• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1649-1660
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• 2015

In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T{_{z{^N_1{\bar{z}}^M_2}}$ on the Bergman space $A^2(\mathbb{D}^2)$, where N and M are positive integers.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.167-171
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• 2010

We will show that if d is a cubefree integer and n is an integer, then with some suitable conditions, there are no primes p and a positive integer m such that d is a cubic residue (mod p), $3\;{\nmid}\;m$, p || n if and only if there are integers x, y, z such that $$x^3\;+\;dy^3\;+\;d^2z^3\;-\;3dxyz\;=\;n$$.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.345-354
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• 2020

In this paper, we first give some representations for four new mock theta functions defined by Andrews [1] and Bringmann, Hikami and Lovejoy [5] using divisor sums. Then, some transformation and summation formulae for these functions and corresponding bilateral series are derived as special cases of ₂𝜓₂ series $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a,c;q)_n}{(b,d;q)_n}}z^n$$ and Ramanujan's sum $${\sum\limits_{n=-{{\infty}}}^{{\infty}}}{\frac{(a;q)_n}{(b;q)_n}}z^n$$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.16 no.1
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• pp.19-23
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• 1979

$S_nO_2$ and $Z_nO$ based semiconductor combustible gas sensors have been fabricated and measured their charactcnstics. Adding about 0.5 wt % $P_dCf_2$ to the mixture of $S_n0_2$ and $Z_nO$ improved the sensitivity. The devices were fired for one hoar in air in the tewerature range of $400^{\circ}C$ to $1000^{\circ}C$. Their electrical conductivity was changed by t he change of atmosphenc pressure around then.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.245-261
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• 2006

In this paper, we prove the generalized Hyers-Ulam stability of ring homomorphisms over the p-adic field $\mathbb{Q}_p$ associated with the Cauchy functional equation f(x+y) = f(x)+f(y) and the Cauchy-Jensen functional equation $2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.89.2-89.2
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• 2012

We present our analysis of a newly discovered galaxy-galaxy gravitational lens system in the First Look Survey (FLS) field. This object shows a highly distorted background galaxy (z=0.245) image by a nearby elliptical galaxy (z=0.08), which can be interpreted as a result of gravitational lensing. We model the lens with elliptical isothermal sphere model, and present the mass and potential distribution of the system.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.315-321
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• 2010

Waring's problem deals with representing any nonconstant function in a set of functions as a sum of kth powers of nonconstant functions in the same set. Consider ${\sum}_{i=1}^p\;f_i(z)^k=z$. Suppose that $k{\geq}2$. Let p be the smallest number of functions that give the above identity. We consider Waring's problem for the set of linear fractional transformations and obtain p = k.

• The Journal of Engineering Geology
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• v.19 no.1
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• pp.81-88
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• 2009

Two dimensional Monte-Carlo simulations of a non-reactive solute plume in isotropic porous media which are physically and chemically heterogeneous are conducted to determine the variations of moment. Retardation factors of 1, 2 and 5 are given to ascertain how the second moments are changed as adsorption increased. Retarded longitudinal second spatial moment, ${Z_{11}}^{'R}(t',l')$, increased during the transport process and as the dimensionless lengths of line plume source, $l_2'$, increased. ${Z_{11}}^{'R}(t',l')$ decreased as the retardation factors increased, and the simulated moments fit well to the first-order analytical results. Retarded longitudinal plume centroid variance, ${Z_{11}}^{'R}(t',l')$, decreased as the dimensionless lengths of line plume source, $l_2'$, increased and as the retardation factor increased. The result indicates that the uncertainty about the plume center decreased, and the ergodic condition for the second spatial moments is far from reaching. Simulated longitudinal one particle displacement covariance, ${Z_{11}}^{'R}(t')$, well consistent with the first-order analytical results for the three degrees of retardation factors of 1, 2 and 5 respectively. It is, consequently, concluded that the retarded longitudinal second moments could be produced by stochastic simulation, and that the first-order analytical results definitely provides very close values of the longitudinal retarded moments.

• Restorative Dentistry and Endodontics
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• v.25 no.1
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• pp.109-115
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• 2000

This study was designed to evaluate the microhardness of restorative composite resin and dual-cured composite resin cement which were light cured through the 1.5mm thickness composite overlay. For restorative materials, Z100 and Tetric Ceram were used. For dual cured composite cements, Variolink II((VL II) of three consistency (low, high, ultra high) were used. To determine the optimal microhardness of Z100, Tetric Ceram and Variolink II, each material was packed into the 1mm thickness teflon mold without composite overlay and light cured for 60 seconds. Then the microhardnesses of each sample were measured, averaged and regarded as optimal hardness of each material. To evaluate the microhardness of restorative composite resin and dual-cured composite resin cement which were light cured through the 1.5mm thickness composite overlay, the composites were packed into 1mm thickness teflon mold, coverd with celluloid strip, and then precured composite overlay which was made of Targis(Ivoclar/Vivadent, Liechtenstein) was positioned. 2 types of visible light curing machine, the power density of one of which was 400$mW/cm^2$ and the other was 900$mW/cm^2$, and one type of argon laser were used to cure the restorative composite and dual cured cement. For each group, 10 sample were assigned. The light curing tip was positioned over the composite overlay and light cured for 1min., 2min. or 3min with visible light curing machine or 15sec, 30 sec, 45sec, and 60 sec with argon laser. The Vickers hardnesses of upper and lower surface of Z100, Tetric Ceram, and 3 types of VL II cement were measured. When the 900 $mW/cm^2$ curing light was used, 2min. was needed for optimal curing of Z100 and Tetric Ceram. Variolink II did not be cured optimally even though the curing time was extended to 3min. When 400$mW/cm^2$ curing light was used, 3min. was necessary for Z100, whereas 3min. was not enough for Tetric Ceram. Variolink II was not cured optimally even though the curing time was extended to 3min. When argon laser was used, Z100, Tetric Ceram and Variolink II were not cured optimally in 60 seconds.

• Korean Journal of Materials Research
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• v.11 no.3
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• pp.171-177
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• 2001

The thermal and mechanical properties of amorphous Z $r_{62-x}$N $i_{10}$C $u_{20}$A $l_{8}$ $Ti_{x}$ (x=3, 6, 9at%) alloys were investigated. The crystallization process was confirmed as amorphous longrightarrow amorphous + Z $r_2$A $l_3$+ Zr + (Ni,Ti) longrightarrow Z $r_2$Cu + Al + (Ni,Ti) for 3at%Ti, amorphous longrightarrow amorphous + Al longrightarrow $Al_2$Ti + NiZr + CuTi for 6at%Ti and amorphous longrightarrow amorphous + Zr + Al longrightarrow Zr + $Al_2$Zr + Al $Ti_3$+ CuTi for 9at%Ti. lickers hardness ( $H_{v}$ ) increased with increasing volume fraction( $V_{f}$ ) of pricipitates for all concerned compositions. Tensile fracture strength ($\sigma_{f}$ ) showed a maximum value 1219MPa at $V_{f}$ = 38% for 3at%Ti, 1203MPa at $V_{f}$ = 2% for 6at%Ti and 1350MPa at $V_{f}$ = 5% for 9at%Ti. The $\sigma_{f}$ was rapidly decreased after showing the maximum value. The $V_{f}$ corresponding to rapidly decreased $\sigma_{f}$ coincided with the $V_{f}$ transited from ductile to brittle fracture surface.ace.