In this paper, we illustrate a method to enumerate two-dimensional directed animals, with compact sources, on both the square and the triangular lattice. We give a recursive description of these structures from which we deduce their generating function, according to various parameters: the area, the right half-width and the number of compact sources. We determine the average number of compact s...

Photographic slides of an aperiodic heptagonal tiling were used as two-dimensional diffraction gratings (as a standard approach) to describe and demonstrate the basic properties dodecagonal quasicrystals. The paper completes our earlier two publications dealing with (1) Penrose (decagonal) Ammann (octagonal) quasicrystals (2) quasicrystals, which constructed presented in analogous manner.

The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of twoand three-state vertex models. These models include the six-vertex model, the 15-vertex A (1) 2 model and the 19-vertex models of Izergin-Korepin and ZamolodchikovFateev. In each case the eigenspectra is determined by a...

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q > 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q ≥ 7), triangular lattice (q ≥ 11), hexagonal lattice (q ≥ 4), and Kag...

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q > 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q 7), triangular lattice (q 11), hexagonal lattice (q 4), and Kagom e l...

The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set V (G) can be partitioned into disjoint classes X1, . . . , Xk, where vertices in Xi have pairwise distance greater than i. For the 2-dimensional square lattice Z it is proved that χρ(Z ) ≥ 12, which improves the previously known lower bound 10.

The phononic band structures of two-dimensional solid phononic crystals with different lattice and scatterer symmetry are studied numerically, with three types of lattice (square, triangular and rectangular) and four different scatterer shapes (circle, hexagon, square and rectangle) considered. XY and Z vibration modes are investigated separately. Two types of phononic crystal are considered: o...

In the title dinuclear complex, [Cu(2)(C(14)H(20)ClN(4)O)ClO]·3H(2)O, one Cu(II) cation assumes a distorted square-planar coordination geometry and the other a distorted square-pyramidal coordination geometry. Both Cu(II) cations are N,N',O-chelated by one arm of the 2,6-bis-[(2-amino-eth-yl)imino-meth-yl]-4-chloro-phenolate anion, and one oxide anion bridges the two Cu(II) cations, forming a d...

an extended octagonal ring (eor) transducer was designed and developed to measure forces inside the compression chamber of a large square baler in different directions. the transducer was calibrated by applying forces in three directions simultaneously and independently. the sensor revealed excellent linearity along with small cross sensitivities. horizontal and vertical primary sensitivities o...