• 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

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.853-867
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• 2013

In this paper we study the cardinality of the dot product set generated by two subsets of vector spaces over finite fields. We notice that the results on the dot product problems for one set can be simply extended to two sets. Let E and F be subsets of the d-dimensional vector space $\mathbb{F}^d_q$ over a finite field $\mathbb{F}_q$ with q elements. As a new result, we prove that if E and F are subsets of the paraboloid and ${\mid}E{\parallel}F{\mid}{\geq}Cq^d$ for some large C > 1, then ${\mid}{\Pi}(E,F){\mid}{\geq}cq$ for some 0 < c < 1. In particular, we find a connection between the size of the dot product set and the number of lines through both the origin and a nonzero point in the given set E. As an application of this observation, we obtain more sharpened results on the generalized dot product set problems. The discrete Fourier analysis and geometrical observation play a crucial role in proving our results.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07b
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• pp.642-645
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• 2002

Microwave dielectric properties of $ZnWO_4$ ceramic were investigated with calcination and sintering temperatures. The dielectric properties required for such application are high dielectric constant$(\varepsilon_r)$, high $Q{\times}f_o$ value and low temperature coefficient of resonant frequency$(\tau_f)$. These requirement correspond to necessities for size reduction, excellent frequency selectivity, good temperature stability of devices. $ZnWO_4$ ceramics could be sintered at low $1075^{\circ}C$, which was comparatively low temperature for microwave dielectrics. As a result, $ZnWO_4$ showed the dielectric constant of 13, quality factor($Q{\times}f_o$ value) of 22000 and 'temperature coefficient of resonant frequency$(\tau_f)$ of $-65{\pm}5ppm/^{\circ}C$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.659-668
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• 2021

Let R be a semiprime ring with maximal right ring of quotients Q_mr(R), and let n₁, n₂, …, n_k be k fixed positive integers. Suppose that R is (n₁+n₂+⋯+n_k)!-torsion free, and that f : 𝜌 → Q_mr(R) is an additive map, where 𝜌 is a nonzero right ideal of R. It is proved that if [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ 𝜌, then [f(x), x] = 0 for all x ∈ 𝜌. This gives the result of Beidar et al. [2] for semiprime rings. Moreover, it is also proved that if R is p-torsion, where p is a prime integer with p = Σ^k_i=1 n_i and if f : R → Q_mr(R) is an additive map satisfying [[…[f(x), x^n₁], …], x^n_k] = 0 for all x ∈ R, then [f(x), x] = 0 for all x ∈ R.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.163-173
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• 2010

We consider the system $$\{{{-{\Delta}_pu\;=\;{\lambda}f(\upsilon),\;\;\;x\;{\in}\;{\Omega}, \atop -{\Delta}_q{\upsilon}\;=\;{\mu}g(u),\;\;\;x\;{\in}\;{\Omega},} \atop u\;=\;\upsilon\;=\;0,\;\;\;x\;{\in}\;{\partial\Omega},}$$ where ${\Delta}_pu\;=\;div(|{\nabla}_u|^{p-2}{\nabla}_u)$, ${\Delta}_{q{\upsilon}}\;=\;div(|{\nabla}_{\upsilon}|^{q-2}{\nabla}_{\upsilon})$, p, $q\;{\geq}\;2$, $\Omega$ is a ball in $\mathbf{R}^N$ with a smooth boundary $\partial\Omega$, $N\;{\geq}\;1$, $\lambda$, $\mu$ are positive parameters, and f, g are smooth functions that are negative at the origin and f(x) ~ $x^m$ g(x) ~ $x^n$ for x large for some m, $n\;{\geq}\;0$ with mn < (p - 1)(q - 1). We establish the existence and uniqueness of positive radial solutions when the parameters $\lambda$ and $\mu$ are large.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.37-42
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• 2005

We analyzed spectral attenuation of coda waves and estimated coda Q values in the crust of the Korean peninsula. 574 NS-component seismograms registered by the Korea Meteorological Administration (KMA) and Korea Institute of Geology, Mining and Materials (KIGAM) seismic networks with epicentral distances less than 100 km and sampling rate greater than 80 Hz were selected for this study. We estimated coda Q values using the single isotropic scattering model at center frequencies of 1.5, 3, 6, 9, 12, 15, and 18 Hz with 20 s time window starting from double of the S-wave arrival times. Estimated coda Q value at 1 Hz ($Q_0$) and n value range 50 to 250 and 0.5 to 1.0, respectively, and they are well correlated with the regional geology in the Korean peninsula. The $Q_0$ values in western Korea agree well with those of eastern China.

