Given a matrix A ∈ Rm×n (n vectors in m dimensions), we consider the problem of selecting a submatrix (subset of the columns) with maximum volume. The motivation to study such a problem is that if A can be approximately reconstructed from a small number k of its columns (A has “numerical” rank k), then any set of k independent columns of A should suffice to reconstruct A. However, numerical sta...

Let ? be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in field K. We prove comparison theorems between MacLane–Vaquié key polynomials for valuations ??? and abstract ?. Also, some results invariants associated to limit are obtained. In particular, if char(K)=0, we show that all unbounded continuous families augmentations have numerical character equal one.

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

There are different methods to reduce drag in high speed hulls. One of these methods is a change in the shape of the body by adding longitudinal side tunnels. In this paper it has been attempted to determine the influence of the tunnel height on hydrodynamic characteristics of the hull to achieving an optimum shape for the tunnel. To achieve this purpose, numerical simulation of the problem has...

‎three infinite families of finite abelian groups will be‎ ‎described such that each member of these families has‎ ‎the r'edei $k$-property for many non-trivial values of $k$‎.

We study asymptotic properties of the approximation of a suuciently smooth convex body K in R d by the convex hulls of n points in the boundary of K, for n ! 1. The deviation is measured by the Hausdorr distance. The asymptotic distribution of the vertices of best-approximating polytopes is determined. Further results involve prescribed densities for the vertices and describe the strength of ap...

 Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical...

Abstract A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple sets judiciously apply these obtain strong yet computationally tractable relaxations. We invoke matrix perspective function—the analog function—to explicitly hull epigraphs functions under constraints. Further, we combine function with orthogo...

2 The Server Problem 5 2.1 Convex Hulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The Equipoise Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Lower Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 The Work Function Algorithm for k Servers . . . . . . . . . . . . . . . . . . . . 17 2.3.1 A Conject...

It is challenging and inspiring for us to achieve high spatiotemporal resolutions in dynamic cardiac magnetic resonance imaging (MRI). In this paper, we introduce two novel models and algorithms to reconstruct dynamic cardiac MRI data from under-sampled k - t space data. In contrast to classical low-rank and sparse model, we use rank-one and transformed sparse model to exploit the correlations ...