• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.961-973
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• 1994

A stochastics process $X = {X(t) : t \in T}$, with an index set T, is said to be infinitely divisible (ID) if its finite dimensional distributions are all ID. An ID process X is said to be a stochastic integral process if $X = {X(t) : t \in T} =^D {\int f_td\Lambda : t \in T}$ where $f : T \times S \to R$ is a deterministic function and $\Lambda$ is an ID random measure on a $\delta$-ring S of subsets of an arbitrary non-empty set S with the property; there exists an increasing sequence ${S_n}$ of sets in S with $U_n S_n = S$. Here $=^D$ denotes equality in all finite dimensional distributions.

• Advances in nano research
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• v.16 no.6
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• pp.565-577
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• 2024

Vibration investigation of fluid-filled functionally graded cylindrical shells with ring supports is studied here. Shell motion equations are framed first order shell theory due to Sander. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Langrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is immersed in a fluid which is a non-viscous one. These shells are stiffened by rings in the tangential direction. For isotropic materials, the physical properties are same everywhere where the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. After these, ring supports are located at various positions along the axial direction round the shell circumferential direction. The influence of the ring supports is investigated at various positions. Effect of ring supports with empty and fluid-filled shell is presented using the Rayleigh - Ritz method with simply supported condition. The frequency behavior is investigated with empty and fluid-filled cylindrical shell with ring supports versus circumferential wave number and axial wave number. Also the variations have been plotted against the locations of ring supports for length-to-radius and height-to-radius ratio. Moreover, frequency pattern is found for the various position of ring supports for empty and fluid-filled cylindrical shell. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down. It is found that due to inducting the fluid term frequency result down than that of empty cylinder. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.5
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• pp.303-311
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• 2003

Since the MPEG-4 visual standard enables content-based functionalities, it is necessary to extract video object from natural video sequences. Segmentation algorithms can largely be classified into automatic segmentation and user-assisted segmentation. In this paper, we propose a user-assisted VOP generation method based on the geometric active contour. Since the geometric active contour, unlike the parametric active contour, employs the level set method to evolve the curve, we can draw the initial curve independent of the shape of the object. In order to generate the edge function from a smoothed image, we propose a vector-valued diffusion process in the LUV color space. We also present a discrete 3-D diffusion model for easy implementation. By combining the curve shrinkage in the vector field space with the curve expansion in the empty vector space, we can make accurate extraction of visual objects from video sequences.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.7
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• pp.677-682
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• 2007

Concurrent competition for finite resources by multiple parts in flexible manufacturing systems(FMS's) and inappropriate initial marking or net structure of Petri net with share resources results in deadlock. This is an important issue to be addressed in the operation of the systems. Deadlock is a system state so that some working processes can never be finished. Deadlock situation is due to a wrong resource allocation policy. In fact, behind a deadlock problem there is a circular wait situation for a set of resources. Deadlock can disable an entire system and make automated operation impossible. Particularly, an unmanned system cannot recover from such a status and a set of jobs waits indefinitely for never-to-be-released resources. In this paper, we proposed a deadlock prevention method using siphon and trap of Petri net. It is based on potential deadlock which are siphon that eventually became empty. This method prevents the deadlock by the control of transition fire and initial marking in the Petri net. An given example of FMS is shown to illustrate our results with deadlock-free.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.65-77
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• 2020

In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by A^pc_I, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that A^pc_{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which A^pc_I = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

• Language and Information
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• v.17 no.2
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• pp.67-91
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• 2013

This paper describes Korean Nominal Bank, a project that provides argument structure for instances of the predicative nouns in the Sejong parsed Corpus. We use the language resources of the Sejong project, so that the same set of data is annotated with more and more levels of annotation, since a new type of a language resource building project could bring new information of separate and isolated processing. We have based on the annotation scheme based on the Sejong electronic dictionary, semantically tagged corpus, and syntactically analyzed corpus. Our work also involves the deep linguistic knowledge of syntaxsemantic interface in general. We consider the semantic theories including the Frame Semantics of Fillmore (1976), argument structure of Grimshaw (1990) and argument alternation of Levin (1993), and Levin and Rappaport Hovav (2005). Various syntactic theories should be needed in explaining various sentence types, including empty categories, raising, left (or right dislocation). We also need an explanation on the idiosyncratic lexical feature, such as collocation and etc.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1171-1187
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• 2011

Silverman [14] proved a height inequality for a jointly regular family of rational maps and the author [10] improved it for a jointly regular pair. In this paper, we provide the same improvement for a jointly regular family: let h : ${\mathbb{P}}_{\mathbb{Q}}^n{\rightarrow}{{\mathbb{R}}$ be the logarithmic absolute height on the projective space, let r(f) be the D-ratio of a rational map f which is de ned in [10] and let {$f_1,{\ldots},f_k|f_l:\mathbb{A}^n{\rightarrow}\mathbb{A}^n$} bbe finite set of polynomial maps which is defined over a number field K. If the intersection of the indeterminacy loci of $f_1,{\ldots},f_k$ is empty, then there is a constant C such that $ \sum\limits_{l=1}^k\frac{1}{def\;f_\iota}h(f_\iota(P))>(1+\frac{1}{r})f(P)-C$ for all $P{\in}\mathbb{A}^n$ where r= $max_{\iota=1},{\ldots},k(r(f_l))$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.507-524
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• 2013

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.483-501
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• 2018

In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.