and Applied Analysis 3 On the other hand, for a function f defined by 1.6 and in the class C p, α , Lemma 1.2 yields ap 1 ≤ p ( p − α ( p 1 )( p 1 − α . 1.10 In view of the coefficient inequalities 1.9 and 1.10 , it would seem to be natural to introduce and study here two further classes T ∗ ε p, α and Cε p, α of analytic and p-valent functions, where T ∗ ε p, α denotes the subclass of T ∗ p, α...

in a bounded polyhedral domain Ω ⊂ R with a Lipschitz boundary ∂Ω and 0 < ǫ ≤ 1,b ∈ [H(Ω) ∩ L∞(Ω)]d, c ∈ L∞(Ω), f ∈ L(Ω), c− 1 2∇ · b ≥ 0. Let {Ωk} be a non-overlapping macro partition with Ω = ∪k=1Ωk. The goal of the well-known DDM of Robin type (Lions [1990]) is to enforce (in appropriate trace spaces) continuity of the solution u and of the diffusive and advective fluxes ǫ∇u·nkj resp.− 1 2 (...

Let Ω be an open convex domain of C. We study constants K such that Ω is K-spectral or complete K-spectral for each continuous linear Hilbert space operator with numerical range included in Ω. Several approaches are discussed.

Let Ω be a complete graph on an even number n = 2m of vertices V = V(Ω) = {ω1, . . . , ωn} and assume that K = {k1, . . . , kn−1} is a 1-factorization of Ω. Identify every k ∈ K with the fixed point free involution of Sym(V) which interchanges the ends of every edge in k and set GK = 〈K〉. Then K is said to be self-invariant if Kk = K for all k ∈ K. Heiss [Hei] studied self-invariant 1-factoriza...

Let Ω be a complex manifold and let V be a (holomorphic) subvariety of Ω of pure (complex) dimension k. Then integration over V defines a closed current of dimension 2k in Ω, denoted by [V ]. More generally, let {Vj} be a locally finite family of irreducible holomorphic subvarieties of Ω of pure dimension k and let {nj} be integers. Then T = ∑ nj [Vj ] is a 2kcurrent in Ω—these are the holomorp...

The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u = (u1,u2) ∈ K such that for all v = (v1,v2) ∈ K, ∫ Ω∇u1∇(v1 −u1)+ ∫ Ω∇u2∇(v2−u2)+(f ,v−u)≥ 0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K = {v ∈H1 0(Ω)×H 0(Ω) : v1 ≥ v2 a.e. in Ω}. 2000...

We study numerically the influence of non-resonant effects on the dynamics of a single π-pulse quantum CONTROL-NOT (CN) gate in a macroscopic ensemble of four-spin molecules at room temperature. The four nuclear spins in each molecule represent a four-qubit register. The qubits are " labeled " by the characteristic frequencies, ω k , (k = 0 to 3) due to the Zeeman interaction of the nuclear spi...

We prove the consistency result from the title. By forcing we construct a model of g = ℵ1, b = cf(Sym(ω)) = ℵ2. We recall the definitions of the three cardinal characteristics in the title and the abstract. We write A ⊆ * B if A \ B is finite. We write f ≤ * g if f, g ∈ ω ω and {n : f (n) > g(n)} is finite. Definition 0.1. (1) A subset G of [ω] ω is called groupwise dense if – for all B ∈ G, A ...

Hasse-Minkowski’s theorem asserts that a quadratic form over a number field k admits a nontrivial zero if it does over completions at all places of k. One could look for analogues of Hasse principle for function fields. Let k be a field of characteristic not 2 and Ω a set of discrete valuations of k. Let k̂v denote the completion of k at v. We say that k satisfies Hasse principle with respect to...