The Borel Conjecture is the statement that C = [R]<ü,i , where C is the class of strong measure zero sets; it is known to be independent of ZFC. The Generalized Borel Conjecture is the statement that C = [R]<c. We show that this statement is also independent. The construction involves forcing with an «2-stage iteration of strongly proper orders; this latter class of orders is shown to include s...

In this paper, by using the concept of the resolvent operator, we study the behavior and sensitivity analysis of the solution set for a class of parametric generalized strongly nonlinear mixed quasivariational inclusion problem in Banach spaces. The results presented in this paper are new and generalize many known results in this field. Mathematics Subject Classification: 49J40, 90C20

We introduce a notion of strongly C×-graded, or equivalently, C/Zgraded generalized g-twisted V -module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V -module if V admits an additional C-grading compatible with g. Let V = ∐ n∈Z V(n) be a vertex operator algebra such that V(0)...