The effects of the ring-exchange Hamiltonian H3 = J3 ∑ 〈ijk〉(Si · Sj)(Si · Sk) on the triangular lattice are studied using classical Monte Carlo simulations. Each spin Si is treated as a classical XY spin taking on Q equally spaced angles (Q-states clock model). For Q = 6, a first-order transition into a stripe-ordered phase preempts the macroscopic classical degeneracy. For Q > 6, a finite win...

Recent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points which is not discrete contains <(3/4)2” open sets, and that this inequality is best possible. We use the correspondence between finite TO-topologies and partial orders to find all non-homeomorphic topologies with n points and >(7/16)2” open sets. We determine which of these topologies are TO, and in the...

Hence, it is easy to count the orbits of GL n q under the conjugation action of U n q but seems hard to do the same for the group U n q itself! We fix some further notation. Let V n q be the vector space of column vectors, a module for GL n q . Recall that a flag is a totally ordered set of n− 1 nonzero proper subspaces of V n q . For g in GL n q let f g be the number of flags fixed by g, so it...

In this paper the existence of unique positive solutions for system (p,q,r)-Lapalacian Sturm-Liouville type two-point fractional order boundary vaue problems is established by an application n-fixed point theorem ternary operators on partially ordered metric spaces.

The phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box. A superball's interior is defined by the inequality |x|(2q)+|y|(2q)+|z|(2q)≤1 , which provides a versatile family of convex particles (q≥0.5) with cubelike and octahedronlike shapes as well as concave particles (q<0.5) with octahedronlike shapes. Here, we consider the convex c...

The structure Dense(Q)/nwd and gaps in analytic quotients of P(ω) have been studied in the literature. We prove a that in ZFC you can prove that structures Dense(Q)/nwd and P(Q)/nwd have gaps of type (add(M ), ω) and that there are no (λ, ω)-gaps for λ < add(M ), where add(M ) is the additivity of the meager ideal. We also give a direct proof of the existence of (ω1, ω1)-gaps. In this paper we ...

We consider the stochastic joint replenishment problem in which several items must be ordered in the face of stochastic demand. Previous authors proposed multiple heuristic policies for this economically-important problem. We show that several such policies are not good approximations to an optimal policy, since as some items grow more expensive than others, the cost rate of the heuristic polic...

The phase transitions of random-field q-state Potts models in d=3 dimensions are studied by renormalization-group theory exact solution a hierarchical lattice and, equivalently, approximate Migdal-Kadanoff solutions cubic lattice. recursion, under rescaling, coupled and random-bond (induced rescaling random fields) probability distributions is followed to obtain diagrams. Unlike the Ising model...

Abstract We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the L q -norm of solution and p -Laplace operator. prove multiplicity positive solutions for problem, where number doubles “positive bumps” term. The are also ordered according to their -norms.

In this article, we study the existence of tripled coincidence and tripled common fixed point theorems in partially ordered complete quasi-metric spaces for nonlinear contraction condition related to Q-function q. Our results generalize and modify several comparable results in the literature. We also provide illustrative examples in support of our new results. Mathematics Subject Classification...