• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.346-350
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• 2002

The effect of Ca-doping on the superconducting properties of Nd-Ba-Cu-O bulk superconductors, fabricated by the oxygen-controlled melt growth process, has been systematically investigated. Various c-axis textured bulk samples were grown using precursors with the nominal compositions of N $d_{1.8-x}$C $a_{x}$B $a_{2.4}$C $u_{3.4}$ $O_{y}$ (x = 0.00, 0.02, 0.05, 0.10, 0.15) in a reduced oxygen atmosphere of 1% $O_2$ in Ar. Magnetization measurements revealed that the critical temperatures( $T_{c}$) were almost linearly depressed from 95K to 86K with increasing the Ca dopant from x = 0.0 to 0.15, respectively, and thus critical current densities( $J_{c}$) at 77K and for H//c-axis of specimens were gradually degraded with increasing x. Compositional analyses revealed that although the amounts of the Ca dopant both in NdB $a_2$C $u_3$ $O_{y}$(Nd123) and N $d_4$B $a_2$C $u_2$ $O_{10}$(Nd422) were increased with increasing x, only less than half of the initial Ca compositions were detected in melt-grown Ca-doped Nd-Ba-Cu-O bulk crystals. The supression of $T_{c}$ is attributed to an increased Nd substitution for the Ba site in the Nd123 superconducting matrix with increasing the amount of the Ca dopant.t.opant.t.t.t.t.t.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.247-263
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• 2016

Let $M_{1}f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}f(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_{2}f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$. Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_{1}f(x,y),t){\geq}N({\rho}M_{2}f(x,y),t)$ where ρ is a fixed real number with |ρ| < 1, and (0.2) $N(M_{2}f(x,y),t){\geq}N({\rho}M_{1}f(x,y),t)$ where ρ is a fixed real number with |ρ| < $\frac{1}{2}$.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.357-371
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• 2006

Let $X\;=\;(X_t,\;t{\in}[0, T])$ be a generalized Brownian motion(gBm) determined by mean function a(t) and variance function b(t). Let $L^2({\mu})$ denote the Hilbert space of square integrable functionals of $X\;=\;(X_t - a(t),\; t {in} [0, T])$. In this paper we consider a class of nonlinear functionals of X of the form F(. + a) with $F{in}L^2({\mu})$ and discuss their analysis. Firstly, it is shown that such functionals do not enjoy, in general, the square integrability and Malliavin differentiability. Secondly, we establish regularity conditions on F for which F(.+ a) is in $L^2({\mu})$ and has its Malliavin derivative. Finally we apply these results to compute the price and the hedging portfolio of a contingent claim in our financial market model based on a gBm X.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.15-26
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• 2012

Some oscillation results are presented for the second-order neutral dynamic equation of mixed type on a time scale unbounded above $$\(r(t)[x(t)+p_1(t)x(t-{\tau}_1)+p_2(t)x(t+{\tau}_2)]^{\Delta}\)^{\Delta}+q_1(t)x(t-{\tau}_3)+q_2(t)x(t+{\tau}_4)=0.$$ These criteria can be applied when $\mathbb{T}=\mathbb{R}$, $\mathbb{T}=h{\mathbb{Z}}$ and $\mathbb{T}=\mathbb{P}_{a,b}$. Two examples are also provided to illustrate the main results.

• The Pure and Applied Mathematics
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• v.10 no.4
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• pp.273-277
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• 2003

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then $A^{\ast}= X. In this paper, we show that if A is $\omega$-hyponormal and $B^{\ast}$ is invertible $\omega$-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then $A^{\ast}X = XB^{\ast}$.

