• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1737-1751
• /
• 2015

For every doubling gauge g, we prove that there is a Cantor set of positive finite $H^g$-measure, $P^g$-measure, and $P^g_0$-premeasure. Also, we show that every compact metric space of infinite $P^g_0$-premeasure has a compact countable subset of infinite $P^g_0$-premeasure. In addition, we obtain a class of uniform Cantor sets and prove that, for every set E in this class, there exists a countable set F, with $\bar{F}=E{\cup}F$, and a doubling gauge g such that $E{\cup}F$ has different positive finite $P^g$-measure and $P^g_0$-premeasure.

• Journal of the Korean Wood Science and Technology
• /
• v.27 no.4
• /
• pp.51-56
• /
• 1999

Finite element method was utilized to analyze crack tip stress and displacement field under drying stress case as stepwise loading. Opening mode of single-edge-notched model was employed and analyzed by linear elastic fracture mechanics of plane stress case. The drying stresses were applied as stepwise loads at the boundary elements of the model with 10 steps of time serial. The stress intensity factor($K_I$) for opening mode reached to its maximum just prior to the stress reversal. The $K_I$ from the displacement fields revealed 1.7 times higher than those from stress fields. By comparing the two sets of $K_I$ from displacement and stress fields, single parameter $K_I$ showed its validity to characterize displacement fields around the crack tip front while stress field could not be characterized due to large variations between two sets of data.

• The Journal of Information Technology and Database
• /
• v.3 no.1
• /
• pp.97-108
• /
• 1996

In this paper we obtain several function defined on finite partially ordered sets(posets) which may indicate constraints of comparability on sets of teams(tasks, etc.) for which evaluation is computationally simple, a relatively rare condition in graph-based algorithms. Using these functions a set of numerical coefficients and associated distributions obtained from a computer simulation of certain families of random graphs is determined. From this information estimates may be made as to the actual linearity of complicated posets. Applications of these ideas is to all areas where obtaining rankings from partial information in rational ways is relevant as in, e.g., team_, scaling_, and scheduling theory as well as in theoretical computer science. Theoretical consideration of special and desirable properties of various functions is provided permitting judgment concerning sensitivity of these functions to changes in parameters describing (finite) posets.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.1911-1916
• /
• 2003

Parameter set of an LPV system is divided into a number of subsets so that robust feedback gains may be designed for each subset of parameters. A concept of quasi-invariant set is introduced, which allows finite steps of delay in reentrance to the set. A feasible and positively invariant set with respect to a gain-scheduled state feedback control can be easily obtained from the quasi-invariant set. A receding horizon control strategy can be derived based on this feasible and invariant set.

• Bulletin of the Korean Mathematical Society
• /
• v.21 no.2
• /
• pp.87-89
• /
• 1984

Let X be a Banach space, and let B(X) (resp. CB(X), K(X), CV(X)) denote the family of all nonvoid (resp. closed bounded, compact, convex) subsets of X. The Kuratowski measure of noncompactness is defined by the mapping .alpha.$_{k}$: B(X).rarw. $R_{+}$ with .alpha.$_{k}$(A) = inf {r>0 vertical bar A can be covered by a finite number of sets with diameter less than r}.an r}.

• Journal of KSNVE
• /
• v.3 no.1
• /
• pp.77-82
• /
• 1993

In general, the dynamic analysis with FEM(Finite Element Method) of large structures requires large computer memory space and long computational time. For the purpose of economical dynamic analysis of large structures, most of engineers want to use an efficient solution algorithm. This paper reports the modified CMS(Component Mode Synthesis) method which uses more efficient algorithm than the classical CMS method. In this paper, it is shown that Ritz vector sets can play the role of normal mode vector sets of substurctures in the CMS algorithm. The modified CMS method has good convergence performance compared with that of the classical CMS method.

• The Mathematical Education
• /
• v.21 no.1
• /
• pp.19-21
• /
• 1982

In this paper, we define the z-S-closed spaces using the notions of zero-sets and S-closed spaces introduced by T. Thompson, and investigate some properties of these spaces. We also obtain the following results. If a space X is z-S-closed, then every cover of z-regular semiopen sets has a finite proximate subcover. A z-extremally disconnected z-QHC space is z-S-closed, z-S-closed is contagious.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.317-326
• /
• 2003

We classify all possible level Artinian O-sequences of socle degree 5 and type 3. Moreover, we show how to construct level Artinian algebras with those Hilbert functions using the sum of two ideals of finite sets of points in $P^2$ such that the ideal of the union of two sets is level.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1993.06a
• /
• pp.1175-1176
• /
• 1993

This paper introduces a new model for forecasting groundwater level on the basis of analysing defect of finite element method. The new model is built with fuzzy sets and neural networks. It is convenient for use. We computed the groundwater level of one city in P. R. China with it and got a very satisfactory result. It can be popularized to corecast groundwater level of mine.

• International Journal of Control, Automation, and Systems
• /
• v.1 no.4
• /
• pp.412-430
• /
• 2003

In many practical problems in signal processing and control, the signal values are often restricted to belong to a finite number of levels. These questions are generally referred to as "finite alphabet" problems. There are many applications of this class of problems including: on-off control, optimal audio quantization, design of finite impulse response filters having quantized coefficients, equalization of digital communication channels subject to intersymbol interference, and control over networked communication channels. This paper will explain how this diverse class of problems can be formulated as optimization problems having finite alphabet constraints. Methods for solving these problems will be described and it will be shown that a semi-closed form solution exists. Special cases of the result include well known practical algorithms such as optimal noise shaping quantizers in audio signal processing and decision feedback equalizers in digital communication. Associated stability questions will also be addressed and several real world applications will be presented.