• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.13 no.3
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• pp.89-95
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• 2014

The increasing level of demand for multi-tasking machines requires a saddle with an ultra-precise machining accuracy level of $15{\mu}m$, as such a saddle is one of the main components of these machines. The manner of achieving ultra-precise machining accuracy mainly depends on the fixed forces. In this paper, we optimized the number of contact points and the contact positions to reduce the deformation of the saddle while it is machined. The performance levels of the proposed optimal jig and fixture are determined by measuring the flatness, parallelism and perpendicularity of a machined saddle. The machining accuracy is found to be lower than $15{\mu}m$ at all measured points.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.603-616
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.493-506
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• Bulletin of the Korean Chemical Society
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• v.7 no.5
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• pp.376-379
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• 1986

A relatively simple method of locating the saddle point is presented. In this method a single determination of the saddle point location by constrained energy minimizations for points selected on the assumed saddle surface provides us with the structure, location and energy of the TS, the reaction path at the saddle point and characterization as the TS. Some examples were given.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.529-540
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• 1996

The dynamic buckling mechanism of a single-degree-of-freedom dissipative/nondissipative gradient system is thoroughly studied, employing energy criteria. The model is chosen in such a manner, that its corresponding static response is associated with all types of distinct critical points. Under a suddenly applied load of infinite duration, it is found that dynamic buckling, occurring always through a saddle, leads to an escaped motion, which is finally attracted by remote stable equilibrium positions, belonging sometimes also to complementary paths. Moreover, although the existence of initial imperfection changes the static behaviour of the system from limit point instability to bifurcation, it is established that the proposed model is dynamically stable in the large, regardless of the values of all other parameters involved.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.837-847
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• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.

• Korean journal of food and cookery science
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• v.22 no.5 s.95
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• pp.666-680
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• 2006

To obtain basic data for the utilization of saltwort (Salicornia herbacea L.) as a functional ingredient in steamed foam cake, the optimum component ratios for major raw ingredients (saltwort, salt, and wheat flour) as independent variables that affect the product quality were scientifically determined using RSM (response surface methodology) technique. A three-factor and five-level rotational central composite design was used for treatment arrangement. The complete design consisted of 16 experimental points. The three independent variables selected for the RSM experiment were amounts of saltwort (X$_1$, 5${\sim}$25 g), salt (X$_2$, 0${\sim}$10 g), and wheat flour (X$_3$, 470${\sim}$530 g). The optimum responses in specific gravity of the batter and volume, color, texture, and sensory evaluation result of the cake were obtained. The specific gravity and viscosity of the batter at p<0.01 was verified from the regression curve. The characteristic of the batter was influenced by all independent variables, but was extremely dependent on the amount of saltwort ordinary points of the surface responses from the batter formed the minimum points for specific gravities of the batter while viscosities of the batter appeared with the saddle points. Analysis of the response indicated that the amount of saltwort was the most influential factor over the physical properties of the cake, among the dependent variables. Ordinary points of the surface responses from the cake formed the maximum points for loaf volume, hardness gumminess, and chewiness, while Hunter colorimetric parameters appeared with the saddle points. The result indicated that level of the saltwort deviating more or less from the optimal amount decreased the volume and increased the specific gravity with less tender product. Ordinary points of the surface responses of the sensory evaluation scores from the cake formed the maximum points for appearance, flavor, softness, and overall acceptability, while color values appeared with the saddle points. The result also indicated that the level of the saltwort deviating more or less from the optimal amount reduced the preference for the product. Integration of the optimum responses common to all dependent variables that overlapped all the contour maps finally indicated that the combination of 8.3${\sim}$13.8 g saltwort, 2.5${\sim}$6.6 g salt, and 486.5${\sim}$511.5 g wheat flour under the selected preparation recipe optimized the physical and sensory properties in the teamed foam cakes. Practical preparation of the product with median amounts of the ingredients, i.e., 11.0 g saltwort, 4.6 g salt, and 499.0 g wheat flour resulted in similar qualities to the predicted responses. In conclusion, these study results indicated that preparation of steamed foam cake with added saltwort ingredient could potentially produce a more nutritious product with less salt. Further research is required to acquire the optimum levels for sub-ingredients to improve the product quality.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.255-267
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• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1355-1364
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• 2001

Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder, where the Taylor's hypothesis does nut hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV for various planes of view. The convection velocities of the Karman and secondary vortices are evaluated from the trajectory of the vortex center. Then, saddle points are determined by applying the critical point theory. It is shown that the inclination angle of the secondary vortices agrees well with the previous experimental data. The flow fields in a moving frame of reference have several critical points and the mushroom-like structure appears in the streamline patterns of the secondary vortices. Since the distributions of fluctuating Reynolds stresses defined by triple decomposition are closely related with the existence of secondary vortices, the physical meaning of them is explained in conjunction with the vortex center and saddle point trajectories.