We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wavelets by polynomials of the random parameters leads to a modular solver for the parameter dependence, which combines with any discretization on the spatial domain. We show optimality properties of this solver, and present numerical computations. Introduction ...

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...

fusion is a developmental anomaly defined as the :union: of two normally separated tooth buds or the partial splitting of one tooth bud into two buds. depending on the stage of development, fusion may be either complete or incomplete. the significance of this particular case was that this fusion occurred in a posterior permanent mandibular tooth, while such a manifestation is more reported in m...

The problem of exact null-controllability is considered for a wide class of linear neutral-type systems with distributed delay. The main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families. A complete characterization of this problem is given. The minimal time of controllability is specified. The results are based o...

We show how it is possible to diagonalize a certain class of homogeneous linear operators in a biorthogonal wavelet basis. Given a linear operator and a biorthogonal wavelet basis we construct a new biorthog-onal wavelet basis such that by analyzing a function in the new basis and multiplying the wavelet coeecients by a scale dependent factor we get the wavelet coeecients of the transformed fun...

Let H be a (separable) Hilbert space and {ek}k≥1 a fixed orthonormal basis of H. Motivated by many papers on scaled projections, angles of subspaces and oblique projections, we define and study the notion of compatibility between a subspace and the abelian algebra of diagonal operators in the given basis. This is used to refine previous work on scaled projections, and to obtain a new characteri...