Let Fn be the set of cuspidal automorphic representations π GLn over a number field with unitary central character. We prove two unconditional large sieve inequalities for Hecke eigenvalues π∈Fn, one on integers and primes. The second leads to first zero density estimate family L-functions L(s,π) associated which we make log-free. As an application estimate, hybrid subconvexity bound L(12,π) su...

For every Banach space Z with a shrinking unconditional basis satisfying an upper p-estimate for some p > 1, an isomorphically polyhedral Banach space is constructed which has an unconditional basis and admits a quotient isomorphic to Z. It follows that reflexive Banach spaces with an unconditional basis and non-trivial type, Tsirelson's original space and (P c0) ℓp for p ∈ (1, ∞), are isomorph...

In this paper we investigate the parallel difference schemes of parabolic equation, in particular, two kinds of difference schemes with intrinsic parallelism are constructed. Firstly we combine the values of previous two time levels at the interface points to get the (Dirichlet) boundary condition for the sub-domain problems. Then the values in the sub-domains are calculated by fully implicit s...

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo derivative is constructed. In line with this goal, drift term and time are discretized by a finite difference approximation. The energy method used to investigate rate of convergence unconditional stability temporal discretization. interpolation moving Kriging technique then approximate s...

Let X be a Banach space with an unconditional finite-dimensional Schauder decomposition (E n). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each E n. For example, we show that if sup dim E n < ∞ and X has Gordon-Lewis local unconditional structure then X has an unconditional basis of...

The main result is that a separable Banach space with the weak∗ unconditional tree property is isomorphic to a subspace as well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is isomorphic to a subspace of a space with an unconditional basis iff it is isomorphic to a quotient of a space with an unconditional basis, which solves...

Systems of nonlinear partial differential equations modeling turbulent fluid flow and similar processes present special challanges in numerical analysis. Regions of stability of implicit-explicit methods are reviewed, and an energy norm based on Dahlquist’s concept of G-stability is developed. Using this norm, a time-stepping Crank-Nicolson Adams-Bashforth 2 implicit-explicit method for solving...

A numerical method for the two-dimensional, incompressible Navier–Stokes equations in vorticity-streamfunction form is proposed, which employs semi-Lagrangian discretizations for both the advection and diffusion terms, thus achieving unconditional stability without the need to solve linear systems beyond that required by the Poisson solver for the reconstruction of the streamfunction. A descrip...