Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

De-agrarianization, re-agrarianization and local economic development: re-orientating livelihoods in African artisanal mining communities

This article contributes to the debate on livelihood diversification in rural sub-Saharan Africa, focusing specifically on the growing economic importance of artisanal and small-scale mining (ASM) in the region. The precipitous decline in the value of many export crops and the removal of subsidies on crucial inputs such as fertilizers have made smallholder production unviable, forcing many farmers to ‘branch out’ into non-farm activities to supplement their incomes. One of the more popular destinations for poor farmers is the low-tech ASM sector which, because of its low barriers to entry, has absorbed millions of rural Africans over the past two decades, the majority of whom are engaged in the extraction of near-surface mineral deposits located on concessions that have been demarcated to multinational corporations. The efforts made hitherto to control this illegal mining activity, both through force and regulation, however, have had little effect, forcing many of the region’s governments and private sector partners to ‘re-think’ their approaches. One strategy that has gained considerable attention throughout the region is intensified support for agrarian-orientated activities, many of which, despite the problems plaguing smallholder agricultural sector and challenges with making it more economically sustainable, are being lauded as appropriate ‘alternative’ sources of employment to artisanal mining. After examining where artisanal mining fits into the de-agrarianization ‘puzzle’ in sub-Saharan Africa, the article critiques the efficacy of ‘re-agrarianization’ as a strategy for addressing the region’s illegal mining problem. A case study of Ghana is used to shed further light on these issues.

Assessment of the RE(OH)3 Ising magnetic materials as possible candidates for the study of transverse-field-induced quantum phase transitions

The LiHoxY1−xF4 Ising magnetic material subject to a magnetic field perpendicular to the Ho3+ Ising direction has shown over the past 20 years to be a host of very interesting thermodynamic and magnetic phenomena. Unfortunately, the availability of other magnetic materials other than LiHoxY1−xF4 that may be described by a transverse-field Ising model remains very much limited. It is in this context that we use here a mean-field theory to investigate the suitability of the Ho(OH)3, Dy(OH)3, and Tb(OH)3 insulating hexagonal dipolar Ising-type ferromagnets for the study of the quantum phase transition induced by a magnetic field, Bx, applied perpendicular to the Ising spin direction. Experimentally, the zero-field critical (Curie) temperatures are known to be Tc≈2.54, 3.48, and 3.72 K, for Ho(OH)3, Dy(OH)3, and Tb(OH)3, respectively. From our calculations we estimate the critical transverse field, Bxc, to destroy ferromagnetic order at zero temperature to be Bxc=4.35, 5.03, and 54.81 T for Ho(OH)3, Dy(OH)3, and Tb(OH)3, respectively. We find that Ho(OH)3, similarly to LiHoF4, can be quantitatively described by an effective S=1/2 transverse-field Ising model. This is not the case for Dy(OH)3 due to the strong admixing between the ground doublet and first excited doublet induced by the dipolar interactions. Furthermore, we find that the paramagnetic (PM) to ferromagnetic (FM) transition in Dy(OH)3 becomes first order for strong Bx and low temperatures. Hence, the PM to FM zero-temperature transition in Dy(OH)3 may be first order and not quantum critical. We investigate the effect of competing antiferromagnetic nearest-neighbor exchange and applied magnetic field, Bz, along the Ising spin direction ẑ on the first-order transition in Dy(OH)3. We conclude from these preliminary calculations that Ho(OH)3 and Dy(OH)3 and their Y3+ diamagnetically diluted variants, HoxY1−x(OH)3 and DyxY1−x(OH)3, are potentially interesting systems to study transverse-field-induced quantum fluctuations effects in hard axis (Ising-type) magnetic materials.

Epitaxial growth of ultrathin palladium films on Re{0001}

Ultrathin bimetallic layers create unusual magnetic and surface chemical effects through the modification of electronic structure brought on by low dimensionality, polymorphism, reduced screening, and epitaxial strain. Previous studies have related valence and core-level shifts to surface reactivity through the d-band model of Hammer and Nørskov, and in heteroepitaxial films this band position is determined by competing effects of coordination, strain, and hybridization of substrate and overlayer states. In this study we employ the epitaxially matched Pd on Re{0001} system to grow films with no lateral strain. We use a recent advancement in low-energy electron diffraction to expand the data range sufficiently for a reliable determination of the growth sequence and out-of-plane surface relaxation as a function of film thickness. The results are supported by scanning tunneling microscopy and X-ray photoemission spectroscopy, which show that the growth is layer-by-layer with significant core-level shifts due to changes in film structure, morphology, and bonding.

A comparison of extra-tropical cyclones in recent re-analyses; ERA-Interim, NASA MERRA, NCEP CFSR and JRA-25

Extra-tropical cyclones are identified and compared using data from four recent re-analyses for the winter periods in both hemispheres. Results show the largest differences occur between the older lower resolution JRA25 re-analysis when compared with the newer high resolution re-analyses, in particular in the Southern Hemisphere (SH). Spatial differences between the newest re-analyses are small in both hemispheres and generally not significant except some common regions associated with cyclogenesis close to orography. Intensities are generally related to spatial resolution except NASA-MERRA which has larger intensities for several different measures. Matching storms between re-analyses shows the number matched between ERA-Interim and the other re-analyses are similar in the Northern Hemisphere (NH). In the SH the number matched between JRA25 and ERA-Interim is lower than in the NH, but for NASA-MERRA and NCEP-CFSR the number matched is similar to the NH. The mean separation of the identically same cyclones is typically less than 20 geodesic in both hemispheres for the latest re-analyses, whereas JRA25 compared with the other re-analyses has a broader distribution in the SH indicating greater uncertainty. The instantaneous intensity differences for matched storms shows narrow distributions for pressure while for winds and vorticity the distributions are much broader indicating larger uncertainty typical of smaller scale fields. Composite cyclone diagnostics show that cyclones are very similar between the re-analyses, with differences being related to the intensities, consistent with the intensity results. Overall, results show NH cyclones correspond well between re-analyses, with a significant improvement in the SH for the latest re-analyses, indicating a convergence between re-analyses for cyclone properties.

Retention rates, re-investment and depreciation in European office markets

The retention rate of a company has an impact on its earnings and dividend growth. Lease structures and performance measurement practice force real estate investment managers to adopt full distribution policies. Does this lead to lower income growth in real estate? This paper examines several European office markets across which the effective retention rates vary. It then compares depreciation rates across these markets. It is concluded that there is evidence of a relationship between retention and depreciation. Those markets with particularly inflexible lease structures exhibit low retention rates and higher levels of rental value depreciation. This poses interesting questions concerning the appropriate way to measure property performance across markets exhibiting significantly different retention rates and also raises important issues for global investors.