Motivated by applications in quantum information and quantum control, a new type of C-numerical range, the relative C-numerical range denoted W K (C, A), is introduced. It arises upon replacing the unitary group U (N) in the definition of the classical C-numerical range by any of its compact and connected subgroups K ⊂ U (N). The geometric properties of the relative C-numerical range are analys...

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.

Parallel magnetic resonance (MR) imaging techniques use multiple receiver coils for data acquisition. Sensitivity responses of these coils usually vary in space and must be estimated via a separate calibration process. We present an algorithm for jointly estimating MR images and coil sensitivity maps from subsampled k-space measurements. We pose the joint estimation problem as the recovery of a...

‎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 $k$‎.

normal range of joint motion is an important factor in joint examination in clinical practice which is related to factors such as age, sex and geographic region. there is no data in the literature on the range of joint motions in healthy iranian adults. we studied joint motions in 100 healthy volunteer subjects, 49 men and 51 women, from 19 and 58 years of age. the joint mobility was examined i...

OBJECTIVES To determine whether erosive osteoarthritis shares the same pattern of joint involvement and risk profile as increasing grades of non-erosive hand osteoarthritis. METHODS Participants were from two population-based cohorts, aged ≥50 years, reporting hand symptoms in the previous month. Interphalangeal joints were assessed for erosive osteoarthritis (Verbruggen-Veys erosive or remod...

Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from phase retrieval and from blind deconvolution, which are designed to yield rank-1 solutions. An algorithm is described based on solving a certain constrained ...

We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let S be a set of n points in the plane, where each point p in S is assigned a weight w(p) that is polynomial in n, and define the rank of p to be r(p) = blogw(p)c. Then the priority range tree can be used to report all points in a threeor four-sided quer...