• Tribology and Lubricants
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• v.27 no.4
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• pp.209-212
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• 2011

The capacitive application(prove) can be used to measure the complex permittivity of dielectric material of various thickness and cross section. This paper presents that we designed the analysis system of engine oil permittivity to know the relation between the engine oil deterioration and the prove dimension. Each of the dimension of capacitive prove is changed and then electric capacity is measured by LCR {Inductance(L), Capacitance (C), and Resistance (R)} meter. The engine oil permittivity has extracted in the prove measurement. As the additional research, this paper suggest the best of the prove dimension for the permittivity measurement.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.315-326
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• 2005

In this paper, we define the weak dimension and the chain-weak dimension of an ordered set by using weak orders and chain-weak orders, respectively, as realizers. First, we prove that if P is not a weak order, then the weak dimension of P is the same as the dimension of P. Next, we determine the chain-weak dimension of the product of k-element chains. Finally, we prove some properties of chain-weak dimension which hold for dimension.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.633-648
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• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.759-769
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• 2005

We first discuss jump discontinuity in higher dimension, and then prove a local convergence theorem for wavelet approximations in higher dimension. We also redefine the concept of Gibbs phenomenon in higher dimension and show that wavelet expansion exhibits Gibbs phenomenon.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.303-311
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• 2024

In this paper, our focus lies in exploring the concept of Cohen-Macaulay dimension within the category of homologically finite complexes. We prove that over a local ring (R, 𝔪), any homologically finite complex X with a finite Cohen-Macaulay dimension possesses a finite CM-resolution. This means that there exists a bounded complex G of finitely generated R-modules, such that G is isomorphic to X and each nonzero G_i within the complex G has zero Cohen-Macaulay dimension.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.493-498
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• 2000

In this paper we find some properties of distinguished prime submodules of modules and prove theorems about the dimension of modules.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1389-1406
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• 2020

Let Λ be an Artin algebra and mod Λ the category of finitely generated right Λ-modules. We prove that the radical layer length of Λ is an upper bound for the radical layer length of mod Λ. We give an upper bound for the extension dimension of mod Λ in terms of the injective dimension of a certain class of simple right Λ-modules and the radical layer length of DΛ.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1327-1338
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• 2015

In this paper, we introduce and study the w-weak global dimension w-w.gl.dim(R) of a commutative ring R. As an application, it is shown that an integral domain R is a $Pr\ddot{u}fer$ v-multiplication domain if and only if w-w.gl.dim(R) ${\leq}1$. We also show that there is a large class of domains in which Hilbert's syzygy Theorem for the w-weak global dimension does not hold. Namely, we prove that if R is an integral domain (but not a field) for which the polynomial ring R[x] is w-coherent, then w-w.gl.dim(R[x]) = w-w.gl.dim(R).