Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...

in this paper, a new design of optical channel drop filter based on two- dimensional photonic crystal ring resonators with triangular lattice is proposed. the rods of this structure is silicon with the refractive index nsi=3.46 and the surrounding environment is air with the refractive index of nair=1.the widest photonic band gap obtains for the filling ratio of r/a = 0.2. the filter’s transmis...

We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with twoand three-body interactions on the triangular lattice. These results provide us with numerous examples to further ve...

In this paper, the connection between triangular number , square number for construction and counting the lattice number in lattice vector quantization is presented. We also observe that unique hexagonal lattice can be formed from two triangular numbers and a square number combination. Furthermore, the number of multistage lattice is derived from lattice number . Analysis of the number of latti...

We consider the problem of unfolding lattice trees and polygons in hexagonal or triangular lattice in two dimensions. We show that a hexagonal/triangular lattice chain (resp. tree) can be straightened in O(n) (resp. O(n)) moves and time, and a hexagonal/triangular lattice polygon can be convexified in O(n) moves and time. We hope that the techniques we used shed some light on solving the more g...

In this study, the hybrid Au-Ag hexagonal lattice of triangular and square lattice of quadrate periodic nanoparticle arrays (PNAs) were designed to investigate their extinction spectra of the localized surface plasmon resonances (LSPRs). First, their simulating extinction spectra were calculated by discrete dipole approximation (DDA) numerical method by changing the media refractive index. Simu...

A conjecture is given for the exact location of the multicritical point in the phase diagram of the ±J Ising model on the triangular lattice. The result pc = 0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, pc = 0.9327041, again in excellent agree...

A conjecture is given for the exact location of the multicritical point in the phase diagram of the ±J Ising model on the triangular lattice. The result pc = 0.8358058 agrees well with a recent numerical estimate. From this value, it is possible to derive a comparable conjecture for the exact location of the multicritical point for the hexagonal lattice, pc = 0.9327041, again in excellent agree...

In this paper we study the 3-state Potts model on the triangular lattice which has twoand three-site interactions. Using a Peierls argument we obtain a rigorous bound on the transition temperature, thereby disproving a conjecture on the location of its critical point. Low-temperature series are generated and analyzed for three particular choices of the coupling constants; a phase diagram is the...