• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.4
• /
• pp.437-445
• /
• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.14 no.4
• /
• pp.1562-1578
• /
• 2020

Vector data compression algorithm can meet requirements of different levels and scales by reducing the data amount of vector graphics, so as to reduce the transmission, processing time and storage overhead of data. In view of the fact that large threshold leading to comparatively large error in Douglas-Peucker vector data compression algorithm, which has difficulty in maintaining the uncertainty of shape features and threshold selection, a segmented Douglas-Peucker algorithm based on node importance is proposed. Firstly, the algorithm uses the vertical chord ratio as the main feature to detect and extract the critical points with large contribution to the shape of the curve, so as to ensure its basic shape. Then, combined with the radial distance constraint, it selects the maximum point as the critical point, and introduces the threshold related to the scale to merge and adjust the critical points, so as to realize local feature extraction between two critical points to meet the requirements in accuracy. Finally, through a large number of different vector data sets, the improved algorithm is analyzed and evaluated from qualitative and quantitative aspects. Experimental results indicate that the improved vector data compression algorithm is better than Douglas-Peucker algorithm in shape retention, compression error, results simplification and time efficiency.

• Journal of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.193-203
• /
• 2002

Weyl structure can be viewed as generalizations of Riemannian metrics. We study Weyl structures which are critical points of the squared L$^2$ norm functional of the full curvature tensor, defined on the space of Weyl structures on a compact 4-manifold. We find some relationship between these critical Weyl structures and the critical Riemannian metrics. Then in a search for homogeneous critical structures we study left-invariant metrics on some solv-manifolds and prove that they are not critical.

• Journal of English Language & Literature
• /
• v.64 no.1
• /
• pp.25-37
• /
• 2018

The turning point is one of the more evocative concepts in the critic's arsenal, as it is equally suited to the evaluation and analysis of a given moment in one's day as to those of a historical event. But how does one recognize a turning point? As we find ourselves always "in the middest," both spatially and temporally, we inhabit sites that may be points at which many things may be seen to turn. Indeed, it is usually only possible to identify a turning point, as it were, from a distance, from the remove of space and time which allows for a sense of recognition, based in part on original context and in part of perceived effects. In this article, Robert T. Tally Jr. argues that the apprehension and interpretation of a turning point involves a fundamentally critical activity. Examining three models by which to understand the concept of the turning point-the swerve, the trope, and peripety (or the dialectical reversal)-Tally demonstrates how each represents a different way of seeing the turning point and its effects. Thus, the swerve is associated with a point of departure for a critical project; the trope is connected to continuous and sustained critical activity in the moment, and peripety enables a retrospective vision that, in turn, inform future research. Tally argues for the significance of the turning point in literary and cultural theory, and concludes that the identification, analysis, and interpretation of turning points is crucial to the project of criticism today.

• Journal of Institute of Control, Robotics and Systems
• /
• v.4 no.2
• /
• pp.246-255
• /
• 1998

This paper presents a novel method for real-time malfunction detection of plasma etching process using EPD signal traces. First, many reference EPD signal traces are collected using monochromator and data acquisition system in normal etching processes. Critical points are defined by applying differentiation and zero-crossing method to the collected reference signal traces. Critical parameters such as intensity, slope, time, peak, overshoot, etc., determined by critical points, and frame attributes transformed signal-to symbol of reference signal traces are saved. Also, UCL(Upper Control Limit) and LCL(Lower Control Limit) are obtained by mean and standard deviation of critical parameters. Then, test EPD signal traces are collected in the actual processes, and frame attributes and critical parameters are obtained using the above mentioned method. Process malfunctions are detected in real-time by applying SPC(Statistical Process Control) method to critical parameters. the Real-time malfunction detection method presented in this paper was applied to actual processes and the results indicated that it was proved to be able to supplement disadvantages of existing quality control check inspecting or testing random-selected devices and detect process malfunctions correctly in real-time.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.587-595
• /
• 2008

It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.167-178
• /
• 2010

We discuss the critical points of the functional $F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g$ on the spaces of all almost Hermitian structures AH(M) with $(\lambda,\mu){\in}R^2-(0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $F_{\lambda,\mu}(J,g)$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.

• Korean journal of food and cookery science
• /
• v.2 no.2
• /
• pp.76-83
• /
• 1986

Time and temperature, pH and Aw, and microbiological evaluation were made to identify critical control points during various phases in product flow of chicken soup preparation in a university foodservice establishment. The results are summarised as follows: 1) Time and temperature data indicated that the phases of cooling after cooking, post-preparation, and holding ingredients at room temperature before assembly were critical. 2) pH and Aw values were in favorable for microbial growth. 3) Microbiological data indicated that the phases of basic ingredients. post-preparation and holding ingredients before assembly were critical. 4) Critical control points identified were; basic ingredients, cooling after cooking, post-preparation, holding before assembly and service, and assembly and service. 5) Several guidelines were suggested for the effective qualitly control program.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1541-1547
• /
• 2011

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

• Journal of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.1257-1269
• /
• 2013

Using the three critical points theorem by B. Ricceri [23], we obtain a multiplicity result for a class of nonlocal problems in Orlicz-Sobolev spaces. To our knowledge, this is the first contribution to the study of nonlocal problems in this class of functional spaces.