sigma}_{e{\in}E_v}\;f(e)}{d(v)}}\right)$, where $E_v$ denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,${\cdots}$,p+q}. Such an injective function f is called a super vertex mean labeling of a graph G and G is called a Super Vertex Mean Graph.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.331-357
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• 2020

Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := p^λ(z)(α+βp(z)+γ/p(z)+δzp'(z)/p^j(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))² - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v² < 2u - 1.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.329-337
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• 2007

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for BVPs $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u(0)\;-\;B(u'({\eta}))\;=\;0,\;u'(1)\;=\;0}$$ and $$\{^{\;(\phi_p(u'))'\;+\;q(t)f(t,u)=0,\;0\;<\;t\;<\;1,}_{\;u'(0)\;=\;0,\;u(1)+B(u'(\eta))\;=\;0.}$$. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.417-426
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• 2017

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter h in a polynomial ring $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ is the finite field of order q with characteristic not equal to 2. This result resolves the second part of Lehmer's project for the function field case.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.599-611
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• 2016

Let $k={\mathbb{F}}_q(t)$ be a rational function field over the finite field ${\mathbb{F}}_q$. In this paper we obtain formulas of average values of L-functions of some family of Artin-Schreier extensions over k.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.385-397
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• 2009

We study codes over the polynomial ring ${\mathbb{F}}_q[D]$ and their projections to the finite rings ${\mathbb{F}}_q[D]/(D^m)$ and the weight enumerators of self-dual codes over these rings. We also give the formula for the number of codewords of minimum weight in the projections.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.07a
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• pp.143-148
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• 2001

PbWO$_4$ can be densified at 85$0^{\circ}C$ and it shows fairy good microwave dielectric properties; dielectric constant($\varepsilon$$_{r}$) of 21.5, quality factor(Q $\times$f$_{0}$) of 37,224 GHz, and temperature coefficient of resonant frequency($\tau$/suf f/) of -31ppm/$^{\circ}C$. Due to its low sintering temperature, PbWO$_4$ can be used as a multilayered chip component at microwave frequency with high electrical performance by using high conductive electrode metals such as Ag and Cu. However, in order to use this material for microwave communication devices, the $\tau$$_{f}$ of PbWO$_4$ must be stabilized to near zero with high Q$\times$f$_{0}$. In present study, PbWO$_4$ was modified by adding TiO$_2$, B$_2$O$_3$, and CuO in order to improve the microwave dielectric properties without increasing the sintering temperature. The addition of TiO$_2$ increased the $\tau$$_{f}$ and $\varepsilon$$_{r}$, due to its high rr(200ppm/$^{\circ}C$) and $\varepsilon$$_{r}$(100). However, the addition of TiO$_2$ reduced the Q$\times$f$_{0}$ value. When the mot ratio of PbWO$_4$ and TiO$_2$ was 0.913:7.087, near zero $\tau$$_{f}$(0.2ppm/$^{\circ}C$) was obtaibed with $\varepsilon$$_{r}$=22.3, and Q$\times$f/$_{0}$=21,443GHz. With this composition, various amount of B$_2$O$_3$ and CuO were added in order to improve the quality factor. The addition, of B$_2$O$_3$ decreased the $\varepsilon$$_{r}$. However, increased Q$\times$f$_{0}$ and $\tau$$_{f}$. When 2.5 wt% of B$_2$O$_3$ was added to the 0.913PbWO$_4$-0.087TiO$_2$ ceramic, $\tau$$_{f}$ =8.2, $\varepsilon$$_{r}$=20.3, Q$\times$f$_{0}$=54784 GHz. When CuO added to the 0.913PbWO$_4$-0.087TiO$_2$ ceramic, $\tau$$_{f}$ was continuously decreased. And $\varepsilon$$_{r}$ . and Q$\times$f$_{0}$ were increased up to 1.0 wt% then decreased. At 0.1 wt% of CuO addition, the 0.913PbWO$_4$-7.087Ti0$_2$ Ceramic Showed $\varepsilon$$_{r}$=23.5, $\tau$$_{f}$=4.4ppm/$^{\circ}C$, and Q$\times$f$_{0}$=32,932 GHz.> 0/=32,932 GHz.X>=32,932 GHz.> 0/=32,932 GHz.

• Proceedings of the Korean Magnestics Society Conference
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• 2007.05a
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• pp.70.1-70.1
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• 2007