• Bulletin of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1405-1417
• /
• 2018

The aim of this work is to introduce several different volume computational methods of graph polytopes associated with various types of finite simple graphs. Among them, we obtained the recursive volume formula (RVF) that is fundamental and most useful to compute the volume of the graph polytope for an arbitrary finite simple graph.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1247-1260
• /
• 2021

We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein Fano polytope is of type B_∞. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope X of dimension 1, 3 or 5, X is Kähler-Einstein if and only if it is of type B_∞.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.4
• /
• pp.195-213
• /
• 2023

Discrete volumes of poset polytopes for a variant of up-down posets introduced in [4] were studied. We obtained the generating functions for the discrete volumes of poset polytopes for a variant of up-down poset using the characteristic matrices.

• Journal of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.195-210
• /
• 1995

Let $\Omega_n$ denote the set of all $n \times n$ doubly stochatic matrices. Then it is well known that $\Omega_n$ forms convex polytope of dimension $(n-1)^2$ with n! extreme points in the $n^2$-dimensional Euclidean space.

• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.41-47
• /
• 2017

The aim of this short paper is to give a new necessary and sufficient condition, topological in nature, for certain real toric manifolds to be orientable in terms of the connectedness of their particular submanifolds of codimension zero.

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.32B no.10
• /
• pp.1259-1268
• /
• 1995

This note presents the robust root clustering problem of interval systems whose characteristic equation might be given as either a family of interval polynomials or a family of polytopes. Corresponding to damping ratio and robustness margin approximately, we consider a certain class of D-region such as parabola, left-hyperbola, and ellipse in complex plane. Then a simpler D-stability criteria using rational function mapping is presented and prove. Without .lambda. or .omega. sweeping calculation, the absolute criteria for robust D-stability can be determined.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2002.05a
• /
• pp.561-564
• /
• 2002

With Rapid Prototyping system, the efficient packing in a fixed work volume reduces build time when multiple parts are built in a process. In this paper, an efficient and rapid packing algorithm is developed for SLS system that has cylindrical workspace. A genetic algorithm is implemented to place as many part as possible in a vat. For fast computation, a collision detection algorithm "k-DOPs Tree" is implemented.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.1221-1230
• /
• 2018

We derive a sharp decomposition formula for the state polytope of the Hilbert point and the Hilbert-Mumford index of reducible varieties by using the decomposition of characters and basic convex geometry. This proof captures the essence of the decomposition of the state polytopes in general, and considerably simplifies an earlier proof by the authors which uses a careful analysis of initial ideals of reducible varieties.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.4
• /
• pp.1-10
• /
• 1998

We consider the precedence-constrained knapsack problem. which is a knapsack problem with precedence constraints imposed on the set of variables. Especially, we focus on the case where the precedence constraints cir be represented as a bipartite graph, which occurs most frequently in applications. Based on the previous studios for the general case, we specialize the polyhedral results on the related polytope and derive stronger results on the facet-defining properties of the inequalities.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.129-137
• /
• 2014

In this paper, a new proof of the following result is given: The product of the volumes of an origin-symmetric convex bodies K in $\mathbb{R}^2$ and of its polar body is minimal if and only if K is a parallelogram.