Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ < g in Pp iif(p) < g(p) for all p £ P. We prove that if P and Q are finite, connected partially ordered sets and Pp = Q<¡ then Psg. Is a partially ordered set determined by its order-preserving mappings? L. M. Gluskin [4] has shown that the set of order-preserving mappings of a part...

An ordered partition with k blocks of [n] := {1, 2, . . . , n} is a sequence of k disjoint and nonempty subsets, called blocks, whose union is [n]. Clearly the number of such ordered partitions is k!S(n, k), where S(n, k) is the Stirling number of the second kind. A statistic on ordered partitions of [n] with k blocks is called Euler-Mahonian statistics if its generating polynomial is [k]q!Sq(n...

Electronic energy spectra «~q! of antiferromagnetically ordered media may display nonreciprocity; that is, the energies corresponding to Bloch states with wave numbers q and 2q may be different. In this paper a simple Kronig-Penney model, which includes a staggered microscopic magnetic and electric fields of the proper symmetry, is employed to estimate the magnitude of nonreciprocity effects in...

A completion of an n-ordered set P = 〈P, 1, . . . , n〉 is defined, by analogy with the case of posets (2-ordered sets), as a pair 〈e,Q〉, where Q is a complete n-lattice and e : P → Q is an n-order embedding. The Basic Theorem of Polyadic Concept Analysis is exploited to construct a completion of an arbitrary nordered set. The completion reduces to the Dedekind–MacNeille completion in the dyadic...

We investigate the continuum q-Potts model at its transition point from the disordered to the ordered regime, with particular emphasis on the coexistence of disordered and ordered phases in the high-q case. We argue that the occurrence of a phase transition can be seen as a percolation in the related random cluster representation, similarly to the lattice Potts model, and investigate the typica...

For prime powers q we use “strongly orthogonal” linear sudoku solutions of order q to construct ordered orthogonal arrays of type OOA(4, s, 2, q), and for each q we present a range of values of s for which these constructions are valid. These results rely strongly on flags of subspaces in a four dimensional vector space over a finite field.

Distinctive orderings and phase diagram structures are found, from renormalization-group theory, for odd q-state clock spin-glass models in d=3 dimensions. These models exhibit asymmetric phase diagrams, as is also the case for quantum Heisenberg spin-glass models. No finite-temperature spin-glass phase occurs. For all odd q≥5, algebraically ordered antiferromagnetic phases occur. One such phas...

We investigate the electromagnetic form factor $F({q}^{2})$ of meson by using solvable ${\ensuremath{\phi}}^{3}$ scalar field model in ($1+1$) dimensions. As transverse rotations are absent dimensions, advantage light-front dynamics (LFD) with time ${x}^{+}={x}^{0}+{x}^{3}$ as evolution parameter is maximized contrast to usual instant (IFD) ordinary ${x}^{0}$ parameter. In LFD, individual ${x}^...

Neutron elastic and inelastic scattering measurements have been performed in order to investigate the spin structure and the magnetic excitations in the impurity-induced antiferromagnetic ordered phase of the doped spin gap system Tl(Cu 1−x Mg x)Cl 3 with x = 0.03. The magnetic Bragg reflections indicative of the ordering were observed at Q Q Q = (h, 0, l) with integer h and odd l below T N = 3...

and Applied Analysis 3 2. Preconditioned Explicit Decoupled Group SOR (EDG SOR) For convenience, we will now briefly explain some of the definitions used in this paper. Definition 2.1 see 15 . A matrix A of order n has property A if there exists two disjoint subsets S and T of W {1, 2, . . . , n} such that if i / j and if either aij / 0 and aij / 0, then i ∈ S and j ∈ T or else i ∈ T and j ∈ S....