Note on “approximation space on novel granulations”

A note on modular hyperconvex space

A note on Diophantine approximation

Given a set of nonnegative real numbers Λ= {λi}i=0, a Λ-polynomial (or Müntz polynomial) is a function of the form p(x)=ni=0 aizi (n∈N). We denote byΠ(Λ) the space of Λ-polynomials and byΠZ(Λ) := {p(x)=ni=0 aizi ∈Π(λ) : ai ∈ Z for all i≥ 0} the set of integral Λ-polynomials. Clearly, the sets ΠZ(Λ) are subgroups of infinite rank of Z[x] wheneverΛ⊂N, #Λ=∞ (by infinite rank, wemean that the real ...

A Note on Belief Structures and S-approximation Spaces

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory...

a note on modular hyperconvex space

A Note On Space Noncommutativity

We consider a two-point spatial lattice approximation to an open string moving in a flat background with B field. It gives a constrained dipole system under the influence of a vector potential. Solving and quantizing this system recover all the essential features of a noncommutative space. In particular, open string interactions induce a canonical product structure on the Hilbert space of the d...