• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1065-1081
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• 2011

For any field F, a polynomial f $\in$ F[$x_1,x_2,{\ldots},x_k$] can be associated with a polytope, called its Newton polytope. If the polynomial f has integrally indecomposable Newton polytope, in the sense of Minkowski sum, then it is absolutely irreducible over F, i.e., irreducible over every algebraic extension of F. We present some results giving new integrally indecomposable classes of polygons. Consequently, we have some criteria giving many types of absolutely irreducible bivariate polynomials over arbitrary fields.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2713-2716
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• 2003

This paper presents a dynamic manipulability analysis method of the limb moving in viscous fluid. The key idea of the presented method is that the boundary of joint velocity can be converted to the velocity-dependant dynamic manipulability polytope through the coriolis, centrifugal and drag terms in dynamic equation. The velocity-dependant dynamic manipulability polytope is added to the inertial and restoring force manipulability polytope to get overall manipulability polytope of the limb moving in the fluid Each of the torque and velocity bounds arc considered in the infinite norm sense in joint space, and the drag force of a limb moving in fluid viscous is modeled as a quadratic form An analysis example with proposed analysis scheme is presented to validate the method.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.1
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• pp.99-104
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• 2009

This article describes the analysis of stable grasping for multi-fingered robot. An analysis method of stable grasping, which is based on the three-dimensional acceleration convex polytope, is proposed. This method is derived from combining dynamic equations governing object motion and robot motion, force relationship and acceleration relationship between robot fingers and object's gravity center through contact condition, and constraint equations for satisfying no-slip conditions at every contact points. After mapping no-slip condition to torque space, we derived intersected region of given torque bounds and the mapped region in torque space so that the intersected region in torque space guarantees no excessive torque as well as no-slip at the contact points. The intersected region in torque space is mapped to an acceleration convex polytope corresponding to the maximum acceleration boundaries which can be exerted by the robot fingers under the given individual bounds of each joints torque and without causing slip at the contacts. As will be shown through the analysis and examples, the stable grasping depends on the joint driving torque limits, the posture and the mass of robot fingers, the configuration and the mass of an object, the grasp position, the friction coefficients between the object surface and finger end-effectors.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.211-223
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• 2013

We consider permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing identity submatrix. We determine the minimum permanents and minimizing matrices on the given faces of the polytope using the contraction method.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.225-228
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• 2004

The generalized knapsack problem, or gknap is the combinatorial optimization problem of optimizing a nonnegative linear functional over the integral hull of the intersection of a polynomially separable 0 - 1 polytope and a knapsack constraint. Among many potential applications, the knapsack, the restricted shortest path, and the restricted spanning tree problem are such examples. We prove via the ellipsoid method the equivalence between the fully polynomial approximability and a certain pseudo-polynomial separability of the gknap polytope.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.409-439
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• 2021

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a partial matching, and the lattice polytope associated with a pair of lattice presentations, and we investigate transformations with minimal area.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.34C no.7
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• pp.51-60
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• 1997

Prototype based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a fuzzy clustering method that involves adaptively expanding convex polytopes. Thus, the dependency on the use of prototypes can be eliminated. The proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. Specifically, nonlinear membership functions are utilized to determine whether a new cluster is created or which vertex of the cluster should be expanded. For this, the membership function of a new vertex is assigned according to not only a distance measure between an incoming pattern vector and a current vertex, but also the amount how much the current vertex has been modified. Therefore, cluster expansion can be only allowed for one cluster per incoming pattern. Several experimental results are given to show the validity of our mehtod.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.1
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• pp.105-112
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• 1998

Regarding the measure of dexterity of robot manipulators, two geometric tools, manipulability ellipsoids and manipulability polytopes, are examined and compared with each other. Even though the manipulability ellipsoid approach is the most widely used technique, it is shown that the manipulability ellipsoid transforms the inexact joint velocity constraints into task space and so it may fail to give an exact measure of dexterity and optimal direction of motion in task space. After showing that the polytope approach can handle such problems, we propose a practical polytope method which can be applied to 3-dimensional task space in general. The relation between manipulability ellipsoids and manipulability polytopes are also explored for a redundant case and a non-redundant one.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.836-840
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• 1999

Linear motion and angular motion in task space are handled separately in joint velocity planning for redundant robot manipulators. In solving inverse kinematic equations with given joint velocity limits, we consider the order of priority for linear motion and angular motion. The proposed method will be useful in such applications where only linear motions are important than angular motions or vice versa.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.5
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• pp.26-33
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• 2002

The design method of robust $H_{\infty}$ filtering for discrete-time uncertain linear systems is investigated in this paper. The uncertain parameters are assumed to be unknown but belonging to known convex compact set of polytope type. The objective is to design a stable robust $H_{\infty}$ filter guaranteeing the asymptotic stability of filtering error dynamics and present an $L_2$ induced norm bound analytically for the modified $H_{\infty}$ performance measure. The sufficient condition for the existence of robust $H_{\infty}$ filter and the filter design method are established by LMI(linear matrix inequality) approach, which can be solved efficiently by convex optimization. The proposed algorithm is checked through an example.