Scarf’s lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N -person game. Over the last four decades, the usefulness of Scarf’s lemma has been demonstrated in several important combinatorial problems. However, the complexity of the computational version of Scarf’s lemma (Scarf) is unknown. In this paper, we prove that Scarf is complete for t...

The Scarf algorithm was the Þrst practical, almost surely convergent method for computing general equilibria of competitive models. The current focus of much computational research is computing equilibrium of dynamic stochastic models. While many of these models are examples of Arrow-Debreu equilibria, Scarf’s algorithm and subsequent homotopy methods cannot be applied directly since they have ...

Bamboo-bundle laminated veneer lumber (BLVL) was produced by joint lengthening technology. The objective of this study was to evaluate the effect of joint form and the values of key parameters on mechanical properties of BLVL. Two joint forms, i.e., finger joint and scarf joint, and two corresponding joint parameters, i.e., finger length and scarf angle, were investigated in laminates. The resu...

Scarf’s lemma is one of the fundamental results in combinatorics, originally introduced to study the core of an N -person game. Over the last four decades, the usefulness of Scarf’s lemma has been demonstrated in several important combinatorial problems seeking stable solutions ([12], [1] [2], [15]). However, the complexity of the computational version of Scarf’s lemma (Scarf) remained open. In...

The purpose of the present study was to examine the effects of different types of personal cooling equipments (PCE) on the alleviation of heat strain during red pepper harvest simulated in a climatic chamber. The experiment consisted of eight conditions: 1) Control, 2) Neck cooling scarf A with a cooling area of 68 cm2, 3) Neck cooling scarf B (cooling area 154 cm2), 4) Brimmed hat with a froze...

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian positiondependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM – Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-l...

We formulate the famous Scarf Lemma in terms of oiks. This lemma has two fundamental applications in game and graph theory. In 1967, Scarf derived from it core-solvability of balanced cooperative games. Recently, it was shown that kernelsolvability of perfect graphs also results from this lemma. We show that Scarf’s combinatorially defined oiks are in fact realized by polytopes, and that Scarf’...