The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...

A manifold M is like a curve in 2D and a surface in 3D. It is a set of points with topology (or neighbor structures), and locally looks like R. Example: our earth. Locally it is planar. Rigidly, for a patch U ⊂ M , we have a local coordinate system xU : U 7→ R as i = 1 · n local coordinates. Typically M can be covered by several such patches. (eg, A sphere can be covered by 2 patches but not on...

A [0, m]-space is a linear space with the following property: For any point-line pair (x, G) there are at most m lines through x which are coplanar with G and which have no point in common with G. For every [0, m]-space (M, 90l) we define an order o r d M in a natural way. For dimM~>3 and o r d M ~ > 3 m + 2 , every [0, m]-space (M, 991) can be embedded in a projective space (P, £) with dim P =...

Given a 1-connected Poincaré duality space M of dimension 2p, with p > 2, we give criteria for deciding when homotopy classes S −→ M are represented by framed Poincaré embedded p-spheres.

Modern signal processing and multimedia embedded systems increasingly have heterogeneous system architectures. In these systems, programmable processors provide flexibility to support multiple applications, while dedicated hardware blocks provide high performance for time-critical application tasks. The heterogeneity of these embedded systems and the varying demands of their growing number of t...

The optimal density function assigns to each symplectic toric manifold M a number 0 < d ≤ 1 obtained by considering the ratio between the maximum volume of M which can be filled by symplectically embedded disjoint balls and the total symplectic volume of M . In the toric version of this problem, M is toric and the balls need to be embedded respecting the toric action on M . The goal of this not...

We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R given a noisy sample from the manifold. Under certain conditions, we show that the optimal rate of convergence is n−2/(2+d). Thus, the minimax rate depends only on the dimension of the manifold, not on the dimension of the space in which M is embedded.