Lattices and Periodic Functions

Mini-emulsion preparation, kinetics of reaction and physical properties of acrylic terpolymer lattices

In this study, stable lattices of terpolymer butyl acrylate, methyl methacrylate, and styrene were synthesized by a mini-emulsion polymerization technique using tert-butyl hydroperoxide TBHP/Fe2 /ethylenediaminetetraacetic acid/sodium formaldehyde sulfoxylate redox initiators at room temperature, and the kinetics of the reaction were studied. The reaction rate was obtained from periodic samplin...

Exact partition functions of the Ising model on M × N planar lattices with periodic–aperiodic boundary conditions

Abstract. The Grassmann path integral approach is used to calculate exact partition functions of the Ising model onM×N square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodicperiodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/...

Periodic harmonic functions on lattices and points count in positive characteristic

Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling

In this paper, we present algorithms for the approximation of multivariate periodic functions by trigonometric polynomials. The approximation is based on sampling of multivariate functions on rank-1 lattices. To this end, we study the approximation of periodic functions of a certain smoothness. Our considerations include functions from periodic Sobolev spaces of generalized mixed smoothness. Re...

Alternative approaches to obtain t-norms and t-conorms on bounded lattices

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...

INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...