• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.677-682
• /
• 2007

The unique positive zero of $F_m(z):=z^{2m}-z^{m+1}-z^{m-1}-1$ leads to analogues of $2(\array{2n\\k}\)$(k even) by using hypergeometric functions. The minimal polynomials of these analogues are related to Chebyshev polynomials, and the minimal polynomial of an analogue of $2(\array{2n\\k}\)$(k even>2) can be computed by using an analogue of $2(\array{2n\\k}\)$. In this paper we show that the analogue of $2(\array{2n\\2}\)$. In this paper we show that the analygue $2(\array{2n\\2}\)$ is the only real zero of its minimal polynomial, and has a different representation, by using a polynomial of smaller degree than $F_m$(z).

• Progress in Superconductivity
• /
• v.13 no.1
• /
• pp.12-17
• /
• 2011

We investigated the effects of Ba and Cu co-substitution on the structural and superconducting properties of ($Ru_{1-y}Cu_y$)($Sr_{1.67-x}Ba_xEu_{0.33}$)($Eu_{1.34}Ce_{0.66}$)$Cu_2O_z$ samples. X-ray diffraction(XRD) reveals that single-phase samples can be obtained in the range from x = 0.1 to 0.2 for ($Ru_{0.5}Cu_{0.5}$)($Sr_{1.67-x}Ba_xEu_{0.33}$)($Eu_{1.34}Ce_{0.66}$)$Cu_2O_z$ and from y = 0.25 to 0.5 for ($Ru_{1-y}Cu_y$)($Sr_{1.47}Ba_{0.2}Eu_{0.33}$)($Eu_{1.34}Ce_{0.66}$)$Cu_2O_z$, respectively. All samples with compositions of ($Ru_{0.5}Cu_{0.5}$)($Sr_{1.67-x}Ba_xEu_{0.33}$) ($Eu_{1.34}Ce_{0.66}$)$Cu_2O_z$ (x = 0 - 0.33) show superconducting transition behavior and the onset transition temperature decreases slightly with increasing x in consistent with the change of hole concentration estimated from room temperature thermoelectric power measurements. The XRD and resistivity measurements for the ($Ru_{1-y}Cu_y$)($Sr_{1.47}Ba_{0.2}Eu_{0.33}$)($Eu_{1.34}Ce_{0.66}$) $Cu_2O_z$ system indicate that the partial substitution of Cu for Ru is necessary to form phase pure samples, but result in a small change in transition temperature in the single-phase region from x = 0.25 to 0.5.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.23 no.5
• /
• pp.1165-1172
• /
• 1998

In this paper, we present a construction for binary pseudorandom sequences of period $2^{m}-1$ with ideal autocorraltion property using the polynomial $z^{d}+(z+1)^{d}$. We show that the sequence obtained from the polynomial becomes an m-sequence for certain values of d. We also find a few values of d which yield new binary sequences with ideal autocorrelation property when m is $3k{\pm}1$, where k is a positive integer. These new sequences are represented using trace function and the results are tabulated.

• Journal of the Chungcheong Mathematical Society
• /
• v.4 no.1
• /
• pp.11-38
• /
• 1991

Let $E_n$ be the real ordered space of all $n{\times}n$ Hermitian Matrices and let T be a positive linear operator from $E_2$ to $E_3$. We prove in this paper that T is extreme if and only if T is unitarily equivalent to a map of the form $S_z$ for some $z{\in}C^2$ where $S_z$ is defined by $S_z(xx^*)=ww^*$, $w_i=x_iz_i$ for i = 1, 2 and $w_3=0$.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.563-572
• /
• 2005

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability of the additive-quadratic functional equation f(x + y, z + w) + f(x + y, z - w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w).

• Journal of the Korean earth science society
• /
• v.33 no.7
• /
• pp.596-607
• /
• 2012

The R-Z relationship is one of important error factors to determine the accuracy of radar rainfall estimation. In this study, we have explored the effect of the R-Z relationships derived from disdrometer data in estimating the radar rainfall. The heavy rain event that produced flooding in St-Remi, Quebec, Canada has been occurred. We have tried to investigate the severity of rain for this event using high temporal (2.5 min) and spatial resolution ($1^{\circ}$ by 250 m) radar data obtained from the McGill S-band radar. Radar data revealed that the heavy rain cells pass directly over St-Remi while the coarse raingauge network was not sufficient to detect this rain event. The maximum 30 min (1 h) accumulation reaches about 39 (42) mm in St-Remi. During the rain event, the two disdrometers (POSS; Precipitation Occurrence Sensor System) were available: One used for the reflectivity calibration by comparing disdrometer Z and radar Z and the other for deriving disdrometric R-Z relationships. The result shows the significant improvement with the disdrometric reflectivity-dependent R-Z relationships against the climatological R-Z relationship. The bias in radar rain estimation is reduced from +12% to -2% and the root-mean squared error from 16 to 10% for daily accumulation. Using the estimated radar rainfall rate with disdrometric R-Z relationships, the flood event was well captured with proper timing and amount.

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.221-230
• /
• 2005

In this paper, we define a multifunction $F:X{\rightarrow}Y$ to be upper (lower) Z -supercontinuous if $F^{+}(V)(F^{-}(V))$ is z-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) Z-supercontinuous multifunctions.

• Korean Journal of Mathematics
• /
• v.11 no.2
• /
• pp.79-84
• /
• 2003

In this paper, we obtain the sharp estimates for co-efficients of harmonic, orientation-preserving, univalent mappings defined on ${\Delta}=\{z:{\mid}z{\mid}>1\}$ when harmonic mappings are of bounded variation on ${\mid}z{\mid}=1$.

• Progress in Superconductivity
• /
• v.11 no.1
• /
• pp.67-71
• /
• 2009

The effect of Cu substitution on the structural and superconducting properties of the $(Ru_{1-x}Cu_x)Sr_2(Eu_{1.34{\cdot}}Ce_{0.66})Cu_2O_z$ system with x = 0, 0.25 and 0.5 prepared under ambient pressure have been investigated. The X-ray diffraction patterns indicated that the Ru ions are replaced by the Cu ions. It is found that the Cu substitution for Ru significantly reduces the ferromagnetic component of field-cooled magnetic susceptibility, but results in a small change in diamagnetic onset transition temperature of zero-field-cooled magnetic susceptibility. In contrast to the Ru $Sr_2(Eu_{1.34{\cdot}}Ce_{0.66})Cu_2O_z$, bulk Meissner effect is observed in the field-cooled magnetization measurements of the Cu doped samples. The experimental results are discussed in connection with the spontaneous vortex phase interpretation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.4
• /
• pp.319-328
• /
• 2011

Let $\mathbf{c}=\{c_n\}_{n{\in}\mathbb{Z}}\in{\ell}^1(\mathbb{Z})$ and $\{f_n\}_{n{\in}\mathbb{Z}}$ be a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$. We obtain necessary and sufficient conditions of $\mathbf{c}$ under which $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame (Riesz basis, respectively) of $L^2(\mathbb{R})$, where ${\lambda}$ > 0 and $(\mathbf{c}{\ast}_{\lambda}f)(t)\;:=\;{\sum}_{n{\in}\mathbb{Z}}c_nf(t-n{\lambda})$. When $\{\mathbf{c}{\ast}_{\lambda}f_n\}_{n{\in}\mathbb{Z}}$ becomes a frame of $L^2(\mathbb{R})$, we present its frame operator and the canonical dual frame in a simple form. Some interesting examples are included.