• Journal of Powder Materials
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• v.26 no.4
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• pp.299-304
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• 2019

Nb-Si-B alloys with Nb-rich compositions are fabricated by spark plasma sintering for high-temperature structural applications. Three compositions are selected: 75 at% Nb (Nb0.7), 82 at% Nb (Nb1.5), and 88 at% Nb (Nb3), the atomic ratio of Si to B being 2. The microstructures of the prepared alloys are composed of Nb and $T_2$ phases. The $T_2$ phase is an intermetallic compound with a stoichiometry of $Nb_5Si_{3-x}B_x$ ($0{\leq}x{\leq}2$). In some previous studies, Nb-Si-B alloys have been prepared by spark plasma sintering (SPS) using Nb and $T_2$ powders (SPS 1). In the present work, the same alloys are prepared by the SPS process (SPS 2) using Nb powders and hypereutectic alloy powders with composition 67at%Nb-22at%Si-11at%B (Nb67). The Nb67 alloy powders comprise $T_2$ and eutectic ($T_2+Nb$) phases. The microstructures and hardness of the samples prepared in the present work have been compared with those previously reported; the samples prepared in this study exhibit finer and more uniform microstructures and higher hardness.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.137-146
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• 2016

In this paper we study the oscillation criteria for the second order nonlinear differential equation with delay and advanced arguments of the form $$([x(t)+a(t)x(t-{\sigma}_1)+b(t)x(t+{\sigma}_2)]^{\alpha})^{{\prime}{\prime}}+q(t)x^{\beta}(t-{\tau}_1)+q(t)x^{\gamma}(t+{\tau}_2)=0,\;t{\geq}t_0$$ where ${\sigma}_1$, ${\sigma}_2$, ${\tau}_1$ and ${\tau}_2$ are nonnegative constants and ${\alpha}$, ${\beta}$ and ${\gamma}$ are the ratios of odd positive integers. Examples are provided to illustrate the main results.

• Journal of Powder Materials
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• v.19 no.2
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• pp.146-150
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• 2012

The effects of nano $Fe_xC$ addition to superconducting properties of $in$ $situ$ processed $MgB_2$ superconductors was examined. 0.1 wt.% and 1 wt.% nano $Fe_xC$ powders were mixed with boron and magnesium powders by ball milling. The powder mixtures were made into pellets by uniaxial pressing. The pellets were heat-treated at $700^{\circ}C-900^{\circ}C$ in argon atmosphere for $MgB_2$ formation. It was found by powder X-ray diffraction that the raw powders were completely converted into $MgB_2$ after the heat treatment. The superconducting transition temperature ($T_c$) and critical current density ($J_c$), estimated from susceptibility-temperature and $M-H$ curves, were decreased by nano $Fe_xC$ addition. The $T_c$ and $J_c$ decrease by nano $Fe_xC$ addition are attributed to the incorporation of iron and carbon with $MgB_2$ lattices (Fe substitution for Mg and C substitution for B) due to the high reactivity of the nano $Fe_xC$ powder.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.621-634
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• 2022

The scaled inverse of a nonzero element a(x) ∈ ℤ[x]/f(x), where f(x) is an irreducible polynomial over ℤ, is the element b(x) ∈ ℤ[x]/f(x) such that a(x)b(x) = c (mod f(x)) for the smallest possible positive integer scale c. In this paper, we investigate the scaled inverse of (xⁱ - x^j) modulo cyclotomic polynomial of the form Φ_p^s (x) or Φ_p^sq^t (x), where p, q are primes with p < q and s, t are positive integers. Our main results are that the coefficient size of the scaled inverse of (xⁱ - x^j) is bounded by p - 1 with the scale p modulo Φ_p^s (x), and is bounded by q - 1 with the scale not greater than q modulo Φ_p^sq^t (x). Previously, the analogous result on cyclotomic polynomials of the form Φ_2ⁿ (x) gave rise to many lattice-based cryptosystems, especially, zero-knowledge proofs. Our result provides more flexible choice of cyclotomic polynomials in such cryptosystems. Along the way of proving the theorems, we also prove several properties of {x^k}_k∈ℤ in ℤ[x]/Φ_pq(x) which might be of independent interest.