• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.31-43
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• 1992

• Kyungpook Mathematical Journal
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• v.32 no.1
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• pp.21-30
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• 1992

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.575-583
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• 2024

Let R be a commutative ring with 1 ≠ 0. Let Id(R) be the set of all ideals of R and let δ : Id(R) → Id(R) be a function. Then δ is called an expansion function of the ideals of R if whenever L, I, J are ideals of R with J ⊆ I, then L ⊆ δ (L) and δ (J) ⊆ δ (I). Let δ be an expansion function of the ideals of R and m ≥ n > 0 be positive integers. Then a proper ideal I of R is called an (m, n)-closed δ-primary ideal (resp., weakly (m, n)-closed δ-primary ideal ) if a^m ∈ I for some a ∈ R implies aⁿ ∈ δ(I) (resp., if 0 ≠ a^m ∈ I for some a ∈ R implies aⁿ ∈ δ(I)). Let f : A → B be a ring homomorphism and let J be an ideal of B. This paper investigates the concept of (m, n)-closed δ-primary ideals in the amalgamation of A with B along J with respect to f denoted by A ⋈^f J.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.247-257
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• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• ETRI Journal
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• v.11 no.4
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• pp.98-104
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• 1989

Closed form solution of nonlinear 2-DEG concentration formula is proposed. This allows us to model continuous 2-DEG charge concentration as the function of gate voltage covering subthreshold region of the I-V curves. Comparisons of the Ids-Vgs characteristics and transconductance with the measured data were performed to show the accuracy of the proposed model. This way we have completely closed form I-V characteristics in subthreshold, triode and saturation region incorporating accurate charge control mechanism for HEMTs.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.293-314
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• 2009

The notions of pre-local function, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of $P-\mathcal{I}$-open sets and $P-\mathcal{I}$-closed sets in ideal topological spaces are discussed. Relations between $\mathcal{I}$-open sets and $P-\mathcal{I}$-open sets are provided, and several properties related to $P-\mathcal{I}$-open sets, pre-local functions, semi-local functions and ${\alpha}$-local functions with respect to a topology and an ideal are investigated.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.157-169
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• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.145-149
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• 2014

I consider the optimal consumption and portfolio selection problem with nonnegative wealth constraints using the dynamic programming approach. I use the constant relative risk aversion (CRRA) utility function and disutility to derive the closed-form solutions.