Generalized adjoint with modified discretization and generalized coarse-grain adjoint are derived for a vector system of equations that contains parameterized on/off switches. With vector examples, it is shown that the conventional adjoint minimization may have a convergence problem in multidimensional space. The problem can be solved by the generalized adjoint with modified discretization or b...

We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

We study tangential convergence of convolutions with approximate identities of functions defined on a homogeneous type space and having a certain regularity. Our results contain those already known for the Euclidean case and give new ones for stratified nilpotent Lie groups and for solutions of the Dirichlet problem on Lipschitz domains.

We study the GKM theory for a equivariant stratified space having orbifold structures in tis successive quotients. Then, we introduce notion of an \emph{almost simple polytope}, as well \emph{divisive toric variety} generalizing concept divisive weighted projective space. employ to compute generalized cohomology theories varieties associated almost polytopes and varieties.

we discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (nod) random variables by generalized gaussian techniques. as a corollary, a cesaro law of large numbers of i.i.d. random variables is extended in nod setting by generalized gaussian techniques.

Abstract The generalized Schwarz algorithm for a class of elliptic quasi-variational inequalities related to impulse control problems is studied in this paper. principal result prove the error estimate $L^{\infty}$ L ∞ -norm m subdomains with overlapping nonmatching gri...