A hereditary class P is called finitely generated if the set of all minimal forbidden induced subgraphs for P is finite. For a pair of hereditary classes P and Q, we define a hereditary class P ∗ Q of all graphs G which have a partition A ∪ B = V (G) such that G(A) ∈ P and G(B) ∈ Q, where G(X) denotes the subgraph of G induced by X ⊆ V (G). We investigate the problem of recognizing finitely gen...

We develop a novel optimization approach to tone. Its grammatical component consists of the similarityand proximity-based correspondence constraint framework of Agreement by Correspondence theory (ABC). Its representational component (Q theory) decomposes segments (Q) into temporally ordered, quantized subsegments (q), which comprise unitary sets of distinctive features, including tone. ABC+Q u...

An antiferroquadrupolar ordering at T(Q)=0.11  K has been found in a Pr-based superconductor PrIr(2)Zn(20). The measurements of specific heat and magnetization revealed the non-Kramers Γ(3) doublet ground state with the quadrupolar degrees of freedom. The specific heat exhibits a sharp peak at T(Q)=0.11  K. The increment of T(Q) in magnetic fields and the anisotropic B-T phase diagram are consi...

In this note I examine conditions under which a probability relation on a set of events is lexicographic. Chipman (1971) discussed the question of the minimal ordinal CT such that there exists an order-preserving function from an ordered set A (in his; paper A is fR with any order on it) to lRa with the lexicographic order on it. Since there always exists an ordinal /? such that there is an ord...

One partially ordered set, Q, is a Tukey quotient of another, P – denoted P?TQ if there map ?:P?Q carrying cofinal sets to Q. Let X be space and denote by K(X) the set compact subsets X, inclusion. For certain separable metrizable spaces M, upper lower bounds K(M) are calculated. Results on invariants K(M)'s deduced. The structure all under ?T investigated. Particular emphasis placed position w...

Richard Stanley introduced the order polytope O(P ) and the chain polytope C(P ) arising from a finite partially ordered set P , and showed that the Ehrhart polynomial of O(P ) is equal to that of C(P ). In addition, the unimodular equivalence problem of O(P ) and C(P ) was studied by the first author and Nan Li. In the present paper, three integral convex polytopes Γ(O(P ),−O(Q)), Γ(O(P ),−C(Q...

We study effects of higher-order antinematic interactions on the critical behavior antiferromagnetic (AFM) $XY$ model a triangular lattice, using Monte Carlo simulations. The parameter $q$ generalized (ANq) interaction is found to have pronounced effect phase diagram topology by inducing new quasi-long-range ordered phases due competition with conventional AFM as well geometrical frustration. F...

A number of physically intuitive results for the calculation multi-time correlations in phase-space representations quantum mechanics are obtained. They relate time-dependent stochastic samples to observables, and rely on presence derivative-free operator identities. In particular, expressions time-ordered normal-ordered observables positive-P distribution derived which replace Heisenberg opera...

We continue the study of prime simple modules for quantum affine algebras from perspective q-fatorization graphs. In this paper we establish several properties related to whose q-factorization graphs are afforded by trees. The two most important them proved type A. first completes classification with three q-factors giving a precise criterion primality 3-vertex line which is not totally ordered...

We have investigated the origin of magnetic dipole correlations $\langle \sigma_{\boldsymbol{Q}}^z \sigma_{\boldsymbol{-Q}}^z \rangle$ characterized by modulation wave vector $\boldsymbol{k} \sim (\tfrac{1}{2},\tfrac{1}{2},\tfrac{1}{2})$ observed in frustrated pyrochlore magnet Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$. This short-range order cannot be accounted for adding further-neighbor exchange interac...