Necessary and sufficient conditions are presented for several families of planar curves to form a set stable sampling the Bernstein space BΩ over convex Ω⊂R2. These ‘essentially’ describe mobile property these Paley-Wiener spaces PWΩp,1≤p<∞.

In this work, we defined a new category called 4-Dimensional 2-crossed modules. We identified the subobjects and ideals in category. The notion of subobject is generalization ideas like subsets from set theory, subspaces topology, subgroups group theory. then exemplified A quotient object dual concept subobject. Concepts sets, spaces, groups, graphs, etc. are generalized with object. Using idea...

Abstract A periodic lattice in Euclidean space is the infinite set of all integer linear combinations basis vectors. Any can be generated by infinitely many different bases. This ambiguity was partially resolved, but standard reductions remain discontinuous under perturbations modelling atomic displacements. paper completes a continuous classification 2-dimensional lattices up to isometry (or c...