• Journal of the Korean Ceramic Society
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• v.40 no.4
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• pp.350-353
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• 2003

Millimeter-wave dielectric ceramics have been used like applications for ultrahigh speed wireless LAN because it reduces the resources of electromagnetic wave, and Intelligent Transport System (ITS) because of straight propagation wave. For millimeterwave, the dielectric ceramics with high quality factor (Q$.$f), low dielectric constant($\varepsilon$), and nearly zero temperature coefficient of resonant frequency ($\tau$) are needed. No microwave dielectric ceramics with these three properties exist except Ba(Mg$\_$1/3/Ta/sub1/3/)O$_3$ (BMT), which has a little high s: In this paper, alumina (Al$_2$O$_3$) and fosterite (Mg$_2$SiO$_4$), candidates for millimeter-wave applications, were studied with an objective to get high q$.$f and nearly zero $\tau$$\_$f/ For alumina ceramics, q$.$f more than 680,000 GHz was obtained but it was difficult to obtain nearly zero Qf. On the other hand, for forsterite ceramics, q$.$f was achieved from 10,000 GHz of commercial for sterite to 240,000 GHz of highly purified MgO and SiO$_2$ raw materials, and $\tau$$\_$f/ was reduced a few by adding TiO$_2$ with high positive $\tau$$\_$f/.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.2
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• pp.67-72
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• 2004

The microwave dielectric properties and microstructure of the (1-x)$Mg_4Ta_2O_{9-x}TiO_2$(X=0, 0.3, 0.4) ceramic were, investigated. The specimens were prepared by the conventional mixed oxide method with sintering temperature of $1350^{\circ}C$∼$1425^{\circ}C$. According to the XRD patterns, the (1-x)$Mg_4Ta_2O_{9-x}TiO_2$(X=0, 0.3, 0.4) ceramics have the $Mg_4Ta_2O_{9}$ phase(hexagonal). The dielectric constant($\varepsilon$$_{\gamma}$) and density increased with sintering temperature and mole fraction of x. To improve the quality factor and the temperature coefficient of resonant frequency, TiO$_2$($\varepsilon_{r}$=100, $Q{\times}f_{r}$=40,000GHz, $\tau$$_{f}$=＋450 ppm/$^{\circ}C$) was added in $Mg_4Ta_2O_{9}$ ceramics. In the case of the $0.7Mg_4Ta_2O_{9}$-$0.3TiO_2$ and the $0.6Mg_4Ta_2O_{9}$-$0.4TiO_2$ceramics sintered at $1400^{\circ}C$ for 5hr., the microwave dielectric properties were $\varepsilon$$_{\gamma}$=11.72, $Q{\times}f_{r}$=126,419GHz, $\tau_{f}$=-31.82 ppm/$^{\circ}C$ and $\varepsilon_{r}$=12.19, $Q{\times}f_{r}$=109,411GHZ, $\tau$$_{f}$= -17.21 ppm/$^{\circ}C$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.63-79
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• 1997

Consider an oparator equation of the form : $$ (1.1) H[y](x) = \alpha(x)\delta^2 y(x) + \beta(x)\delta y(x) = \lambda_n y(x), $$ where $\alphs(x)$ and $\beta(x)$ are polynomials of degree at most two and one respectively, $\lambda_n$ is the eigenvalue parameter, and $\delta$ is Hahn's operator $$ (1.2) \delta f(x) = \frac{(q - 1)x + \omega}{f(qx + \omega) - f(x)}, $$ for real constants $q(\neq \pm 1)$ and $\omega$.