An index theory for uniformly locally finite (ULF) graphs is developed based on the adjacency operator A acting on the space of bounded sequences defined on the vertices. It turns out that the characterization by upper and lower nonnegative eigenvectors is an appropriate tool to overcome the difficulties imposed by the `∞–setting. A distinctive property of the spectral radius r∞(A) in `∞ is the...

We investigate the residual-free bubble method (RFB) for the linearized incompressible Navier–Stokes equations. Starting with a nonconforming inf-sup stable element pair for approximating the velocity and pressure, we enrich the velocity space by discretely divergence-free bubble functions to handle the influence of strong convection. An important feature of the method is that the stabilization...

Let X ,Z be a pair of real linear spaces put in duality by a separating bilinear form 〈, 〉, and endowed with compatible locally convex topologies respectively. A subset F of X is said to be p-bounded if sup p(x) : x ∈ F < ∞. We denote the collection of all nonempty p-bounded subsets of X by p(X ). Given x ∈ X , F ∈ p(X ), and V ⊆ X , write rp(F ; x) = sup p(y − x) : y ∈ F , radp(F ;V ) = inf rp...

and Applied Analysis 3 the hull of f . It is easy to see that if f n is almost periodic, then for all f1 ∈ H f , lim inf n→∞ f n inf n∈Z f n inf n∈Z f1 n , lim sup n→∞ f n sup n∈Z f n sup n∈Z f1 n . 1.7 Definition 1.2. Let f : Z × C → R. Then f is said to be almost periodic in n ∈ Z uniformly on compact set of C, if f n, · is continuous for each n ∈ Z, and for any > 0 and every compact setK ⊂ C...

In this work we consider a stabilized Lagrange multiplier method in order to approximate the Coulomb frictional contact model in linear elastostatics. The particularity of the method is that no discrete inf-sup condition is needed. We study the existence and the uniqueness of solution of the discrete problem.

We construct space-time Petrov–Galerkin discretizations of the heat equation on an unbounded temporal interval, either right-unbounded or left-unbounded. The discrete trial and test spaces are defined using Laguerre polynomials in time and are shown to satisfy the discrete inf-sup condition. Numerical examples are provided.

In a search for spectroscopic binaries in ! Cen, the radial velocities of 310 giant stars have been monitored with multiple observations over more than ten years. The percentage of binaries with periods from those allowed by the Roche lobe limit and up to the limit set by dynamical disruption is about a factor ve smaller than among G dwarfs in the solar vicinity in the same period range. Assumi...