• 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.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.12.2-12
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• 2003

미분 가능한 함수가 독립변수의 각 점에서 미분계수를 가지듯이 가장 일반화된 Cantor집합의 각 점에서 weak local dimension 을 갖는다. 이러한 weak local dimension 은 두 가지가 있는데 weak lower local dimension 과 weak upper local dimension 이 있다 weak lower local dimension 은 국소적인 의미로 perturbed Cantor 집합의 lower Cantor dimension 이고 Hausdorff dimension 과 관련이 있다. weak upper local dimension 은 국소적인 의미로 perturbed Cantor 집합의 upper Cantor dimension 이고 packing dimension 과 관련이 있다. 이때 각 점에 대응하는 유관한 측도는 quasi-self-similar measure 이며 그 점의 weak lower local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 lower local dimension 이 s 가 된다. 마찬가지로 그 점의 weak upper local dimension 이 s 이면 그 점의 s-차원 quasi-self-similar measure 의 upper local dimension 이 s 가 된다. 따라서 이와 같은 사실을 이용하면 가장 일반화된 Cantor집합의 각 점에서의 weak local dimension 을 이용하여 그 집합의 Hausdorff 또는 packing 차원의 정보를 얻을 수 있을 뿐 더러 weak local dimension 을 이용한 spectrum 을 또한 구할 수 있다. 한편 weak local dimension 과 유관한 quasi-self-similar measure 는 집합의 spectrum을 생성하며 이 spectrum 을 이루는 각 부분집합의 차원에 대하여 보다 좋은 정보를 주는 transformed dimension 과 또 다른 관련을 갖게 된다.

• Journal of the Korean Society of Costume
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• v.42
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• pp.231-242
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• 1999

The purpose of this study was to classified the dimension of clothing involvement and the clothing loyalty of 256 male and 271 female college students in Taegu area. data was analyzed by frequency percentage mean factor analysis reliability test validity test correlation and ANOVA by using SPSS/pc. The results of this study were as follows; 1. the dimension of clothing involvement was classified into four factors such as clothing interest dimension clothing symbolism dimension clothing economics dimension and clothing individuality dimension. 2. In the relationship between brand loyalty and four factors of clothing involvement there was positive appearance involvement there was positive appearance in clothing interest clothing symbolism and clothing individuality with brand loyalty but negative appearance in clothing economics. The correlation between clothing interest dimension and clothing symbolism dimension clothing interest dimension and clothing individuality dimension clothing symbolism dimension and clothing economics dimension clothing symbolism dimension and clothing individuality dimension was positive. And there was no relation between clothing economics dimension and clothing individuality dimension clothing economics dimension and clothing interest dimension. 3. According to individual character females than males the group aged 18 to 20 and 24 to 27 than the group aged 21 to 23 showed more active tendency to the clothing involvement dimension and also highertendency to brand loyalty. The students with a major in humanities science than the students with a major in natural science and more expending consumers on clothes showed more active tendency to the clothing symbolism dimension and higher tendency to brand loyalty. 4. On the whole the attitude of consumers on clothes was very high in the clothing interest dimension common in the clothing individuality dimension and very low in the clothing economics dimension.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.79-86
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• 2009

We consider the dimension and interval dimension of bipartite ordered sets and provide a sufficient condition for when the two parameters are equal.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.711-719
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• 2018

In this paper we define and study a new kind of dimension called, semisimple dimension, that measures how far a module is from being semisimple. Like other kinds of dimensions, this is an ordinal valued invariant. We give some interesting and useful properties of rings or modules which have semisimple dimension. It is shown that a noetherian module with semisimple dimension is an artinian module. A domain with semisimple dimension is a division ring. Also, for a semiprime right non-singular ring R, if its maximal right quotient ring has semisimple dimension as a right R-module, then R is a semisimple artinian ring. We also characterize rings whose modules have semisimple dimension. In fact, it is shown that all right R-modules have semisimple dimension if and only if the free right R-module ${\oplus}^{\infty}_{i=1}$ R has semisimple dimension, if and only if R is a semisimple artinian ring.

• Journal of electromagnetic engineering and science
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• v.17 no.4
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• pp.241-243
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• 2017

In this paper, we have presented an equation for estimating the gain of a Fabry-Perot cavity (FPC) antenna with a finite dimension. When an FPC antenna has an infinite dimension and its height is half of a wavelength, the maximum gain of that FPC antenna can be obtained theoretically. If the FPC antenna does not have a dimension sufficient for multiple reflections between a partially reflective surface (PRS) and the ground, its gain must be less than that of an FPC antenna that has an infinite dimension. In addition, the gain of an FPC antenna increases as the dimension of a PRS increases and becomes saturated from a specific dimension. The specific dimension where the gain starts to saturate also gets larger as the reflection magnitude of the PRS becomes closer to one. Thus, it would be convenient to have a gain equation when considering the dimension of an FPC antenna in order to estimate the exact gain of the FPC antenna with a specific dimension. A gain versus the dimension of the FPC antenna for various reflection magnitudes of PRS has been simulated, and the modified gain equation is produced through the curve fitting of the full-wave simulation results. The resulting empirical gain equation of an FPC antenna whose PRS dimension is larger than $1.5{\lambda}_0$ has been obtained.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.29-38
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• 2015

We compute the Hausdorff and packing dimensions of the cylindrical lower or upper local dimension set for a self-similar measure having different minimum and maximum of the local dimension on a self-similar set satisfying the open set condition.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.933-944
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• 2004

Packing dimension of a set is an upper bound for the packing dimensions of measures on the set. Recently the packing dimension of statistically self-similar Cantor set, which has uniform distributions for contraction ratios, was shown to be its Hausdorff dimension. We study the method to find an upper bound of packing dimensions and the upper Renyi dimensions of measures on a statistically quasi-self-similar Cantor set (its packing dimension is still unknown) which has non-uniform distributions of contraction ratios. As results, in some statistically quasi-self-similar Cantor set we show that every probability measure on it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely and it has its subset of full measure whose packing dimension is also its Hausdorff dimension almost surely for almost all probability measure on it.