We consider the recovery of an underlying signal x ∈ C based on projection measurements of the form y = Mx+w, where y ∈ C and w is measurement noise; we are interested in the case l ≪ m. It is assumed that the signal model p(x) is known, and w ∼ CN (w; 0,Σw), for known Σw. The objective is to design a projection matrix M ∈ C to maximize key information-theoretic quantities with operational sign...

A necessary and sufficient condition for existence of a Banach space with a finite dimensional decomposition but without the π-property in terms of norms of compositions of projections is found. 2000 Mathematics Subject Classification. Primary 46B15; Secondary 46B07, 46B28. The problem of existence of Banach spaces with the π-property but without a finite dimensional decomposition is one of the...

Hybrid Dirac fields are fields that are general superpositions of the annihilation and creation parts of four Dirac spin 1/2 fields, ψ (±) (x; ±m), whose annihilation and creation parts obey the Dirac equation with mass m and mass −m. We discuss a specific case of such fields, which has been called " homeotic. " We show for this case, as is true in general for hybrid Dirac fields (except the or...

The reconstruction of 8-connected but not 4-connectedhv-convex discrete sets from few projections is considered. An algorithm is given with worst case complexity of O(mnmin{m, n}) to reconstruct all sets with given horizontal and vertical projections. Experimental results are also presented. It is shown, that using also the diagonal projections the algorithm can be speeded up having complexity ...

Hybrid Dirac fields are fields that are general superpositions of the annihilation and creation parts of four Dirac spin 1/2 fields, ψ (±) (x; ±m), whose annihilation and creation parts obey the Dirac equation with mass m and mass −m. We discuss a specific case of such fields, which has been called " homeotic. " We show for this case, as is true in general for hybrid Dirac fields (except the or...

The problem of reconstructing a convex polyominoes from its horizontal and vertical projections when the projections are defined as the number of cells of the polyomino in the different lines and columns was studied by Del Lungo and M. Nivat (cf [7]). In this paper we study the reconstruction of any convex polyomino when the orthogonal projections are defined as the contour length of the object...

We characterize heirs of so called box types of a polynomially bounded o-minimal structure M . A box type is an n-type of M which is uniquely determined by the projections to the coordinate axes. From this, we deduce various structure theorems for subsets of M, definable in the expansion M of M by all convex subsets of the line. Moreover we obtain a model completeness result for M .

For a finite von Neumann-algebra factor M, the projections form a modular ortholattice L(M) . We show that the equational theory of L(M) coincides with that of some resp. all L(C) and is decidable. In contrast, the uniform word problem for the variety geneated by all L(C) is shown to be undecidable.

Let M be a non-compact connected Riemann surface of finite type, and R ⊂⊂ M be a relatively compact domain such that H1(M,Z) = H1(R,Z). Let R̃ −→ R be a covering. We study the algebra H∞(U) of bounded holomorphic functions defined in some domains U ⊂ R̃. Our main result is a Forelli type theorem on projections in H∞(D).