A basis theorem for perfect sets

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

No-cloning theorem for a single POVM

Cloning of statistics of general quantum measurement is discussed. The presented approach is connected with the known concept of observable cloning, but differs in some essential respects. The reasons are illustrated within some variety of B92 protocol. As it is shown, there exist pairs of states such that the perfect cloning of given POVM is not possible. We discuss some properties of these in...

Strong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces

In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.

Dirichlet Sets and Erdös-kunen-mauldin Theorem

By a theorem proved by Erdös, Kunen and Mauldin, for any nonempty perfect set P on the real line there exists a perfect set M of Lebesgue measure zero such that P +M = R. We prove a stronger version of this theorem in which the obtained perfect set M is a Dirichlet set. Using this result we show that the ideal of additive sets for any family generated by analytic subgroups of the reals contains...

Colorings of Hypergraphs, Perfect Graphs, and Associated Primes of Powers of Monomial Ideals

Let H denote a finite simple hypergraph. The cover ideal of H, denoted by J = J(H), is the monomial ideal whose minimal generators correspond to the minimal vertex covers of H. We give an algebraic method for determining the chromatic number of H, proving that it is equivalent to a monomial ideal membership problem involving powers of J . Furthermore, we study the sets Ass(R/Js) by exploring th...