A two player game (or more correctly, a two player normal-form game) is specified by two m × n payoff matrices R and C corresponding to the row and column player respectively. Each of these matrices has m rows corresponding to the m strategies of the row player and n columns corresponding to the n strategies of the column payer. The row player picks a row i ∈ [m], and the column player picks a ...

We investigate an S = 1/2 two-leg spin ladder with a cyclic four-spin exchange interaction whose interaction constant is denoted by J4, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by Jrung and Jleg, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet (S tot = 0) and th...

In this paper we study the 0-1 inverse maximum stable set problem, denoted by IS{0,1}. Given a graph and a stable set (not necessarily maximum), it is to delete a minimum number of vertices to make the given stable set maximum in the new graph. We also consider IS{0,1} against a specific algorithm such as Greedy and 2opt, which is denoted by IS{0,1},greedy and IS{0,1},2opt, respectively. We pro...

This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by EDS ) and the vertex packing problem (denoted by DS ) are linear programming duals of the edge dominating set problem and the dominating set problem respectively. It is shown that these two problems are equivalent to the set packing problem with respec...

A group is a mathematical structure 〈G; ∗〉 consisting of a non-empty set G and a binary operation ∗ : G×G→ G and satisfying the following axioms: (A1) The operation ∗ is associative, i.e., for any x, y, z ∈ G, x ∗ (y ∗ z) = (x ∗ y) ∗ z. (A2) There exists a neutral element e for ∗, i.e., x ∗ e = e ∗ x = x for all x ∈ G. (A3) Every element x ∈ G has an inverse x̂, i.e., x ∗ x̂ = x̂ ∗ x = e. If ∗ is ...

We describe a novel binary classification technique called Banded SVM (B-SVM). In the standard C-SVM formulation of Cortes and Vapnik [1995], the decision rule is encouraged to lie in the interval [1,∞]. The new B-SVM objective function contains a penalty term that encourages the decision rule to lie in a user specified range [ρ1, ρ2]. In addition to the standard set of support vectors (SVs) ne...

The Stefan problem is one of the best known parabolic two-phase free boundary problems. It is a simple model of phase transitions in liquid-solid systems. Let Ω⊂Rn denote a domain that contains a liquid and a solid separated by an interface Γ. As the melting or cooling take place the boundary moves and we are naturally led to a free boundary problem. The unknowns are the temperatures of the liq...