An analytical work on intrinsic localized modes in a two-dimensional Heisenberg ferromagnet the checkerboard lattice is presented. Taking advantage of an asymptotic method, governing dynamical equations are reduced to one (2 + 1)-dimensional nonlinear Schrödinger equation. In our work, we obtain two types mode solutions, namely, Brillouin zone center and corner modes. The occurrence conditions ...

In this note, we exhibit a weakly holomorphic modular form for use in constructing Fourier eigenfunction four dimensions. Such auxiliary functions may be of to the D4 checkerboard lattice and dimensional sphere packing problem.

BACKGROUND Dental caries develops as a result of the metabolism of carbohydrates by cariogenic bacteria present in a complex biofilm. The present study aimed to examine if bacteria in pooled supragingival plaque samples quantified using a "checkerboard DNA-DNA hybridization" based panel of caries-related bacteria, could reflect the caries experience in a manner similar to saliva samples analyse...

Negative refractive index materials (NRIM) enable unique effects including superlenses with a high degree of sub-wavelength image resolution, a capability that stems from the ability of NRIM to support a host of surface plasmon states. Using a generalized lens theorem and the powerful tools of transformational optics, a variety of focusing configurations involving complementary positive and neg...

Although cuttlefish are capable of showing diverse camouflage body patterns against a variety of background substrates, whether they show background preference when given a choice of substrates is not well known. In this study, we characterized the background choice of post-embryonic cuttlefish (Sepia pharaonis) and examined the effects of rearing visual environments on their background prefere...

Recently we have shown that the single positive deflection in the checkerboard onset evoked potential (EP) of young children of striate origin develops into a negative-positive complex. However, also an early positive peak becomes apparent in the checkerboard onset EP. To determine the origin and development of the activity underlying this early positive deflection we studied the checkerboard o...

Consider the plane as a checkerboard, with each unit square colored black or white in an arbitrary manner. In a previous paper we showed that for any such coloring there are straight line segments, of arbitrarily large length, such that the difference of their white length minus their black length, in absolute value, is at least the square root of their length, up to a multiplicative constant. ...

Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on a 2M×2N checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We...